
566 F.3d 1095 (2009)
UNITED STATES Department of Justice, et al., Appellees
v.
PHILIP MORRIS USA Inc., Formerly Known as Philip Morris Incorporated, et al., Appellees
British American Tobacco (Investments) Ltd., Directly and as Successor to British-American Tobacco Company, Ltd., Appellant
The Council for Tobacco Research-USA, Inc., et al., Appellees.
Nos. 06-5267, 06-5268.
United States Court of Appeals, District of Columbia Circuit.
Argued October 14, 2008.
Decided May 22, 2009.
*1103 Michael A. Carvin and Miguel A. Estrada argued the causes for appellants. With them on the briefs were David S. Eggert, Guy Miller Struve, Charles S. Duggan, David M. Bernick, Robert F. McDermott, Jr., Peter J. Biersteker, Michael S. Fried, John K. Crisham, Michael B. Minton, Bruce D. Ryder, Bruce G. Sheffler, Alan E. Untereiner, Joseph Kresse, and Deborah Israel. Murray R. Garnick, Timothy M. Broas, James A. Goold, Gene E. Voigts, Clausen Ely Jr., Leonard A. Feiwus, James W. Newbold, Edward C. Schmidt, Arnon D. Siegel, Keith A. Teel, Theodore V. Wells, Jr., and Dan K. Webb entered appearances.
Alan E. Untereiner and Bruce G. Sheffler were on the briefs for appellant British American Tobacco (Investments) Limited.
David S. Eggert, Guy Miller Struve, and Charles S. Duggan were on the briefs for appellant Altria Group, Inc.
Daniel J. Popeo, Paul D. Kamenar, Andrew G. McBride, and Thomas R. McCarthy were on the brief for amici curiae National Association of Manufacturers and the Washington Legal Foundation urging reversal.
Scott A. Sinder was on the brief for amicus curiae National Association of Convenience Stores in support of appellants.
Robin S. Conrad, Amar D. Sarwal, Theodore B. Olson, and Matthew D. McGill were on the brief for amicus curiae Chamber of Commerce of the United States of America in support of appellants urging reversal.
Mark B. Stern, Attorney, U.S. Department of Justice, argued the cause for appellees. With him on the brief were Michael F. Hertz, Deputy Assistant Attorney General, Jonathan F. Cohn, Deputy Assistant Attorney General, and Alisa B. Klein, Mark R. Freeman, Sarang Vijay Damle, Melissa N. Patterson, and Christopher J. Walker, Attorneys.
*1104 Howard M. Crystal argued the cause for intervenors Tobacco-Free Kids Action Fund, et al. With him on the briefs were Katherine A. Meyer and G. Robert Blakey.
Michael D. Hausfeld and Victoria S. Nugent were on the brief for amici curiae American College of Occupational and Environmental Medicine, et al. in support of appellee urging affirmance.
William C. Lieblich, Talis J. Colberg, Attorney General, Attorney General's Office of the State of Alaska, Terry Goddard, Attorney General, Attorney General's Office of the State of Arizona, Dustin McDaniel, Attorney General, Attorney General, Attorney General's Office of the State of Arkansas, Edmund G. Brown, Jr., Attorney General, Attorney General, Attorney General's Office of the State of California, Richard Blumenthal, Attorney General, Attorney General's Office of the State of Connecticut, Joseph R. "Beau" Biden III, Attorney General, Attorney General's Office of the State of Delaware, Bill McCollum, Attorney General, Attorney General's Office of the State of Florida, Mark J. Bennett, Attorney General, Attorney General's Office of the State of Hawaii, Lawrence Wasden, Attorney General, Attorney General's Office of the State of Idaho, Lisa Madigan, Attorney General, Attorney General's Office of the State of Illinois, Paul Morrison, Attorney General, Attorney General's Office of the State of Kansas, Greg Stumbo, Attorney General, Attorney General's Office of the State of Kentucky, Charles Foti, Jr., Attorney General, Attorney General's Office of the State of Louisiana, G. Steven Rowe, Attorney General, Attorney General's Office of the State of Maine, Douglas F. Gansler, Attorney General, Attorney General's Office of the State of Maryland, Martha Coakley, Attorney General, Attorney General's Office of the Commonwealth of Massachusetts, Michael A. Cox, Attorney General, Attorney General's Office of the State of Michigan, Lori Swanson, Attorney General, Attorney General's Office of the State of Minnesota, Jim Hood, Attorney General, Attorney General's Office of the State of Mississippi, Jeremiah W. (Jay) Nixon, Attorney General, Attorney General's Office of the State of Missouri, Mike McGrath, Attorney General, Attorney General's Office of the State of Montana, Catherine Cortez Masto, Attorney General, Attorney General's Office of the State of Nevada, Kelly A. Ayotte, Attorney General, Attorney General's Office of the State of New Hampshire, Anne Milgram, Attorney General, Attorney General's Office of the State of New Jersey, Gary King, Attorney General, Attorney General's Office of the State of New Mexico, Andrew M. Cuomo, Attorney General, Attorney General's Office of the State of New York, Marc Dann, Attorney General, Attorney General's Office of the State of Ohio, W.A. Drew Edmondson, Attorney General, Attorney General's Office of the State of Oklahoma, Hardy Myers, Attorney General, Attorney General's Office of the State of Oregon, and Tom Corbett, Attorney General, Attorney General's Office of the Commonwealth of Pennsylvania, Patrick C. Lynch, Attorney General, Attorney General's Office of the State of Rhode Island, Robert E. Cooper, Jr., Attorney General, Attorney General's Office of the State of Tennessee, William H. Sorrell, Attorney General, Attorney General's Office of the State of Vermont, Robert M. McKenna, Attorney General, Attorney General's Office of the State of Washington, Darrell V. McGraw, Attorney General, Attorney General's Office of the State of West Virginia, Bruce A. Salzburg, Attorney General, Attorney General's Office of the State of Wyoming, and Vincent F. Frazer, Attorney General, Attorney General's Office of the Territory of the United States Virgin Islands, were on the brief for amici curiae States in support of appellee.
*1105 Allison M. Zieve and Brian Wolfman were on the brief for amici curiae Public Citizen, Inc., et al. in support of appellee urging affirmance.
Christopher N. Banthin and Stephen M. Kohn were on the brief for amici curiae American Medical Association and Others in support of appellee.
David C. Vladeck was on the brief for amicus curiae Tobacco Control Legal Consortium in support of appellee urging affirmance.
Harvey Kurzweil and Alexander M. Kayne were on the brief of amicus curiae the Citizens' Commission to Protect the Truth in support of appellee and supporting partial reversal.
Kerry S. Lane, appearing pro se, was on the brief as amicus curiae.
Before: SENTELLE, Chief Judge, TATEL and BROWN, Circuit Judges.
Opinion for the Court filed PER CURIAM.
PER CURIAM:
Defendants in this action, cigarette manufacturers and trade organizations, appeal from the district court's judgment finding them liable for conducting the affairs of their joint enterprise through a pattern of mail and wire fraud in a scheme to deceive American consumers. They also appeal from the district court's remedial order, which imposes numerous negative and affirmative duties on Defendants. The government and intervenors cross-appeal from the district court's denial of additional requested remedies. After considering all of the parties' arguments, we affirm in large part the finding of liability, remanding only for dismissal of the trade organizations. We also largely affirm the remedial order, including the denial of additional remedies, but vacate the order with regard to four discrete issues, remanding for further proceedings as directed in this opinion.

I. Background
The United States initiated this civil action under the Racketeer Influenced and Corrupt Organizations Act ("RICO"), 18 U.S.C. §§ 1961-1968, in 1999. The government alleged that nine cigarette manufacturers and two tobacco-related trade organizations violated section 1962(c) and (d) of the Act. Those subsections make it unlawful for "any person employed by or associated with any enterprise engaged in, or the activities of which affect, interstate or foreign commerce, to conduct or participate, directly or indirectly, in the conduct of such enterprise's affairs through a pattern of racketeering activity" or to conspire to do so. 18 U.S.C. § 1962(c), (d). The eleven Defendants were Philip Morris, Inc., now Philip Morris USA, Inc. ("Philip Morris"); R.J. Reynolds Tobacco Company, now Reynolds American ("Reynolds"); Brown & Williamson Tobacco Company, now part of Reynolds ("Brown & Williamson"); Lorillard Tobacco Company ("Lorillard"); The Liggett Group, Inc. ("Liggett"); American Tobacco Company, which merged with Brown & Williamson and is now part of Reynolds ("American"); Philip Morris Companies, now Altria ("Altria"); British American Tobacco (Investments) Ltd. ("BATCo"); B.A.T. Industries p.l.c., now part of BATCo ("BAT Industries"); The Council for Tobacco ResearchUSA, Inc. ("CTR"); and The Tobacco Institute, Inc. ("TI"). The last two entities are trade organizations the cigarette manufacturers created; they do not manufacture or sell tobacco products. The district court dismissed BAT Industries from the case for lack of personal jurisdiction.
The government alleged that Defendants violated and continued to violate RICO by joining together in a decades-long *1106 conspiracy to deceive the American public about the health effects and addictiveness of smoking cigarettes. Specifically, the government alleged that Defendants fraudulently denied that smoking causes cancer and emphysema, that secondhand smoke causes lung cancer and endangers children's respiratory and auditory systems, that nicotine is an addictive drug and Defendants manipulated it to sustain addiction, that light and low tar cigarettes are not less harmful than full flavor cigarettes, and that Defendants intentionally marketed to youth. United States v. Philip Morris USA, Inc., 449 F.Supp.2d 1, 27 (D.D.C.2006). In addition, the government alleged that Defendants concealed evidence and destroyed documents to hide the dangers of smoking and protect themselves in litigation. Id. The government identified 148 racketeering acts of mail and wire fraud Defendants allegedly committed in furtherance of their scheme. Although the district court did not allow the government to prove 650 additional racketeering acts due to their late disclosure, the court did permit the government to introduce evidence supporting those acts to prove other RICO elements, such as the continuity and pattern of racketeering activity, the RICO enterprise and conspiracy, and Defendants' participation in the enterprise.
After years of pretrial proceedings and discovery, the case went to trial in September 2004. The bench trial lasted nine months and included live testimony from 84 witnesses, written testimony from 162 witnesses, and almost 14,000 exhibits in evidence. The government presented evidence that the presidents of Philip Morris, Reynolds, Brown & Williamson, Lorillard, and American assembled together in 1953 to strategize a response to growing public concern about the health risks of smoking and jointly retained a public relations firm to assist in the endeavor. Id. at 37. From the beginning they agreed that no cigarette manufacturer would "seek a competitive advantage by inferring to its public that its product is less risky than others"; they would make no "claims that special filters or toasting, or expert selection of tobacco, or extra length in the butt, or anything else, makes a given brand less likely to cause you-know-what." Id. (quoting public relations firm's Planning Committee Memorandum). Acting on this agreement, the cigarette manufacturers jointly issued "A Frank Statement to Cigarette Smokers," published as a full-page advertisement in newspapers across the country on January 4, 1954. Id. at 39. "The Frank Statement set forth the industry's `open question' position that it would maintain for more than forty yearsthat cigarette smoking was not a proven cause of lung cancer; that cigarettes were not injurious to health; and that more research on smoking and health issues was needed." Id. All of the Defendant manufacturers eventually joined this collective effort.
The government presented evidence from the 1950s and continuing through the following decades demonstrating that the Defendant manufacturers were awareincreasingly so as they conducted more researchthat smoking causes disease, including lung cancer. Evidence at trial revealed that at the same time Defendants were disseminating advertisements, publications, and public statements denying any adverse health effects of smoking and promoting their "open question" strategy of sowing doubt, they internally acknowledged as fact that smoking causes disease and other health hazards. Id. at 146, 164, 168-69. Although the manufacturers conducted their own research and public relations regarding health and other issues, they also relied in part on a series of jointly-created entities. Among these entities were Defendants TI and CTR (formerly the Tobacco Industry *1107 Research Committee). The Defendant manufacturers created TI and CTR, composed their membership, staffed their boards of directors with executives from the manufacturers, and maintained frequent communication between high-level manufacturer and joint-entity officials. Id. at 43-44, 63. Evidence at trial showed that TI and CTR conducted the manufacturers' joint public relations through false and misleading press releases and publications, trained representatives from the manufacturers regarding their coordinated industry message, conducted some cigarette testing for the manufacturers, and funded "special projects" to produce favorable research results and witnesses specifically for use in litigation and for support of industry public statements. Id. at 66, 82, 86, 87, 91.
In addition to the health hazards of smoking, the government presented evidence that Defendants intimately understood the addictiveness of nicotine and manipulated nicotine delivery in cigarettes to create and sustain addiction. Evidence showed that Defendants undertook extensive research into the physiological impact of nicotine, how it operates within the human body, and how the physical and chemical design parameters of cigarettes influence the delivery of nicotine to smokers. Id. at 208, 308-09. As a result of this research, they recognized and internally acknowledged that smoking and nicotine are addictive and they engineered their products around creating and sustaining this addiction. Evidence at trial suggested that despite this internal knowledge, for decades Defendants publicly denied and distorted the truth about the addictive nature of their products, suppressed research revealing the addictiveness of nicotine, and denied their efforts to control nicotine levels and delivery. Id. at 209, 309.
The government also presented evidence tending to show that Defendants marketed and promoted their low tar brands to smokerswho were concerned about the health hazards of smoking or considering quittingas less harmful than full flavor cigarettes despite either lacking evidence to substantiate their claims or knowing them to be false. Id. at 430. Internal industry documents introduced at trial revealed that by the late 1960s and early 1970s, Defendants were aware that lower tar cigarettes are unlikely to provide health benefits because they do not actually deliver the low levels of tar and nicotine advertised. Id. at 430-31. Defendants researched and understood the phenomenon whereby smokers of low tar cigarettes, to satisfy their addiction, modify their smoking behavior to compensate for the reduced nicotine yields by "taking more frequent puffs, inhaling smoke more deeply, holding smoke in their lungs longer, covering cigarette ventilation holes with fingers or lips, and/or smoking more cigarettes." Id. at 431. As a result of this nicotine-driven behavior, smokers of low tar cigarettes boost their intake of tar, so that lower tar cigarettes do not result in lower tar intake and therefore do not yield the touted health benefits or serve as a step toward quitting smoking. Id. Evidence at trial suggested that Defendants understood this conceptfor some time, better than the public health community or government regulatorswhile they promoted lower tar cigarettes as "health reassurance" brands.
Regarding secondhand smoke, the government presented evidence suggesting that Defendants became aware that secondhand smoke poses a health risk to nonsmokers but made misleading public statements and advertisements about secondhand smoke in an attempt to cause the public to doubt the evidence of its harmfulness. Id. at 692. At trial, internal industry *1108 documents revealed that Defendants believed the public perception of secondhand smoke could determine the industry's survival and that secondhand smoke research by the cigarette manufacturers was a sensitive issue due to the absence of "objective science" supporting their position and the risk that their own research would lead to unfavorable results. Id. at 733. As a result, the manufacturers jointly created the Center for Indoor Air Research ("CIAR") to coordinate and fund their secondhand smoke research with the appearance of independence. Id. at 119, 735. The evidence also showed that they "created, controlled, used, or participated in" a vast array of foreign or international entities to conduct their sensitive secondhand smoke research, generate "marketable science" to use for public relations purposes, and coordinate their shared objectives and message. Id. at 119-20, 759.
In addition to these topics, the government also presented evidence to the district court regarding Defendants' targeted marketing to youth under twenty-one years of age and their denials of such marketing, id. at 561, 672, as well as evidence concerning Defendants' employees and attorneys destroying documents relevant to their public and litigation positions and suppressing or concealing scientific research, id. at 801, 832.
During the trial, this court rendered a decision on Defendants' interlocutory appeal from the denial of summary judgment on the government's claim for a disgorgement remedy under RICO section 1964(a). We reversed the district court and held that disgorgement is not an available remedy in civil RICO cases. United States v. Philip Morris USA, Inc. ("Disgorgement Opinion"), 396 F.3d 1190 (D.C.Cir.2005). In response, the district court granted the government leave to reformulate its proposed remedies. After the liability phase of the trial, the district court held a fourteen-day remedies trial. At the close of the remedies phase, several organizations moved to intervene in the litigation to assert their interests in the proposed remedies. The district court granted the American Cancer Society, the American Heart Association, the American Lung Association, Americans for Nonsmokers' Rights, the National African American Tobacco Prevention Network, and the Tobacco-Free Kids Action Fund leave to intervene solely on the subject of remedies.
The district court entered final judgment against Defendants on August 17, 2006, finding that they maintained an illegal racketeering enterprise and each Defendant participated in the conduct, management, and operation of the enterprise in violation of section 1962(c), and that they explicitly and implicitly agreed to do so, in violation of section 1962(d). Philip Morris, 449 F.Supp.2d at 851, 901. The court found that Defendants engaged in a scheme to defraud smokers and potential smokers by (1) falsely denying the adverse health effects of smoking, id. at 854; (2) falsely denying that nicotine and smoking are addictive, id. at 856; (3) falsely denying that they manipulated cigarette design and composition so as to assure nicotine delivery levels that create and sustain addiction, id. at 858; (4) falsely representing that light and low tar cigarettes deliver less nicotine and tar and therefore present fewer health risks than full flavor cigarettes, id. at 859; (5) falsely denying that they market to youth, id. at 861; (6) falsely denying that secondhand smoke causes disease, id. at 864; and (7) suppressing documents, information, and research to prevent the public from learning the truth about these subjects and to avoid or limit liability in litigation, id. at 866. The court concluded that the government failed to prove that Defendants deliberately chose not to utilize or market feasible designs or *1109 product features that could produce less hazardous cigarettes. Id. at 384.
Before granting injunctive relief against Defendants the district court assessed whether they presented a "reasonable likelihood of further violation(s) in the future." Id. at 909 (quoting SEC v. Savoy Indus., Inc., 587 F.2d 1149, 1168 (D.C.Cir. 1978)). The court concluded that Philip Morris, Reynolds, Brown & Williamson, Lorillard, American, Altria, and BATCo were reasonably likely to commit future RICO violations unless enjoined because they continued to make false and misleading statements at the time of trial, their businesses presented continuing opportunities to commit RICO violations, and their corporate leadership continued to consist of veteran employees with longstanding ties to the companies. Id. at 910-13. Defendants argued that no injunction was necessary because their Master Settlement Agreement with forty-six states and the District of Columbia and their individual settlements with four states already sufficiently restrained them. The district court rejected this argument, concluding that the Master Settlement Agreement did not obviate the need for injunctive relief because Defendants had not fully complied with the agreement, parts of the agreement began expiring in 2006, the states could not vigorously enforce all aspects of the agreement, and BATCo and Altria were not subject to the settlement agreement. Id. at 913-15.
The district court found that three DefendantsCTR, TI, and Liggettdid not present a reasonable likelihood of future RICO violations, therefore the court did not order injunctive remedies against them. CTR and TI, the court found, now exist solely for the limited purpose of winding up their activities and each retains only one adviser to support its litigation defense and handle any remaining administrative matters. Id. at 915-18. The court found that Liggett withdrew from the RICO conspiracy by admitting that smoking causes cancer and is addictive, by voluntarily restricting its advertising and including disclosures on its packages, and by cooperating with the United States and state attorneys general in their claims against other tobacco companies. Id. at 906-07, 918-19. The district court concluded that Liggett was not reasonably likely to commit future RICO violations based on this withdrawal, its continued independence from the other Defendants, and its limited opportunity for future violations by virtue of its discount cigarette market and lack of traditional consumer advertising. Id. at 918-19.
Pursuant to section 1964, the district court imposed injunctive remedies against the other seven manufacturer Defendants. Specifically, the court ordered Defendants (1) to refrain from any acts of racketeering relating to the manufacturing, marketing, promotion, health consequences, or sale of cigarettes in the United States; (2) not to participate in the management or control of CTR, TI, or CIAR, and not to reconstitute the form or function of those entities; (3) to refrain from making any material false, misleading, or deceptive representation concerning cigarettes that is disseminated to the United States public; (4) to cease using any express or implied health message or health descriptor for any cigarette brand, such as light or low tar; (5) to make corrective disclosures about addiction, the adverse health effects of smoking and secondhand smoke, their manipulation of cigarette design and composition, and light and low tar cigarettes; (6) to create document depositories providing the government and the public access to all industry documents disclosed in litigation; and (7) to provide their disaggregated marketing data to the government according to the schedule on which they provide it to the Federal Trade Commission. Id. at *1110 938-45. The court also limited the sale and transfer of Defendants' brands, product formulas, and businesses to entities that either are subject to the injunctive order or will sell the brand, use the formula, or conduct the business exclusively outside the United States. Id. at 945.
The district court denied the remainder of the government's requested injunctive relief, including its proposed national smoking cessation program, public education and counter-marketing campaign, and youth smoking reduction plan. Id. at 933-34, 936-37. The court also denied the government's requests that it appoint a monitor to investigate and restructure the Defendant companies, id. at 935, and that it order Defendants to make public all "health and safety risk information" about their products in their own files, id. at 929.
All Defendants except Liggett appealed, raising numerous challenges to the finding of liability and the remedies imposed. The government and the intervenors filed a cross-appeal regarding the remedies that the district court denied. On Defendants' motion we stayed the remedial injunction pending appeal.
We review the district court's conclusions of law de novo. SEC v. Wash. Inv. Network, 475 F.3d 392, 399 (D.C.Cir. 2007). To the extent it is not based on legal error, we review the district court's decision to issue an injunction for abuse of discretion. Id. We may not set aside the district court's findings of fact unless they are clearly erroneous, giving due regard to the court's opportunity to judge the witnesses' credibility. Id. (citing FED. R. CIV. P. 52(a)(6)). This standard applies even when the district court adopts a party's proposed findings verbatim. Anderson v. City of Bessemer City, 470 U.S. 564, 572, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985).
To establish RICO liability, the government had to prove the necessary elements of RICO itselfincluding the existence of an enterprise and a pattern of racketeering activity, 18 U.S.C. § 1962(c)as well as the elements of the underlying conduct constituting the racketeering acts, here, numerous instances of mail and wire fraud under 18 U.S.C. §§ 1341 and 1343. Defendants challenge the district court's findings regarding both RICO and the underlying fraud, as well as the remedies the court imposed. We address Defendants' challenges to RICO liability in Part II, their general challenges to fraud liability in Part III, their challenges to specific aspects of the fraudulent scheme and the liability of specific Defendants in Part IV, their challenges to the finding that they are likely to commit future violations and therefore should be enjoined in Part V, and their challenges to particular remedies the court imposed in Part VI.

II. Challenges to RICO Liability

A. RICO Enterprise
RICO makes it unlawful for "any person ... associated with any enterprise... to conduct or participate, directly or indirectly, in the conduct of such enterprise's affairs through a pattern of racketeering activity." 18 U.S.C. § 1962(c). Thus, in a section 1962(c) suit, the defendants are the "persons" who conduct the "enterprise's" affairs through racketeering activity. Because RICO defines "person" as including "any individual or entity capable of holding a legal or beneficial interest in property," id. § 1961(3), corporations as well as individuals can be liable if they conduct an enterprise's affairs through a pattern of racketeering activity. In language central to the issue before us, section 1961(4) states:
"enterprise" includes any individual, partnership, corporation, association, or other legal entity, and any union or group of individuals associated in fact although not a legal entity.
*1111 Id. § 1961(4). The enterprise as such generally faces no section 1962(c) RICO liability; indeed it may be the innocent vehicle through which unlawful activity is carried out, see Cedric Kushner Promotions, Ltd. v. King, 533 U.S. 158, 164, 121 S.Ct. 2087, 150 L.Ed.2d 198 (2001) ("RICO both protects a legitimate `enterprise' from those who would use unlawful acts to victimize it, and also protects the public from those who would unlawfully use an `enterprise' (whether legitimate or illegitimate) as a `vehicle' through which `unlawful ... activity is committed.'" (quoting United States v. Turkette, 452 U.S. 576, 591, 101 S.Ct. 2524, 69 L.Ed.2d 246 (1981), and Nat'l Org. for Women, Inc. v. Scheidler, 510 U.S. 249, 259, 114 S.Ct. 798, 127 L.Ed.2d 99 (1994))). When the enterprise is an association-in-fact, members of the association may be both part of the "enterprise" and liable as "persons" under RICO if they conduct the enterprise's affairs through racketeering activity. See, e.g., United States v. Richardson, 167 F.3d 621, 626 (D.C.Cir.1999) (upholding conviction of defendant member of association-in-fact enterprise).
Here, defining the RICO enterprise as "a group of business entities and individuals associated-in-fact, including Defendants to this action, their agents and employees, and other organizations and individuals," the district court held that the Defendant cigarette manufacturers and trade organizations had violated section 1962(c) by participating in the conduct of the enterprise's affairs through multiple acts of mail and wire fraud. Philip Morris, 449 F.Supp.2d at 851, 867. Defendants challenge the district court's acceptance of a RICO enterprise made up of individuals and corporations, arguing that the statute provides an exclusive list of possible enterprises that covers groups of individuals associated in fact, not mixed groups of individuals and corporations associated in fact.
In United States v. Perholtz, 842 F.2d 343 (D.C.Cir.1988), however, we squarely rejected this precise argument. There, we held that a group of seven individuals and eleven corporations and partnerships associated in fact may constitute a RICO "enterprise." Id. at 351 n. 12, 353. We explained: "[RICO] defines `enterprise' as including the various entities specified; the list of entities is not meant to be exhaustive." Id. at 353. As such, a group of individuals, corporations, and partnerships associated in fact can qualify as a RICO "enterprise," even though section 1961(4) nowhere expressly mentions this type of association.
In so holding, we joined several other circuits that had reached the same conclusion. Perholtz, 842 F.2d at 353 (citing the Second, Third, Seventh, and Eleventh Circuits, as well as Fifth Circuit Unit B). Indeed, both prior to and since Perholtz, every circuit to consider the question has likewise held that corporations may be part of an association-in-fact enterprise. See United States v. London, 66 F.3d 1227, 1243-44 (1st Cir.1995) (holding that corporations can be part of an association-in-fact enterprise because section 1961(4)'s list is not exhaustive); United States v. Huber, 603 F.2d 387, 394 (2d Cir.1979) (same); United States v. Aimone, 715 F.2d 822, 828 (3d Cir.1983) (same); United States v. Thevis, 665 F.2d 616, 625-26 (5th Cir. Unit B 1982) (same), superseded on other grounds by FED.R.EVID. 804(b)(6) (1997); United States v. Masters, 924 F.2d 1362, 1366 (7th Cir.1991) (same); Atlas Pile Driving Co. v. DiCon Fin. Co., 886 F.2d 986, 995 n. 7 (8th Cir.1989) (same); see also Dana Corp. v. Blue Cross & Blue Shield Mut. of N. Ohio, 900 F.2d 882, 887 (6th Cir.1990) (reaching same outcome and citing Huber, 603 F.2d at 393-94); United States v. Navarro-Ordas, 770 F.2d 959, 969 n. 19 (11th Cir.1985) (same); United States v. Feldman, 853 F.2d 648, 655-56 *1112 (9th Cir.1988) (reaching same outcome based on different statutory analysis); United States v. Najjar, 300 F.3d 466, 484 (4th Cir.2002) (upholding without discussion RICO convictions involving an association-in-fact enterprise that included corporations). The judges of these circuits are equally unanimous, for not one has dissented from the proposition that an association-in-fact enterprise may include corporations.
Defendants argue that Perholtz has no applicability where, as here, the defendants are corporations. Because the Perholtz defendants were individual members of the enterprise, not its corporate members, Defendants here claim that Perholtz applies only when individuals, not corporations, are the RICO defendants. As Defendants see it, Perholtz merely ensures that individuals are unable to escape liability simply by including corporations in their enterprise; Perholtz, they argue, does not mean that the associated-in-fact corporations can themselves incur RICO liability.
But nothing in Perholtz is so limited. Quoting the Supreme Court's statement in United States v. Turkette that "[t]here is no restriction upon the associations embraced by the definition [of enterprise]," 452 U.S. at 580, 101 S.Ct. 2524, Perholtz sets forth its holding in broad terms: "We therefore follow those courts that have held that individuals, corporations, and other entities may constitute an association-in-fact," 842 F.2d at 353. Nowhere does Perholtz suggest that the rule varies depending on the identity of the defendants. Indeed, two of the cases Perholtz relies on involved corporate defendants. Id. (citing Thevis, 665 F.2d at 625-26 (upholding RICO convictions for one individual and one corporate defendant), and Bunker Ramo Corp. v. United Bus. Forms, Inc., 713 F.2d 1272, 1285 (7th Cir. 1983) (upholding RICO charges against one individual and one corporation)). Many other decisions have similarly upheld RICO allegations involving corporate defendants who were also members of the association-in-fact enterprise. See, e.g., City of N.Y. v. Smokes-Spirits.com, Inc., 541 F.3d 425, 450-51 (2d Cir.2008); Odom v. Microsoft Corp., 486 F.3d 541, 553 (9th Cir.2007); Najjar, 300 F.3d at 484; United States v. Goldin Indus., Inc., 219 F.3d 1271, 1274 (11th Cir.2000); Dana Corp., 900 F.2d at 887; Shearin v. E.F. Hutton Group, Inc., 885 F.2d 1162, 1165-66 (3d Cir.1989), overruled on other grounds by Beck v. Prupis, 529 U.S. 494, 506, 120 S.Ct. 1608, 146 L.Ed.2d 561 (2000); Atlas Pile Driving, 886 F.2d at 995; Ocean Energy II, Inc. v. Alexander & Alexander Inc., 868 F.2d 740, 748-49 (5th Cir.1989).
Moreover, Defendants' proposed limitation on Perholtz is contrary to the statute's language. As "persons" under section 1961(3), corporations may be RICO defendants regardless of the kind of enterprise charged. See 18 U.S.C. § 1962(c) ("It shall be unlawful for any person ... associated with any enterprise ... to conduct or participate, directly or indirectly, in the conduct of such enterprise's affairs through a pattern of racketeering activity." (emphases added)). Defendants cite not a single case lending even a shred of support to the idea that the meaning of "enterprise" can fluctuate depending on whom the government or the plaintiff chooses to name as the defendant. Perholtz's interpretation of section 1961(4) thus applies regardless of whether the RICO defendants are individual "persons" or corporate "persons." To hold otherwise would require us to rewrite section 1962(c).
In a further attempt to evade Perholtz, Defendants argue that even if Perholtz was correct when decided, it has been eroded by the Supreme Court's 2001 decision in Cedric Kushner Promotions, Ltd. *1113 v. King, 533 U.S. 158, 121 S.Ct. 2087, 150 L.Ed.2d 198 (2001). Defendants' argument begins with the premise that at the time we decided Perholtz, RICO presented a potential loophole: because the RICO defendant must be distinct from the RICO enterprise, Yellow Bus Lines, Inc. v. Drivers, Chauffeurs & Helpers Local Union 639, 839 F.2d 782, 790 (D.C.Cir.1988) ("[O]ne entity may not serve as the enterprise and the person associated with it...."), vacated on other grounds, 492 U.S. 914, 109 S.Ct. 3235, 106 L.Ed.2d 583 (1989), a sole shareholder who used his alter-ego corporation for racketeering might evade RICO liability because he wouldn't be sufficiently distinct from the alter-ego corporation "enterprise." Defendants rely on Perholtz's suggestion that a definition of "enterprise" that excluded associations-in-fact of corporations would lead to "the bizarre result that only criminals who failed to form corporate shells to aid their illicit schemes could be reached by RICO." 842 F.2d at 353. According to Defendants, we were motivated in Perholtz by the underlying concern "that a criminal defendant conducting the affairs of an `enterprise' that was his own closely held corporation, would be so closely tied to the enterprise that he would escape RICO liability." Defs. Br. 37. Given that the Supreme Court has subsequently eliminated this concernholding in Cedric Kushner that an individual sole shareholder is sufficiently distinct from his alter-ego corporation to sustain RICO liability, 533 U.S. at 160, 121 S.Ct. 2087Defendants assert that Perholtz no longer represents binding authority.
We do not read Perholtz as motivated by the concerns addressed in Cedric Kushner. In contrast to Cedric Kushner, the enterprise in Perholtz involved multiple individuals and numerous corporations, with no indication that the corporations were either all closely held by the individual defendants or in any other way insufficiently distinct. 842 F.2d at 351 n. 12. Indeed, at least some of the Perholtz corporate enterprise members were not closely held. For example, enterprise member International Business Services, Inc. (IBS) existed in its own right prior to the scheme and was related to the defendants through employment relationships that would not have defeated RICO's distinctness requirement: Perholtz himself was a consultant to IBS, and the other RICO defendant, Franklin Jackson, was an IBS project manager. Id. at 348. Similarly, enterprise member Remote Computer Services Corporation, although formed expressly for the purpose of the scheme, was jointly held in equal shares by three individualsPerholtz and two other individual members of the enterprise, id. at 350and thus would have been sufficiently distinct from each of those non-sole shareholders. The enterprise also included two separate real estate companies both of which apparently existed independently of the scheme and were not otherwise affiliated with the individuals. Id. at 351 n. 12. At least one individual enterprise member, John Gentile, worked for the Postal Service and apparently had no formal stake in the corporate enterprise members. Id. at 346, 351 n. 12. In Perholtz, we held that all these corporationsnot just those closely held or created solely for the schemecould be part of an association-in-fact enterprise. Indeed, only after so holding did we turn to Perholtz's entirely separate argument that he, as an individual, was insufficiently distinct from the enterprise. Far from basing our holding on this argument, we simply noted that we had "no occasion to consider the separateness requirement" because Perholtz associated not with himself but with others. Id. at 353.
Given the structure of the Perholtz enterprise and the court's acknowledgement that distinctness was not at issue, we think Perholtz reflected a different concern, *1114 namely that a group of sophisticated racketeers who would otherwise constitute an association-in-fact might evade RICO's grasp by virtue of their ability to operate through corporations and establish complex networks of companies, kickbacks, and contracts to achieve their elicit ends. Indeed, immediately following its reference to "corporate shells," Perholtz emphasized Congress's desire that RICO serve "as a weapon against the sophisticated racketeer as well as (and perhaps more than) the artless." Id. Perholtz itself presented just such a situation: the defendants worked through their own companies and multiple outside corporations in an intricate web of shared commissions to game the bidding process for government contracts. The success of the scheme required the participation of companies to serve as contractors and subcontractors. "This relationship of individuals and corporations is precisely what section 1962(c) was designed to attack." Id. at 354.
Moreover, in asserting their Cedric Kushner argument, Defendants fail to explain how Perholtz's interpretation would even solve the hypothetical problem they posit. According to Defendants, in order to preserve RICO liability for a sole shareholder who would be insufficiently distinct from his alter-ego corporation, the Perholtz court held that an "individual and his shell corporation could together ... constitute an association-in-fact enterprise." Defs. Reply Br. 16. In Defendants' view, the sole shareholder would then be liable under RICO for conducting the affairs of this association-in-fact enterprise. Yet if an individual is insufficiently distinct from his alter-ego corporation, we seriously doubt he would suddenly be sufficiently distinct from an enterprise consisting of his alter-ego corporation and himself. If Perholtz had been concerned with distinctness, its purported "solution" would make little sense.
Further seeking to justify their reliance on Cedric Kushner, Defendants say that the government cites only one post-Cedric Kushner caseUnited States v. Najjar, 300 F.3d 466 (4th Cir.2002)that upheld an association-in-fact enterprise of corporations. The relevance of this is hard to grasp, as other post-Cedric Kushner cases not cited by the government accept association-in-fact enterprises comprised of corporations. See Smokes-Spirits.com, 541 F.3d at 450-51 (holding that the plaintiff adequately pleaded an association-in-fact enterprise consisting of two corporations); Odom, 486 F.3d at 553 (holding that plaintiffs had sufficiently alleged an association-in-fact enterprise of two corporations); United States v. Cianci, 378 F.3d 71, 83 (1st Cir.2004) ("It is uncontroversial that corporate entities, including municipal and county ones, can be included within association-in-fact RICO enterprises."); Living Designs, Inc. v. E.I. Dupont de Nemours & Co., 431 F.3d 353, 361 (9th Cir.2005) ("[T]here is no question that DuPont [corporation] and the law firms together can constitute an `associated in fact' RICO enterprise."). And as we noted above, no circuit has ever held the opposite.
Cedric Kushner thus undermines neither the unanimous judicial view that association-in-fact enterprises may include corporations nor Perholtz's binding effect on this case. Defendants' argument that we should read section 1961(4) as an exhaustive list of possible RICO enterprises is therefore unavailing. Not only is it foreclosed by Perholtz, it is unpersuasive on its own terms. As Perholtz and many other circuits explain, the use of the word "includes" indicates that RICO's list of "enterprises" is non-exhaustive. Indeed, section 1961 makes the non-exhaustive nature of "includes" clear by alternating between the words "means" and "includes" to introduce the section's various definitions. Specifically, five of section 1961's ten subsections *1115 introduce definitions with the word "means." For example, section 1961(1) defines "racketeering activity," explaining that the term "means" any of a list of specific state and federal crimes. Section 1961(2) likewise introduces a definitional list with the term "means": "`State' means any State of the United States, the District of Columbia, the Commonwealth of Puerto Rico, any territory or possession of the United States, any political subdivision, or any department, agency, or instrumentality thereof." 18 U.S.C. § 1961(2); see also id. § 1961(6), (7), (8) (introducing definitions of "unlawful debt," "racketeering investigator," and "racketeering investigation" with the term "means"). Section 1961(4), by contrast, says "`enterprise' includes any individual, partnership, corporation, association, or other legal entity, and any union or group of individuals associated in fact although not a legal entity." Id. § 1961(4) (emphasis added). By switching between "means" and "includes" in the same definitional provision, Congress signaled its intent to distinguish between exhaustive and non-exhaustive lists. See Helvering v. Morgan's, Inc., 293 U.S. 121, 126 n. 1, 55 S.Ct. 60, 79 L.Ed. 232 (1934) (describing a statute that introduced three definitions with the word "includes" and seven definitions with the word "means" and noting that "[t]he natural distinction would be that where `means' is employed, the term and its definition are to be interchangeable equivalents, and that the verb `includes' imports a general class, some of whose particular instances are those specified in the definition").
That Congress provided an exhaustive list of legal entity enterprises by adding the phrase "or other legal entity" hardly converts the list of non-legal entity enterprises into an exhaustive list. Had Congress wanted to limit non-legal entity associations to those expressly listed, the most obvious way to do so would have been the way Congress wrote the five clearly exhaustive definitions in the same section: it could have said "`enterprise' means any individual, partnership, corporation, association, or other legal entity, or any union or group of individuals associated in fact although not a legal entity." But Congress chose to say "`enterprise' includes" the listed entities. Defendants think that the phrase "or other legal entity" would have been unnecessary if the list were otherwise non-exhaustive. Not so. Adding "or other legal entity" serves to ensure that all legal entities are covered while retaining the possibility that some additional non-legal entities beyond those listed are also covered.
Nor does the use of the phrase "including, but not limited to" to indicate a non-exhaustive list in a different section of RICO, section 1964(a), demonstrate that the sole word "includes" in section 1961(4) must introduce an exhaustive list. Section 1964, which establishes civil remedies for RICO violations, lacks section 1961's juxtaposition of the non-exhaustive term "includes" with the exhaustive term "means"; adding "but not limited to" helps to emphasize the non-exhaustive nature of section 1964(a)'s list of remedies. Section 1961 needed no such clarification because it employed the contrasting terms "means" and "includes" to distinguish exhaustive from non-exhaustive definitions.
Contrary to Defendants' argument, nothing about this interpretation renders the definition of "enterprise" devoid of meaning. Although encompassing non-enumerated enterprises, section 1961(4)'s list defines "enterprise," in part, by listing the kinds of entities Congress had in mind. Indeed, the Supreme Court has acknowledged this meaning by requiring enterprises to exhibit common purpose, organization, and continuity. Turkette, 452 U.S. at *1116 583, 101 S.Ct. 2524; see also Richardson, 167 F.3d at 625.
In sum, as Perholtz clearly holds, because RICO's "list of entities is not meant to be exhaustive," "individuals, corporations, and other entities may constitute an association-in-fact." 842 F.2d at 353. This binding precedentconfirmed by the statute's language, buttressed by the unanimity among our sister circuits, and undiminished by Defendants' efforts to escape itrequires that we affirm the district court's holding that the government properly alleged a RICO enterprise of individuals, cigarette manufacturers, and trade organizations.
We also reject Defendants' additional challenges to the district court's findings regarding the existence of a RICO enterprise and their participation in its affairs. The district court foundpermissibly in our viewthat the enterprise had the common purpose of obtaining cigarette proceeds by defrauding existing and potential smokers, Philip Morris, 449 F.Supp.2d at 869; possessed the requisite structure both through informal association and through the formation of several formal organizations, id. at 870-71; functioned as a continuous unit despite personnel changes, id. at 871-72; and constituted a separate entity distinct from each Defendant, id. at 875. Defendants give us neither any basis for concluding that the district court's factual findings were clearly erroneous nor any reason to think them legally insufficient. The district court also foundagain permissiblythat despite competing in some aspects of their business, Defendants jointly committed fraud and so participated in the conduct of not just their own affairs but the enterprise's as well, id. at 875-78, and also that they conspired to do so, id. at 903-05. Accordingly, we affirm the district court's findings that an enterprise existed and that Defendants participated in the conduct of its affairs and conspired to do so.

B. Identifying Racketeering Acts
Defendants complain that the district court failed to identify the racketeering acts that support the finding of liability. While it is true the district court's opinion provided no single, discrete list of specific racketeering acts, the comprehensive findingsdetailing over one-hundred racketeering actsare sufficient to warrant affirmance. Defendants raise numerous challenges to the correctness of the district court's findings that they committed racketeering acts, which we take up in Parts III and IV. In this section, however, we are concerned only with the existence of these findings, not their validity.
By statutory definition, any violation of the mail or wire fraud statutes can qualify as "racketeering activity." 18 U.S.C. § 1961(1). To prove a violation of the mail and wire fraud statutes, the government must show (1) a scheme or artifice to defraud and (2) a mailing or wire transmission in furtherance thereof. Id. §§ 1341, 1343. "Where one scheme involves several mailings, the law is settled that each mailing constitutes a violation of the statute." Hanrahan v. United States, 348 F.2d 363, 366 (D.C.Cir.1965). Where, as here, the mail and wire fraud statutes serve as the predicate offenses for a RICO violation, each racketeering act must be a mailing or wire transmission made in furtherance of a "scheme or artifice to defraud." 18 U.S.C. §§ 1341, 1343. Thus, in order to identify the racketeering acts, the district court must first have found a scheme to defraud, then concluded the alleged mailings or wire transmissions were in furtherance of such scheme. See Philip Morris, 449 F.Supp.2d at 852-54.
Although Defendants question whether the district court clearly found a scheme to *1117 defraud, the finding on this question is explicit: "The Government has proven that the Enterprise knowingly and intentionally engaged in a scheme to defraud smokers and potential smokers, for purposes of financial gain, by making false and fraudulent statements, representations, and promises." Id. at 852. The district court explains, in great detail, the seven components of the scheme to defraud. Id. at 852-67.
The court also held that "each of the alleged mailings and wire transmissions was in furtherance of the overarching scheme to defraud." Id. at 881. Thus it follows that any mailing or wire transmission found to have been made was found to have been a mail or wire fraud offense and therefore a racketeering act.
Seventy-nine of the alleged acts were established by Defendants' own stipulations and admissions. Id. at 882 (enumerating 79 racketeering acts). Altogether, the court enumerated 108 racketeering acts in the opinion, as well as six others which it excluded on First Amendment grounds. See id. at 882, 884, 885 n. 62, 887. This total does not include the many other findings which may be tied to other racketeering acts, but for which the district court did not provide a specific list. See, e.g., id. at 883 ("[I]t is clear beyond any question that Defendants caused the mailings and wire transmissions underlying the 30 Racketeering Acts involving the news media's dissemination of Defendants' press releases and advertisements to their subscribers.").
The RICO statute requires "a pattern of racketeering activity" on the part of each defendant. 18 U.S.C. § 1962(c). "[A]t least two acts of racketeering activity" are necessary to form a pattern. H.J., Inc. v. Nw. Bell Tel. Co., 492 U.S. 229, 237, 109 S.Ct. 2893, 106 L.Ed.2d 195 (1989) (quoting 18 U.S.C. § 1961(5)). The district court found the requisite pattern committed by each Defendant, Philip Morris, 449 F.Supp.2d at 889-91, and this finding is not erroneous. A brief sampling of the 108 enumerated racketeering acts makes the point: Philip Morris, Reynolds, Brown & Williamson, Lorillard, American, and TI committed racketeering acts 24, 132, and 133 by mailing press releases containing false statements about the addictiveness and health consequences of smoking. Id. at 194, 282-83. Philip Morris, Reynolds, Brown & Williamson, Lorillard, American, Liggett, and CTR committed racketeering acts 66, 73, and 88 by mailing letters regarding funding of CTR's "special projects" to create data supporting their fraudulent claims. Id. at 101, 882, 972, 976. BATCo and Brown & Williamson committed racketeering acts 30, 50, 51, 53, and 63 through their mailings to each other concerning the enterprise's position on the health effects and addictiveness of smoking as well as smoker compensation and nicotine. Id. at 253-54, 301, 882, 965, 969. Altria committed racketeering acts 71, 72, 74, and 75 in its efforts to coordinate Defendants' public positions and fund CTR research projects to support their fraudulent claims. Id. at 295, 813, 884, 974. As these examples demonstrate, the district court found each Defendant engaged in a "pattern of racketeering activity," and that finding is not erroneous. See infra Parts III, IV.
The 108 enumerated acts give us ample basis to review the district court's finding. Although the district court may have concluded other racketeering acts were proven as well, we need look no further. Defendants correctly argue we must ensure the remedy imposed is tailored to "the violation found," United States v. Microsoft, 253 F.3d 34, 105 (D.C.Cir.2001); the voluminous findings detailing the contours of the scheme to defraud are more than sufficient to allow this review, see, e.g., Philip Morris, 449 F.Supp.2d at 852-67. *1118 Given that a mailing or wire transmission need not itself be fraudulent, the remedy needs to be tailored to the scheme to defraud, not the specific use of the mail or wires.
For similar reasons, we need not resolve Defendants' challenges to the racketeering acts involving denials of marketing to youth. As the district court imposed no remedies specifically relating to youth marketing, our assessment whether the remedies are tailored to the violation found is unaffected by the associated racketeering acts. The remaining racketeering acts are fully sufficient to support the district court's finding of a pattern of racketeering activity as to each Defendant. Because these challenges have no impact on the outcome of this appeal, we decline to address them. The district court set forth findings sufficient to allow our review of its verdict of liability and imposition of sanction.

III. General Challenges to Fraud Liability

A. Specific Intent
The predicate acts of racketeering in this case were all acts of mail or wire fraud, which require specific intent to defraud. Post v. United States, 407 F.2d 319, 329 (D.C.Cir.1968). Defendants challenge the district court's conclusion that they acted with specific intent, arguing that the district court applied an impermissible "collective intent" standard and that the government did not present any evidence to support a finding of specific intent under the correct formulation.
Corporations may be held liable for specific intent offenses based on the "knowledge and intent" of their employees. N.Y. Cent. & Hudson River R.R. Co. v. United States, 212 U.S. 481, 495, 29 S.Ct. 304, 53 L.Ed. 613 (1909); see United States v. A & P Trucking Co., 358 U.S. 121, 125, 79 S.Ct. 203, 3 L.Ed.2d 165 (1958). Because a corporation only acts and wills by virtue of its employees, the proscribed corporate intent depends on the wrongful intent of specific employees. See Saba v. Compagnie Nationale Air France, 78 F.3d 664, 670 (D.C.Cir.1996). Thus, to determine whether a corporation made a false or misleading statement with specific intent to defraud, we look to the state of mind of the individual corporate officers and employees who made, ordered, or approved the statement. Southland Sec. Corp. v. INSpire Ins. Solutions Inc., 365 F.3d 353, 366 (5th Cir.2004).
A person's state of mind is rarely susceptible of proof by direct evidence, so specific intent to defraud may be, and most often is, inferred from the totality of the circumstances, including indirect and circumstantial evidence. United States v. Alston, 609 F.2d 531, 538 (D.C.Cir.1979); United States v. Reid, 533 F.2d 1255, 1264 (D.C.Cir.1976). We refer to this inference when, in the common law fraud context, we say that the factfinder "is permitted to impute knowledge of the falsity of the statements to the accused, not as a matter of law but as a consequence of inferences reasonably drawn from the facts shown." United States v. Avant, 275 F.2d 650, 653 (D.C.Cir.1960).
Here, the district court concluded that the chief executive officers and other highly placed officials in the Defendant corporations made or approved statements they knew to be false or misleading, evincing their specific intent to defraud consumers. In some instances, the court found by direct evidence that representatives of the Defendant companies "willfully stat[ed] something which they knew to be untrue." Philip Morris, 449 F.Supp.2d at 895. For example, the court found that, in a televised interview in 1971, Philip Morris President Joseph Cullman III denied that cigarettes posed a health hazard to pregnant *1119 women or their infants, "contradict[ing] the information Helmut Wakeham, Philip Morris's Vice President for Corporate Research and Development, had given him two years earlier." Id. at 193-94. In the main, however, the district court relied on indirect and circumstantial evidence indicating that the senior corporate officials knew that their public statements, and those that they approved for their corporations, were false or misleading.
In the majority of instances, the authors of the fraudulent statements alleged as Racketeering Acts were executives, including high level scientistsCEOs, Vice Presidents, Heads of Research & Development, not entry level employeesat each of the Defendant companies who would reasonably be expected to have knowledge of the company's internal research, public positions, and long term strategies.
Id. at 897. The court reasoned:
[I]t is absurd to believe that the highly-ranked representatives and agents of these corporations and entities had no knowledge that their public statements were false and fraudulent. The Findings of Fact are replete with examples of C.E.O.s, Vice-Presidents, and Directors of Research and Development, as well as the Defendants' lawyers, making statements which were inconsistent with the internal knowledge and practice of the corporation itself.
Id. at 853. The district court did not commit legal error by imputing to Defendants' executives knowledge of the falsity of their statements based on inferences reasonably drawn from the facts shown, and sufficient evidence supported these inferences.
The government presented decades of evidence that scientists within the Defendant corporations and outside scientists hired by the corporations and their joint entities were continually conducting research and reviewing the research of other scientists regarding cigarettes and health, addiction, nicotine and tar manipulation, and secondhand smoke. The evidence at trial demonstrated that the results of this researchessential to the core of Defendants' operations, including strategic planning, product development, and advertisingwere well known, acknowledged, and accepted throughout the corporations. These results established that cigarette smoking causes disease, that nicotine is addictive, that light cigarettes do not present lower health risks than regular cigarettes due to smoker compensation, and that secondhand smoke is hazardous to health. Dr. William Farone, a scientist who worked at Philip Morris for eighteen years and whom the district court found to be "impressive and credible as both a fact and expert witness," id. at 186, testified about the understanding within Philip Morris on the question of whether cigarette smoking is a cause of lung cancer and other diseases:
There was widespread acceptance that smoking caused disease. I never talked with a scientist at Philip Morris who said that smoking doesn't cause disease. [This was based on the] compelling epidemiology such as that recounted in the Surgeon's [sic] General's reports, and our knowledge about the chemicals that were created by cigarettes and what was delivered to the smoker, hundreds of times per day on average.
Id. at 187 (quoting Farone testimony). When asked whether, in his discussions with Philip Morris executives, any of them challenged the validity of the scientific evidence that smoking causes disease, Farone answered,
No. Their comments generally focused on how the company could or should respond, not to whether the scientific *1120 evidence was valid. Remember, a main reason why they hired me in 1976 was to help develop a less hazardous cigarette. It seemed to me at the time I was hired, and certainly was the case during my entire time there, that hiring me for that job was itself implicit recognition that the cigarettes that were out there being sold were causing disease.
Id. (quoting Farone testimony).
The Defendant corporations documented the results of the studies regarding disease, nicotine addiction, and smoker compensation in numerous memoranda and reports; the evidence at trial, including internal corporate documents, demonstrated that the executives crafted their corporate priorities and strategies in response to these findings. See, e.g., id. at 165, 180, 218, 219, 232, 240, 258-59, 270, 336, 720. Defendants' own documents also support the inference that Defendants' executives were aware that their public relations strategy of creating the impression of an "open question" about the link between smoking and disease did not square with their own knowledge about the established link between the two. For example, William Kloepfer, Vice President of Public Relations for the Tobacco Institute, wrote to Earle Clements, President of the Tobacco Institute, admitting that "[o]ur basic position in the cigarette controversy is subject to the charge, and may be subject to a finding, that we are making false or misleading statements to promote the sale of cigarettes." Id. at 855. Other documents demonstrate that Defendants' top officials were directly informed of negative research results. For example, in 1977 Philip Morris Assistant General Counsel Alexander Holtzman sent a "warning" to the company's President, Joseph Cullman, informing him that a research project jointly sponsored by a group of the Defendant companies had concluded that exposure to cigarette smoke causes emphysema. Id. at 183.
The government presented similar evidence regarding the other aspects of Defendants' scheme, such as addiction and nicotine. A few examples cannot adequately present the volumes of evidence underlying the district court's findings of fact, but the following provide a fair sample: A 1991 Reynolds Research and Development report acknowledged that "[w]e are basically in the nicotine business." Id. at 237. Dr. Farone testified that during his time at Philip Morris there was "widespread acceptance internally throughout the companyamong executives, scientists, and marketing people" that nicotine was primarily responsible for addiction to smoking. Id. at 858. Indeed, the district court found that "internal documents and testimony from former company employees affirmed that within their corporate walls, Defendants openly recognized the addictiveness of cigarettes." Id. Regarding light cigarettes, internal research reports and memoranda at the Defendant companies revealed that they understood the phenomena of smoker compensation and studied how to manipulate it in order to make their light brands appealing to addicted smokers while continuing to be able to advertise the brands as low tar. For example, a 1978 BATCo memorandum about that company's internal research acknowledged that "a majority of habitual smokers compensate for changed delivery" and explained that if smokers "choose [a] lower delivery brand ... than their usual brand" they "will in fact increase the amounts of tar and gas phase that they take in, in order to take in the same amount of nicotine." Id. at 861. Dr. Farone testified that Defendants' superior knowledge of compensation (compared to that of scientists outside the industry, including the government) was closely held within Philip Morris and the tobacco industry and there was an "effort on the part of [his] coworkers at Philip Morris, *1121 including [his] supervisors, to restrict any public acknowledgment on the part of Philip Morris of the phenomena of compensation." Id.
As these examples and hundreds more findings in the district court's opinion demonstrate, the court had before it sufficient evidence from which to conclude that Defendants' executives, who directed the activities of the Defendant corporations and their joint entities, knew about the negative health consequences of smoking, the addictiveness and manipulation of nicotine, the harmfulness of secondhand smoke, and the concept of smoker compensation, which makes light cigarettes no less harmful than regular cigarettes and possibly more. The government presented evidence indicating that specific high-ranking corporate officials were directly informed about these matters, as well as evidence of pervasive knowledge and acceptance of these propositions throughout the Defendant organizations. The overwhelming indirect and circumstantial evidence was sufficient to allow the district court to reasonably infer that the high level executives, including "CEOs, Vice Presidents, [and] Heads of Research & Development" for Defendants knew about their respective companies' "internal research, public positions, and long term strategies," id. at 897, that is, the "internal knowledge and practice" of the company, id. at 853. These executives then made, caused to be made, and approved public statements contrary to this knowledge. See, e.g., id. at 190 (Philip Morris Vice President and General Counsel declaring "[n]obody has yet been able to find any ingredient as found in tobacco or smoke that causes human disease"); id. at 166, 201 (28 years after Reynolds scientists declared the presence of carcinogenic compounds in cigarettes was "now well established," a Reynolds press release and newspaper advertisement declared the connection between smoking and disease "an open controversy"); id. at 772 (TI published booklet declaring that secondhand smoke had not been shown to be a health hazard to nonsmokers); id. at 796 (Lorillard general counsel testified at trial that the company's public position has always been and continues to be that secondhand smoke is not a proven health hazard); id. at 273 (President and CEO of Philip Morris quoted in TIME magazine from deposition testimony claiming that cigarettes are not addictive unless a similar attachment to Gummi Bears is an addiction); id. at 285 (TI's Vice President for Public Affairs on television programs flatly denying that nicotine is addictive, stating the attachment is like being a "news junkie" or "chocoholic").
Specific intent to defraud may be inferred where, as here, there is a pattern of corporate research revealing a particular proposition, for example, that smoking is addictive; an ensuing pattern of memoranda within the corporation acknowledging that smoking is addictive, even though the memoranda may or may not have gone directly to the executive who makes the contrary statement; and the corporate CEO or other official of high corporate status then makes a public statement stating that smoking is not addictive, contrary to the knowledge within the corporation. Based on this sort of evidence and the inferences reasonably drawn from it, a factfinder could permissibly infer that the speaker harbored specific intent to defraud at the time he or she made the false or misleading statement. Moreover, such pervasive knowledge throughout the organizations demonstrates that Defendants' executives at least acted with reckless disregard for the truth or falsity of their statements. As the district court correctly held, such reckless disregard suffices to demonstrate the requisite intent. Id. at 897. The law then imputes this specific intent to the corporation.
*1122 Defendants argue that, even if the previous discussion presents a correct statement of the law, it is not the standard that the district court applied here. Rather, Defendants assert that the district court relied on an impermissible "collective intent" theory to find specific intent based on public statements contradicting the "collective knowledge" of the Defendant corporations without finding that any employee harbored specific intent to defraud. Like Defendants and other courts, we are dubious of the legal soundness of the "collective intent" theory. Saba, 78 F.3d at 670 n. 6 ("corporate knowledge of certain facts [can be] accumulated from the knowledge of various individuals, but the proscribed intent (willfulness) depend[s] on the wrongful intent of specific employees"); see, e.g., Southland Sec. Corp., 365 F.3d at 366; Nordstrom, Inc. v. Chubb & Son, Inc., 54 F.3d 1424, 1435 (9th Cir. 1995); United States v. Bank of New Eng., N.A., 821 F.2d 844, 855 (1st Cir.1987); Woodmont, Inc. v. Daniels, 274 F.2d 132, 137 (10th Cir.1960); First Equity Corp. v. Standard & Poor's Corp., 690 F.Supp. 256, 260 (S.D.N.Y.1988). We need not pass on the merits of such a standard here, however, because the district court relied on a permissible view of specific intent. Although at times the court articulated a "collective intent" standard, see Philip Morris, 449 F.Supp.2d at 895-97, it also based its holding on a proper view of specific intent, see id. at 853, 897, and we are satisfied that the court's conclusions based on the proper standard are sufficient to uphold its judgment.

B. Materiality
In their next general challenge to fraud liability, Defendants argue that their false and misleading statements about the health effects of smoking cannot, as a legal matter, be fraudulent because their statements were not material. This argument is based on a flawed understanding of the materiality requirement.
In order for a false or misleading statement to qualify as mail or wire fraud, it "must concern a material or important fact or matter." United States v. Winstead, 74 F.3d 1313, 1320 (D.C.Cir. 1996). This materiality requirement is met if the matter at issue is "of importance to a reasonable person in making a decision about a particular matter or transaction." Id. Materiality does not require proof that any specific person (or number of people) purchased cigarettes as a result of the false statements. Nor does it require Defendants' false statements to be the cause, reason, or sufficient condition of any person's decision to purchase cigarettes. Moreover, no subjective evidence regarding any particular person is required; the test is only whether a reasonable person would consider the matter to be of importance regarding the transaction.
The false statements identified by the district court would be important to a reasonable person purchasing cigarettes. For example, statements about the adverse health effects of smoking, see Philip Morris, 449 F.Supp.2d at 146-208, would be a matter of importance to a reasonable person deciding to purchase cigarettes. The fact that Defendants continually denied any link between smoking and cancer, see, e.g., id. at 204, suggests they themselves considered the matter material. So, too, regarding Defendants' false statements on other topics, including statements concerning: whether smoking is addictive, id. at 208-308, whether Defendants manipulated their cigarettes to control nicotine delivery, id. at 308-84, whether "light" cigarettes were less harmful than other cigarettes, id. at 430-561, whether secondhand smoke is hazardous to non-smokers, id. at 692-801, and whether Defendants *1123 concealed scientific research and destroyed documents, id. at 801-39.
Each of these topics is an important consideration for a reasonable person because each concerns direct and significant consequences of smoking. When deciding whether to smoke cigarettes, tobacco consumers must resolve initial reservations (or lingering qualms) about the potential for cancer, the risk of addiction, or the hazardous effects of secondhand smoke for friends, family, and others who may be exposed. Defendants' prevarications about each of these issues suggests full awareness of this obvious fact; reasonable purchasers of cigarettes would consider these statements important.
Defendants further argue that, because the scientific community had reached a consensus regarding the severely adverse health consequences of smoking, their statements to the contrary would not be believed. See Defs. Br. 98 (arguing that "the public was aware of smoking's adverse health consequences and thus any inconsistent assertion by defendants could not be material to a reasonable person"). The question, however, is not whether a reasonable person would have believed Defendants' false statements, but only whether a reasonable person would have considered the issue "of importance," and the issues considered by the district court clearly met the materiality threshold.

C. First Amendment
In their final general challenge to fraud liability, Defendants claim at least a portion of their statements qualify as protected activity under the First Amendment. Of course, it is well settled that the First Amendment does not protect fraud. See McIntyre v. Ohio Elections Comm'n, 514 U.S. 334, 357, 115 S.Ct. 1511, 131 L.Ed.2d 426 (1995) (stating that the government "may, and does, punish fraud directly"). Recognizing this fact, Defendants argue their statements were not fraudulent, but those arguments are discussed and rejected elsewhere in this opinion. See supra Part III.A-B; infra Part IV.
Defendants next claim protection under the Noerr-Pennington doctrinea doctrine, rooted in the Petition Clause of the First Amendment, that protects "an attempt to persuade the legislature or the executive to take particular action with respect to a law...." E. R.R. Presidents Conference v. Noerr Motor Freight, Inc., 365 U.S. 127, 136, 81 S.Ct. 523, 5 L.Ed.2d 464 (1961). The protection does not "cover activity that was not genuinely intended to influence government action." Allied Tube & Conduit Corp. v. Indian Head, 486 U.S. 492, 508 n. 10, 108 S.Ct. 1931, 100 L.Ed.2d 497 (1988).
Defendants' attempt to invoke Noerr-Pennington as protection fails because the doctrine does not protect deliberately false or misleading statements. "[N]either the Noerr-Pennington doctrine nor the First Amendment more generally protects petitions predicated on fraud or deliberate misrepresentation." Edmondson & Gallagher v. Alban Towers Tenants Ass'n, 48 F.3d 1260, 1267 (D.C.Cir.1995) (describing the holding in Whelan v. Abell, 48 F.3d 1247 (D.C.Cir. 1995)); see also McDonald v. Smith, 472 U.S. 479, 485, 105 S.Ct. 2787, 86 L.Ed.2d 384 (1985) (finding the Petition Clause does not have "special First Amendment status" and that petitions are not entitled to "greater constitutional protection" than "other First Amendment expressions"); Whelan, 48 F.3d at 1255 ("However broad the First Amendment right to petition may be, it cannot be stretched to cover petitions based on known falsehoods."). The district court's valid findings of fraud in this case take Defendants' statements out of the Noerr-Pennington context because *1124 they were clearly and deliberately false. The district court provided countless examples of deliberately false statements by Defendants: "Cigarette smoking causes disease, suffering, and death. Despite internal recognition of this fact, Defendants have publicly denied, distorted, and minimized the hazards of smoking for decades," Philip Morris, 449 F.Supp.2d at 146; "Defendants have researched and recognized, decades before the scientific community did, that nicotine is an addictive drug.... Notwithstanding the understanding and acceptance of each Defendant that smoking and nicotine are addictive, Defendants have publicly denied and distorted the truth as to the addictive nature of their products for several decades," id. at 208-09; "Defendants have designed their cigarettes to precisely control nicotine delivery levels and provide doses of nicotine sufficient to create and sustain addiction. At the same time, Defendants have concealed much of their nicotine-related research, and have continuously and vigorously denied their efforts to control nicotine levels and delivery," id. at 309; "Defendants have known for decades that filtered and low tar cigarettes do not offer a meaningful reduction of risk, and that their marketing which emphasized reductions in tar and nicotine was false and misleading," id. at 860; "Despite their internal acknowledgment of the hazards of secondhand smoke, Defendants have fraudulently denied that [secondhand smoke] causes disease," id. at 864.
Were these statements false, but not deliberately so, Defendants would have a better argument. But Defendants knew of their falsity at the time and made the statements with the intent to deceive. Thus, we are not dealing with accidental falsehoods, or sincere attempts to persuade; Defendants' liability rests on deceits perpetrated with knowledge of their falsity. Where statements are deliberately false or misleading, Noerr-Pennington does not apply. See Alban Towers, 48 F.3d at 1267. Indeed, if Defendants' statements had not been made with fraudulent intent, there would be no basis for RICO liability in the first place.
The district court found six alleged acts protected by Noerr-Pennington and based its holding on the remaining racketeering activity. Philip Morris, 449 F.Supp.2d at 887. All six excluded acts were instances of testimony to Congress and, given the wealth of unprotected racketeering acts, we need not reach the question whether the district court correctly excluded these acts. The remaining acts were intended to defraud consumers, so Noerr-Pennington protection does not apply.

IV. Specific Challenges to Fraud Liability

A. "Light" Cigarettes
The first specific fraud finding Defendants challenge relates to their marketing of "light" cigarettes. The district court found: "As their internal documents reveal, Defendants engaged in massive, sustained, and highly sophisticated marketing and promotional campaigns to portray their light brands as less harmful than regular cigarettes." Philip Morris, 449 F.Supp.2d at 860. The court concluded "Defendants have known for decades that filtered and low tar cigarettes do not offer a meaningful reduction of risk, and that their marketing which emphasized reductions in tar and nicotine was false and misleading." Id.
Defendants contend they should be immune from liability because the Federal Trade Commission ("FTC") has blessed their use of labels such as "light" and "low tar." This argument is entirely foreclosed by the Supreme Court's recent decision in Altria v. Good, ___ U.S. ____, 129 S.Ct. 538, 172 L.Ed.2d 398 (2008), concluding the FTC has never condoned the use of "light" *1125 or "low tar" descriptors. Id. at 550. Defendants point to a 1966 industry guidance letter from the FTC stating that "a factual statement of the tar and nicotine content (expressed in milligrams) of the mainstream smoke from a cigarette," as measured by the Cambridge Filter Method, was permissible under the FTC Act. Id. at 549. The "Commission made clear, however, that the guidance applied only to factual assertions of tar and nicotine yields and did not invite any `collateral representations... made, expressly or by implication, as to reduction or elimination of health hazards.'" Id.
Despite Defendants' argument to the contrary, "the FTC has in fact never required that cigarette manufacturers disclose tar and nicotine yields, nor has it condoned representations of those yields through the use of `light' or `low tar' descriptors." Id. at 550. Although the FTC never prevented Defendants from using misleading descriptors, "agency nonenforcement of a federal statute is not the same as a policy of approval." Id. As the Supreme Court held, "neither the handful of industry guidances and consent orders on which petitioners rely nor the FTC's inaction with regard to `light' descriptors even arguably justifies the pre-emption" argument advanced by Defendants. Id. at 551. For the same reasons, these actions fail to constitute FTC authorization of the descriptors that could defeat a finding of specific intent to defraud.
It is also worth noting that the district court in this case did not find liability solely based on the use of descriptors such as "light" and "low tar." The court found Defendants orchestrated "highly sophisticated marketing and promotional campaigns to portray their light brands as less harmful than regular cigarettes." Philip Morris, 449 F.Supp.2d at 860. In addition to the misleading use of descriptors, the district court found "[Defendants'] public statements are blatantly false" in relation to the marketing of "light" cigarettes. Id. at 861. The district court went on to find that "[a]s part of the Enterprise's scheme to defraud smokers, Defendants withheld and suppressed their extensive knowledge and understanding of nicotine-driven smoker compensation." Id. These findings reveal that fraudulent activity surrounding "light" cigarettes was not merely limited to the use of misleading descriptors. In addition to the fact that the descriptors were not authorized by the FTC, the district court relied on other fraudulent activity by Defendants.
Independent of their FTC-authorization argument, Defendants also insist terms such as "light cigarettes" are not misleading to the public. They analogize "light" cigarettes to sodas which are "low caffeine" and cookies which are "low fat." According to Defendants, the public knows that drinking many "low caffeine" sodas can result in higher levels of caffeine consumption, and eating many "low fat" cookies can result in higher levels of fat consumption. Defendants thus analogize to "light" cigarettes, maintaining that it is obvious that smoking many "light" cigarettes can result in higher levels of nicotine and tar consumption. But the analogy to "light cigarettes" is inapt. Unlike drinking sodas and eating cookies, the factors behind compensation in "light" cigarettes are largely subconscious: "the smoker will subconsciously adjust his puff volume and frequency, and smoking frequency, so as to obtain and maintain his per hour and per day requirement for nicotine." Philip Morris, 449 F.Supp.2d at 467 (citing internal tobacco company documents). Not only is smoker compensation subconscious, but factors such as puff volume and frequency are not even tied to the number of "light" cigarettes smoked. The analogy to sodas and cookies *1126 fails; the subconscious nature of smoker compensation enabled Defendants to mislead the public about the health effects of "light" cigarettes.
Finally, Defendants argue their descriptors were simply verbal representations of numerical ratings authorized by the FTC, and thus were literally true. Even leaving aside the fact that literally true statements may nevertheless constitute fraud, this claim founders on the district court's finding that "there are lights of certain brands with higher tar levels than regulars of other brands from the same company, and there are also lights and regulars of the same brands that have the same FTC tar rating." Id. at 861. This finding, which Defendants do not attempt to show is clearly erroneous, reveals the descriptors were not simply representations of numerical ratings and thus were not "literally true."

B. Secondhand Smoke
We turn next to Defendants' claim that the district court erred in finding that they fraudulently denied the adverse health effects of secondhand smoke. Federal Rule of Civil Procedure 52 obliges us to uphold the district court's findings of fact unless they are "clearly erroneous." FED.R.CIV.P. 52(a)(6). Under this highly deferential standard, we may disturb the district court's findings only if we are "left with the definite and firm conviction that a mistake has been committed." E.g., Boca Investerings P'ship v. United States, 314 F.3d 625, 630 (D.C.Cir.2003) (quotation marks omitted). This is so even if we "would have decided the case differently," as "[w]here there are two permissible views of the evidence, the factfinder's choice between them cannot be clearly erroneous." Anderson, 470 U.S. at 574, 105 S.Ct. 1504.
Defendants contend that their statements disputing the health hazards of secondhand smoke were merely good-faith expressions of opinion. But the district court found to the contrarythat Defendants' representations were fraudulent and not in good faith. Philip Morris, 449 F.Supp.2d at 853, 864-65. Under Rule 52, then, the question for us is whether this finding was clearly erroneous.
The district court criticized Defendants' statements regarding secondhand smoke as contrary to the scientific consensus. Defendants object, emphasizing that the district court found no scientific consensus emerged until the issuance of the Surgeon General's 1986 report determining secondhand smoke to be hazardous. Moreover, they point to evidence of selected post-1986 scientific opinions casting doubt on the dangers of secondhand smoke, arguing that even then they possessed some basis for disputing the consensus.
Defendants' objections are beside the point. The district court based its finding of fraudulent intent not just on the existence of a consensus but also on evidence of Defendants' own knowledge. Philip Morris, 449 F.Supp.2d at 864-65. Specifically, the district court found that dating back to the 1970s, Defendants' own research and analysis revealed the hazards of secondhand smoke. For example, the district court found that in 1980 a Philip Morris scientist reviewed a paper concluding that secondhand smoke caused "significant damage to airway function" in exposed nonsmokers, and found "little to criticize," deeming the paper "an excellent piece of work which could be very damaging" to the industry. Id. at 709 (quotation marks omitted). In 1982, a Philip Morrissponsored research facility concluded that the "side stream" smoke composing the bulk of secondhand smoke is "more irritating and/or toxic" than the "main stream" smoke inhaled by smokers. Id. at 710 (quotation marks omitted). And several *1127 TI advertisements and press releases claimed that an independent 1981 study showing "a significant correlation between lung cancer and secondhand smoke" suffered from a statistical flaw, id. at 715, yet the district court found that industry consultants told TI, Reynolds, and Brown & Williamson that TI knew at the time not only that the statistical error did not exist, but also that the study was in fact correct. Id. at 717-18.
In addition to these and other findings providing relatively direct evidence that Defendants were aware of the health risks of secondhand smoke, the district court found that Defendants concealed their role in making statements regarding secondhand smoke. While it may be true that purveyors of consumer products, without fraudulent intent, frequently engage in concealed support of positive research in their industries, the concealment of identity by Defendants over so long a period on a subject of such intense controversy is at the very least consistent with knowledge of the falsity of their statements.
Although Defendants insist they had no knowledge of the misleading character of their public statements, they nowhere challenge the accuracy of these or any of the district court's other findings suggestive of their knowledge. Instead, they argue that such findings reveal only facts that were known to the public and that had not, at the time, given rise to a scientific consensus. Again Defendants miss the point. The question is not whether other individuals knew that Defendants' claims were false or misleading; the question is whether Defendants did. Regardless of whether a scientific consensus existed at any point, Defendants may be liable for fraud if they made statements knowing they were false or misleading. Based on voluminous evidence, including that summarized above, the district court circumstantially inferred that Defendants did in fact possess such fraudulent intent. Given these unchallenged findings, we have no basis for saying that the district court clearly erred in drawing that conclusion.

C. Addiction
Defendants also claim that the district court clearly erred in finding their representations disputing the addictiveness of cigarettes to be intentionally misleading. We analyze the district court's factual finding as to the misleading character of Defendants' commercial statements for clear error. E.g., FTC v. Brown & Williamson Tobacco Corp., 778 F.2d 35, 41-42 & n. 3 (D.C.Cir.1985). We find none.
Defendants claim that their statements regarding addiction were not intentionally misleading because the term "addiction" is ambiguous. Pointing to the district court's findings that the meaning of the term "addiction" in the scientific community changed over time, Defendants insist that their statements merely clung to the earlier, narrower, definitions of the term, and claim that the district court erroneously converted a semantic dispute into a fraud case. But the district court did not find only that Defendants insisted on retaining an earlier definition of addiction. It found that they did so as part of a concerted effort to misrepresent the difficulty of quitting smoking. Philip Morris, 449 F.Supp.2d at 208-09, 308, 857-59. Defendants fail to demonstrate that this finding was clearly erroneous.
To begin with, Defendants never challenge the district court's findings documenting the impact of nicotine on the body and, more importantly, Defendants' understanding of its effects. Id. at 209-11, 216-71. As early as 1963, Brown & Williamson's general counsel wrote a confidential memorandum stating: "We are, then, in the business of selling nicotine, an addictive drug effective in the release of stress *1128 mechanisms." Id. at 259 (quotation marks omitted). Further, the district court found that Defendants were aware that cigarette dependence was stronger than mere habit formation. In 1974, a Philip Morris scientist told the company's president that it was "simply not an adequate explanation to say that smoking is a habit, or that it is social behavior." Id. at 223 (quotation marks omitted). In 1981, a Philip Morris executive wrote in an article: "Cigarettes are not just habit formingthe body builds up a requirement for them." Id. at 228 (quotation marks omitted). Although several industry attorneys expressed dismay at the publication of the article, none disagreed with it. Id. In 1985, Philip Morris's top management was informed that research showed that "the majority of smokers wished they did not smoke." Id. at 229 (quotation marks omitted). These and numerous other findingsall unchallengedsupport the district court's conclusion that Defendants were aware that nicotine creates a chemical dependency far stronger than a mere habit.
The district court found that despite their knowledge Defendants made numerous statements trivializing and outright denying the dependence cigarettes cause. For example, in 1982 TI issued a press release summarizing testimony that smoking caused an "attachment" comparable to that produced by "tennis, jogging, candy, rock music, Coca-cola, members of the opposite sex and hamburgers." Id. at 281 (quotation marks omitted). In 1997, Philip Morris's CEO testified, "If [cigarettes] are behaviorally addictive or habit forming, they are much more like ... Gummi Bears, and I eat Gummi Bears, and I don't like it when I don't eat my Gummi Bears, but I'm certainly not addicted to them." Id. at 273 (quotation marks omitted). In a 1994 television interview, a TI official claimed that there was "no chemical addiction" to nicotine and stated, "[S]ometimes we use the word `addiction' in very broad terms. We talk about being, you know, news junkies. We talk about being chocoholics." Id. at 285 (quotation marks omitted). A 1988 TI press release declared that "it has been impossible to establish that the feelings persons have upon giving up smoking are anything but that which would be expected when one is frustrated by giving up any desired habit." Id. at 283 (quotation marks omitted, emphases added). Most directly, the district court found that Defendants had their representatives testify that nicotine "did not cause addiction or dependence," id. at 281 (emphasis added), rendering any supposed ambiguities in the word "addiction" beside the point.
The district court concluded that these and other findings reflected a campaign of statements intended to mislead the public into believing that giving up smoking is not markedly more difficult than giving up everyday habits. Although not every statement Defendants made was literally false, even partially true statements can be actionable fraud if intentionally misleading as to facts. See, e.g., Emery v. Am. Gen. Fin., Inc., 71 F.3d 1343, 1348 (7th Cir. 1995) ("A half truth, or what is usually the same thing a misleading omission, is actionable as fraud, including mail fraud if the mails are used to further it, if it is intended to induce a false belief and resulting action to the advantage of the misleader and the disadvantage of the misled."). The district court concluded that Defendants' statements regarding addiction were misleading in this way, and given the above unchallenged factual findings we are not "left with the definite and firm conviction that a mistake has been committed." Boca Investerings, 314 F.3d at 630.

D. Altria
In addition to the challenges to fraud liability raised by all Defendants, two Defendants *1129 Altria and BATComake a number of arguments specific to them. We begin with Defendant Altria, the holding company owner of Defendant Philip Morris, which raises several challenges to the district court's finding of liability.
As an initial matter, Altria claims that the district court erred in finding that it used the mails in five of the nine predicate acts it allegedly committed directly. The district court specifically found, based on Defendants' routine mailing practices, that at least two of those five predicate acts were committed through use of the mails. See Philip Morris, 449 F.Supp.2d at 884 (Racketeering Acts 69, 80). We need not decide whether this circumstantial inference amounted to clear error, as the other four predicate acts the district court found Altria committed are themselves sufficient to constitute a pattern of racketeering activity. See id. (Racketeering Acts 71-72, 74-75).
Altria's central argument is that mailings sent by lawyers could not possibly be mailings in furtherance of a scheme or artifice to defraud, citing several out-of-circuit cases largely standing for the proposition that ordinary litigation mailings containing false matter typically do not themselves constitute a scheme or artifice to defraud. See United States v. Pendergraft, 297 F.3d 1198, 1209 (11th Cir.2002); Nolan v. Galaxy Scientific Corp., 269 F.Supp.2d 635, 643 (E.D.Pa. 2003); Morin v. Trupin, 711 F.Supp. 97, 105-06 (S.D.N.Y.1989); Paul S. Mullin & Assocs., Inc. v. Bassett, 632 F.Supp. 532, 540 (D.Del.1986); Spiegel v. Cont'l Ill. Nat'l Bank, 609 F.Supp. 1083, 1088-90 (N.D.Ill.1985). Whatever the merit of that proposition, it has nothing to do with the question before us. Altria makes a very different claimthat mailings sent in furtherance of a separately-proven scheme to defraud somehow fall outside the mail fraud statute's coverage because they are drafted and physically sent by lawyers who themselves have no fraudulent intent. This claim is without merit. Nothing in the mail fraud statute requires a mailing to be fraudulent at all, as long as the mailing is in furtherance of a fraudulent scheme. See 18 U.S.C. § 1341 (specifying that the mailing can be "any matter or thing whatever to be sent or delivered" as long as it is in furtherance of "any scheme or artifice to defraud"). Moreover, the statute looks to the intent of the individual who caused the mailing, not the individual who drafted or physically mailed it. See United States v. Diggs, 613 F.2d 988, 998 (D.C.Cir.1979) ("[A] defendant `causes' the use of the mails where he does an act with knowledge that the use of the mails will follow in the ordinary course of business, or where such use can reasonably be foreseen, even though not actually intended." (quotation marks omitted)). Given that the district court permissibly inferred the corporate Defendants' intent from the intent of numerous high-level executives, Philip Morris, 449 F.Supp.2d at 897, and given that it found that Defendants "caused" the mailings in order to further the scheme to defraud, id. at 881, the fact that attorneys participated in the actual drafting and mailing provides no immunity. Thus, we conclude that the district court properly found Altria liable for its direct participation in the conduct of the affairs of the enterprise, leaving it unnecessary for us to consider Altria's objections to the findings that it participated through its control of Philip Morris.
Finally, Altria claims that the district court clearly erred in finding that the company joined a RICO conspiracy. We disagree. The district court's findings of fact regarding Altria's actions in furtherance of the goals of the enterprise, both directly and through Philip Morris, see id. at 907-08, as well as the voluminous findings of concerted action and explicit agreement by *1130 Defendants, amply support the circumstantial inference that Altria conspired with the other Defendants to violate RICO. See, e.g., United States v. Mellen, 393 F.3d 175, 191 (D.C.Cir.2004) ("[A] conspiracy can be inferred from a combination of close relationships or knowing presence and other supporting circumstantial evidence." (quotation marks omitted)).

E. BATCo
Defendant BATCo claims that the district court erred in imposing liability on the basis of its conduct outside the United States. Noting that the district court found that its "activities and statements took place outside of the United States," Philip Morris, 449 F.Supp.2d at 873, BATCo claims that it enjoys immunity from RICO liability because the statute has no extraterritorial reach. We need not decide today whether RICO has true extraterritorial reachthat is, whether it could reach foreign conduct with no impact on the United Statesbecause the district court found BATCo liable on the theory that its conduct had substantial domestic effects. Id. Because conduct with substantial domestic effects implicates a state's legitimate interest in protecting its citizens within its borders, Congress's regulation of foreign conduct meeting this "effects" test is "not an extraterritorial assertion of jurisdiction." Laker Airways Ltd. v. Sabena, Belgian World Airlines, 731 F.2d 909, 923 (D.C.Cir.1984). Thus, when a statute is applied to conduct meeting the effects test, the presumption against extraterritoriality does not apply. See Envtl. Def. Fund, Inc. v. Massey, 986 F.2d 528, 531 (D.C.Cir.1993) (noting that "the presumption [against extraterritoriality] is generally not applied where the failure to extend the scope of the statute to a foreign setting will result in adverse effects within the United States," citing Laker Airways).
BATCo argues that the effects test is inapplicable because the United States had no obligation to prove that Defendants' conduct had any effects whatsoever. Although BATCo attributes this to the fact that 18 U.S.C. § 1964(a) does not require the government to prove that it has been injured, we think it better explained by the fact that the mail and wire fraud statutes punish "the scheme, not its success." Pasquantino v. United States, 544 U.S. 349, 371, 125 S.Ct. 1766, 161 L.Ed.2d 619 (2005). That said, BATCo's point has nothing to do with the case at hand. Here the district court found that BATCo's conduct "had substantial direct effects on the United States." Philip Morris, 449 F.Supp.2d at 873. The fact that some other defendant might commit some other offense without effects in the United States hardly renders BATCo immune from liability for the domestic effects it did cause. Someone who fires a rifle from Canada into the United States and wounds his victim can plainly be convicted of attempted murder. See Laker Airways, 731 F.2d at 922 ("[W]hen a malefactor in State A shoots a victim across the border in State B, State B can proscribe the harmful conduct."). This is so even though in general the government may prove attempted murder without establishing that the attempt had any effect whatsoever. Similarly, the fact that effects are not elements of mail and wire fraud offenses or associated RICO violations provides no immunity to those, like BATCo, whose fraud and racketeering has substantial and direct domestic effects.
Thus, we need decide only whether the district court erred in applying the effects testwhich asks whether conduct has a substantial, direct, and foreseeable effect within the United States, see Consol. Gold Fields PLC v. Minorco, S.A., 871 F.2d 252, 261-62 (2d Cir.1989) (describing substantial effect as direct and foreseeable)to the facts of this case. We see no *1131 error. The district court found that as part of the overall scheme to defraud, BATCo conducted sensitive nicotine research for Brown & Williamson abroad and secretly shared the results with Brown & Williamson in the United States. Philip Morris, 449 F.Supp.2d at 298-304. It further found that BATCo, in concert with other Defendants, founded, funded, and actively participated in various international organizations, which Defendants themselves saw as instrumental to their efforts to perpetuate what the district court found to be their fraudulent scheme in the United States. See id. at 119-23. In one example, TI admitted that "the back-wash from events and attacks affecting the industry in smaller countries comes back powerfully to the USA," id. at 140 (quotation marks omitted), and praised INFOTAB, an international organization of which BATCo was a founding member, id. at 132, for "help[ing] the industry to unite in trying to combat the attacks," id. at 140 (quotation marks omitted). Notwithstanding BATCo's demands for a nearly unattainable level of specificity, these unchallenged findings, together with the findings of the tremendous domestic effects of the fraud scheme generally, see, e.g., id. at 209, 307-08, make clear that the district court committed no error in finding that BATCo's participation had substantial, direct, and foreseeable effects in the United States. Cf. Laker Airways, 731 F.2d at 925-26 (finding allegations that the anticompetitive elimination of a foreign airline increased domestic air fares adequate to support antitrust action without demanding further specificity).

V. Challenges to Likelihood of Future Violations
Having found Defendants' challenges to liability unavailing, we move on to the district court's determination that they are likely to commit future RICO violations if not enjoined. All Defendants challenge this finding on a number of common bases, and four DefendantsAltria, BWH, CTR, and TIalso bring separate challenges to the court's findings regarding them. We address each in turn.

A. Likelihood of Future Violations
Section 1964(a) grants district courts jurisdiction "to prevent and restrain" RICO violations. 18 U.S.C. § 1964(a). Hence, before a district court may order remedies under RICO it must find the defendant exhibits a reasonable likelihood of committing future violations of the Act. Disgorgement Opinion, 396 F.3d at 1198.
Here, the district court found a reasonable likelihood that Defendants would commit future RICO violations. Philip Morris, 449 F.Supp.2d at 908-15. Defendants attack this finding, asserting: (1) the district court applied an erroneous legal standard, (2) the Master Settlement Agreement ("MSA") makes future violations unlikely, and (3) Defendants' business practices and public positions alone preclude future violations. We conclude the district court applied the correct legal standard and its factual conclusions were not clearly erroneous.
In the mid-1990s, the attorneys general of several states brought suit against the major tobacco companies for the reimbursement of state costs associated with smoking. Five Defendants, Philip Morris, Reynolds, Brown & Williamson, Lorillard, and Liggett entered into a settlement agreement, the MSA, with forty-six states and the District of Columbia. The MSA prohibited, inter alia, youth marketing, any material misrepresentations regarding the health consequences of tobacco use, agreements between manufacturers to limit either competition or the distribution of information about the health effects associated with smoking, and other specific marketing *1132 techniques (e.g., cartoon characters and billboards). The MSA specifically required the dissolution of CTR, TI, and CIAR. The National Association of Attorneys General and the individual states' attorneys general enforce the MSA, which requires informal dispute resolution before any enforcement action commences whenever possible.
To obtain equitable remedies, the government must demonstrate a "reasonable likelihood of further violation[s] in the future." Savoy Indus., Inc., 587 F.2d at 1168 (quotation marks omitted). Considered under the totality of the circumstances, three factors determine whether a reasonable likelihood exists: "whether a defendant's violation was isolated or part of a pattern, whether the violation was flagrant and deliberate or merely technical in nature, and whether the defendant's business will present opportunities to violate the law in the future." SEC v. First City Fin. Corp., 890 F.2d 1215, 1228 (D.C.Cir.1989). The district court applied this standarda standard both sides agree is appropriate. Philip Morris, 449 F.Supp.2d at 909; Defs. Br. 39-40; Gov. Br. 182.
Defendants quibble with two aspects of the district court's application. First, Defendants assert the district court could not rely on "inferences drawn from past conduct alone" because the MSA "already proscribes future violations" and "imposes a legal barrier to the repetition of such conduct in the future." Defs. Br. 40. This is an odd argument, suggesting a tort settlement automatically limits the remedial options in a RICO suit. Notably, the first two factors of the First City test focus entirely on inferences arising from past conduct. 890 F.2d at 1228. And, as the district court correctly found, "[t]he likelihood of future wrongful acts is frequently established by inferences drawn from past conduct." United States v. Philip Morris USA, 316 F.Supp.2d 6, 10 n. 3 (D.D.C.2004) (quotation marks omitted); see also SEC v. Bilzerian, 29 F.3d 689, 695 (D.C.Cir.1994) (inferring a likelihood of future violations based on the nature of past conduct); SEC v. Gruenberg, 989 F.2d 977, 978 (8th Cir.1993); First City, 890 F.2d at 1228-29. Defendants attempt to bolster their position by claiming the MSA precludes the need for injunctions by fully addressing their prior misconduct. As discussed infra, future violations remain likely notwithstanding the MSA. Therefore, Defendants' argument fails.
Also, Defendants deftly mischaracterize the district court's opinion. Based on a single footnote in the opinion's section discussing the MSA's failure to alter Defendants' conduct and concluding remedies in this case were appropriate, Philip Morris, 449 F.Supp.2d at 913 n. 82, Defendants accuse the trial court of impermissibly "shift[ing] the burden to defendants to prove that RICO violations will not occur in the future ... under the `absolutely clear' test." Defs. Br. 42. Contrary to Defendants' fears, the district court obviously did not intend to announce a new standard or alter the reigning standard via footnote. The First City standard was carefully articulated at the start of the discussion addressing future violations and conscientiously applied. Philip Morris, 449 F.Supp.2d at 908-09, 911-13. The footnote, regarding voluntary termination of illegal conduct, appears much later in the opinion where the court sought to emphasize the suspension of disbelief necessary to agree with Defendants, noting the court must assume "Defendants have complied with and will continue to comply with the terms of the MSA, and that the MSA has adequate enforcement mechanisms" in order to conclude "the MSA obviates the need for injunctive relief." Id. at 913 (quotation marks omitted). This is a far cry from altering the legal standard. Indeed, *1133 the district court found, under the correct standard, that Defendants continued to commit violations even after 1999, well after the execution of the MSA. Id. at 910-11.
Since the district court applied the standard enunciated in Savoy and First City and gave appropriate weight to the inferences drawn from Defendants' past conduct, we uphold the district court's decision to order remedies.
The district court concluded the MSA "alone [could not] remove the reasonable likelihood of Defendants' future RICO violations." Id. Defendants contend the MSA effectively prevents prospective RICO violations because it prohibits them from participating in an "enterprise" or committing any "predicate acts." The district court, however, found Defendants began to evade and at times even violate the MSA's prohibitions almost immediately after signing the agreement and, consequently, concluded the MSA did not limit the court's ability to order "[a]ppropriate [r]emedies." Id. The court's factual findings are not clearly erroneous.
Defendants assert the MSA prevents their participation in a RICO enterprise because the organizations that allowed for joint activity no longer exist, and neither the government nor the district court identified any "joint activity" between Defendants after 1998, the start of the MSA. Defendants' post-agreement activities belie these statements. For example, though the MSA required Defendants to dissolve CIAR, only two days after signing the MSA Lorillard's general counsel wrote Philip Morris, Reynolds, and Brown & Williamson asking to "discuss the status of the plan to reinstate CIAR." Id. at 798 (quotation marks omitted). Shortly thereafter, Covington & Burling LLP informed the CIAR contractors "[t]he members of CIAR have decided to create a new organization to continue the work.... The members of CIAR that will be members of the new organization intend to continue to fund the research." Gov. Ex. 75,412, at 2. Subsequently, in 2000, Philip Morris initiated a new research program that had the same offices, phone numbers, and board as CIAR and many of the same employees, management, researchers, peer reviewers, and grantees. Philip Morris, 449 F.Supp.2d at 798-99.
CIAR is not the lone example of Defendants' organizations poised to circumvent the MSA's prohibitions against joint activities or participation in an enterprise. The district court found, with the exception of CTR and TI, "all of the other organizations either still exist or can be readily re-activated." Id. at 871. For example, even at the time of trial Defendants continued to participate in the Center for Cooperation in Scientific Research Relative to Tobacco ("CORESTA"), "a nonprofit making association with objectives to enhance the scientific cooperation for research on tobacco" perceived as "unique and very valuable" because it enjoys the perception of "being objective, technical and independent." Gov. Ex. 21,788, at 1.
Defendants presume the MSA's prohibition against joint activity is effective. The record, however, demonstrates the tobacco companies retain both the ability and the desire to continue joint activities. Accordingly, the district court did not commit clear error when it determined the MSA could not effectively prevent Defendants' participation in an enterprise.
Defendants next assert the MSA's "scores of injunctions and related prohibitions" prevent "repetition of the core wrongdoing." Defs. Br. 48. The district court determined the MSA does not prevent Defendants' commission of future racketeering acts because: (1) Defendants have not fully complied with the MSA, (2) the States could not be relied upon "to *1134 vigorously enforce the MSA," see Br. For Amici Curiae States 7-11, (3) some provisions of the MSA have and will expire, and (4) BATCo and Altria are not subject to the agreement. Philip Morris, 449 F.Supp.2d at 913-15.
As evidence of the MSA's failures and pitfalls, the district court noted that despite the MSA Defendants still fraudulently denied the dangers of secondhand smoke, marketed "low tar" cigarettes as a healthier alternative to quitting, and falsely denied manipulating nicotine delivery and marketing to youth. Id. at 910. Defendants offer no rebuttal to these factual findings, but instead argue "failure to comply with all the details or the `spirit' of the MSA does not even begin to approach a RICO violation." Defs. Br. 50. Obviously. But as the district court rightly recognized, Defendants cannot hide behind the MSA to avoid the imposition of RICO remedies when they do not comply with the agreement. Philip Morris, 449 F.Supp.2d at 913. Therefore, the district court did not commit clear error when it determined the MSA does not adequately prevent or restrain Defendants' future racketeering activities and did not abuse its discretion by ordering equitable relief.
Defendants claim they have "admitted for years" that "smoking causes lung cancer" and other serious diseases, "smoking is addictive," and "low tar cigarettes may not be safer." Defs. Br. 53-54, 56. They insist their positions on these issues "preclude future RICO violations." Id. at 53. The district court acknowledged Defendants' varying degrees of lip service to these facts, but disagreed that these admissions translated into a guarantee against later violations.
According to the district court, "Defendants' essential position on the relationship of smoking and health remains virtually unchanged" from the fraudulent positions it first took in the 1950s. Philip Morris, 449 F.Supp.2d at 204; see also id. at 204-08 (citing corporate statements and statements from Defendants' executives). The district court condemned Defendants for failing to embrace the Surgeon General's definition of addiction, to admit nicotine specifically creates and sustains addiction, or to "acknowledge[] ... the reason quitting smoking is so difficult, and not simply a function of individual will power, is because of its addictive nature." Id. at 286; see also id. at 284-88. Finally, examples in the record of Defendants' marketing campaigns and internal documents amply support the district court's conclusion that Defendants "continue to make[] false and misleading statements regarding low tar cigarettes in order to reassure smokers and dissuade them from quitting." Id. at 507-08. While we may not have reached all the same conclusions as the district court, under the highly deferential clearly erroneous standard the district court's factual findings have sufficient evidentiary support; its decision to order equitable relief was not an abuse of discretion.

B. Altria
Altria urges, based on its status as a holding company, no factual basis exists for finding it would violate RICO in the future. According to the district court, though, despite Altria's holding company status it "effectively and actively controls the activities of all of its subsidiaries, including Defendant Philip Morris." Philip Morris, 449 F.Supp.2d at 203-04 n. 12. The record establishes that Altria management oversees subsidiary policies and operations, id. at 907-08, and Altria does not dispute its control over Philip Morris. Moreover, Altria itself "participated directly" in the RICO enterprise and conspiracy. Id. at 907. With direct culpability and this level of plenary power over its subsidiaries, Altria clearly remains capable of future RICO violations. Therefore, we *1135 uphold the district court's issuance of remedies against Altria.

C. BWH
BWH makes an argument similar to that of Altria. In 2004, Brown & Williamson merged all domestic tobacco operations with Reynolds and was reconstituted into Brown & Williamson Holdings ("BWH"). The district court made no factual findings specific to BWH. Rather, the district court focused throughout its opinion on Brown & Williamson. Philip Morris, 449 F.Supp.2d at 31 n. 4 (describing Brown & Williamson as "now part of Reynolds American"). The entire rest of the opinion refers to "Brown & Williamson" without any mention of the reconstituted holding company.
Based on BWH's status as a "passive holding company," BWH argues the district court erred in finding it is likely to commit future RICO violations. As discussed in relation to Altria, a company's status as a holding company by itself does not preclude RICO liability. Where a holding company, such as Altria, participates directly in the original violations and retains control over subsidiary tobacco operations, it remains capable of repeating its misconduct.
BWH could not have participated in this RICO enterprise as it did not then exist. Nonetheless, if it exercises plenary control over the tobacco operations of its subsidiaries, then, like Altria, it could commit later violations. Because the district court failed to make any findings about the extent of BWH's control over tobacco operations, we cannot know the company's current capabilities. Therefore, we cannot determine whether a reasonable likelihood exists that BWH will commit future RICO violations. Accordingly, we remand this issue for further fact finding and clarification.

D. Mootness as to CTR and TI
CTR and TI argue that the district court's findings relating to the likelihood they will commit future violations render the case against them moot. We agree. The MSA demanded the dissolution of both organizations. At the time of trial, CTR and TI only existed to wind up their respective affairs. The district court found "no reasonable likelihood of future violations" on the part of TI or CTR and consequently ordered no remedies against them. Philip Morris, 449 F.Supp.2d at 915. The court actually encouraged the government to reconsider proceeding against these entities as they "seem to have no actual ability to continue alleged past RICO violations." Id. at 916 (quotation marks omitted).
"Federal courts lack jurisdiction to decide moot cases because their constitutional authority extends only to actual cases or controversies." Larsen v. U.S. Navy, 525 F.3d 1, 4 (D.C.Cir.2008) (quotation marks omitted). A case is moot when "the challenged conduct ceases such that there is no reasonable expectation that the wrong will be repeated" in circumstances where "it becomes impossible for the court to grant any effectual relief whatever to the prevailing party." City of Erie v. Pap's A.M., 529 U.S. 277, 287, 120 S.Ct. 1382, 146 L.Ed.2d 265 (2000) (quotation marks omitted). For both CTR and TI these requirements have been met. The government nowhere disputes Defendants' claim that CTR and TI no longer exist. They cannot possibly commit future RICO violations. Accordingly, we vacate the judgment as to CTR and TI and remand with directions to dismiss.

VI. Challenges to Remedies
Finally, as to those Defendants the district court properly found likely to commit future RICO violations, we address their *1136 challenges to particular remedies the district court imposed. We also address the cross-appeal seeking additional remedies the district court denied.

A. Subsidiaries
First, Defendants object to the inclusion of their subsidiaries among the persons bound by the remedial order. Rule 65 of the Federal Rules of Civil Procedure indicates that an injunction binds only the parties; their "officers, agents, servants, employees, and attorneys"; and "other persons who are in active concert or participation with" the aforementioned persons. FED. R. CIV. P. 65(d)(2). The rule derives from the common law doctrine that an injunction "not only binds the parties defendant but also those identified with them in interest, in `privity' with them, represented by them or subject to their control"any person or entity through whom the defendants might carry out enjoined activity and so nullify the order. Regal Knitwear Co. v. NLRB, 324 U.S. 9, 14, 65 S.Ct. 478, 89 L.Ed. 661 (1945). A subsidiary corporation is in privity with its parent "in respect to the common corporate business" to the extent it is "so identified in interest with [the parent] that [it] represents precisely the same legal right in respect to the subject matter involved" in the injunction. Jefferson Sch. of Soc. Sci. v. Subversive Activities Control Bd., 331 F.2d 76, 83 (D.C.Cir. 1963).
The term "subsidiaries" in the remedial order cannot expand the scope of the injunction beyond that defined by Rule 65(d); however, subsidiaries of Defendants may be personally bound by the order to the extent that they are agents of or in privity with Defendants in the common corporate business of manufacturing, designing, marketing, or selling cigarettes. (Like any person with actual notice of the injunction, subsidiaries that act in concert with Defendants to violate the order would also be subject to contempt.) The record on appeal does not reveal facts sufficient for us to evaluate over which subsidiaries, if any, Defendants exercise sufficient control or with which they so identify in interest regarding cigarettes that they would legitimately fall within the purview of the injunction order. We therefore vacate the order to the extent that it binds all Defendants' subsidiaries and remand to the district court for proceedings to determine whether inclusion of Defendants' subsidiaries, and which subsidiaries, satisfies Rule 65(d).

B. General Injunctions
The district court permanently enjoined Defendants "from committing any act of racketeering, as defined in 18 U.S.C. § 1961(1), relating in any way to the manufacturing, marketing, promotion, health consequences or sale of cigarettes in the United States," and from
making, or causing to be made in any way, any material false, misleading, or deceptive statement or representation, or engaging in any public relations or marketing endeavor that is disseminated to the United States public and that misrepresents or suppresses information concerning cigarettes. Such material statements include, but are not limited to, any matter that: (a) involves health, safety, or other areas with which a reasonable consumer or potential consumer of cigarettes would be concerned; (b) a reasonable consumer or potential consumer would attach importance to in determining whether to purchase or smoke cigarettes; or (c) the Defendant, Covered Person or Entity making the representation knows or has reason to know that its recipient regards or is likely to regard as important in determining whether to purchase cigarettes or to smoke cigarettes, even if a reasonable person would not so regard it.
*1137 Philip Morris, 449 F.Supp.2d at 938. Defendants assert that, "in the face of more than 1,600 pages of findings," these injunctions do not sufficiently specify the acts restrained, in violation of Rule 65(d), due process, and the First Amendment. Defs. Br. 137.
Rule 65(d) requires every order granting an injunction to "state its terms specifically [and] describe in reasonable detailand not by referring to the complaint or other documentthe act or acts restrained or required." FED.R.CIV.P. 65(d)(1)(B)-(C). "The Rule was designed to prevent uncertainty and confusion on the part of those faced with injunctive orders." Schmidt v. Lessard, 414 U.S. 473, 476, 94 S.Ct. 713, 38 L.Ed.2d 661 (1974). Because an injunction "prohibits conduct under threat of judicial punishment, basic fairness requires that those enjoined receive explicit notice of precisely what conduct is outlawed." Id. Under this standard, we have held injunctions to be too vague when they enjoin all violations of a statute in the abstract without any further specification, or when they include, as a necessary descriptor of the forbidden conduct, an undefined term that the circumstances of the case do not clarify. See Wash. Inv. Network, 475 F.3d at 407 (order enjoined all future violations of the applicable statutes, without clarifying the acts restrained); Gulf Oil Corp. v. Brock, 778 F.2d 834, 843 (D.C.Cir.1985) (order enjoined "substantially similar" conduct without further specification in a case that provided no examples of what is "similar"); Common Cause v. NRC, 674 F.2d 921, 926-27 (D.C.Cir.1982) (order enjoined conduct "similar in nature" without further specification in a case that provided no examples of what is "similar"); SEC v. Savoy Indus., Inc., 665 F.2d 1310, 1318-19 (D.C.Cir.1981) (defendant enjoined not "to engage in any act, practice or course of business which operates or would operate as a fraud or deceit upon any person"); see also Schmidt, 414 U.S. at 476, 94 S.Ct. 713 (enjoined "the present Wisconsin scheme"). Even if it tracks statutory language, a general injunction is not too vague if it relates the enjoined violations to the context of the case. See Savoy Indus., Inc., 665 F.2d at 1316-17 (tracking language of the statute in context of defendant's relationship with issuers of securities). Indeed, we must always apply the fair notice requirement "in the light of the circumstances surrounding (the injunction's) entry: the relief sought by the moving party, the evidence produced at the hearing on the injunction, and the mischief that the injunction seeks to prevent." Common Cause, 674 F.2d at 927 (quotation marks omitted).
The two injunctions at issue here sufficiently specify the activities enjoined as to provide Defendants with fair notice of the prohibited conduct. The district court did not abstractly enjoin Defendants from violating RICO or making false statements, but instead specified the matters about which Defendants are to avoid making false statements or committing racketeering acts: the manufacturing, marketing, promotion, health consequences, and sale of cigarettes, along with related issues that Defendants have reason to know are of concern to cigarette consumers. This is not a generalized injunction to obey the law, especially when read in the context of the district court's legal conclusions and 4,088 findings of fact about fraud in the manufacture, promotion, and sale of cigarettes. These injunctions may be broad, but breadth is warranted "to prevent further violations where[, as here,] a proclivity for unlawful conduct has been shown." Savoy Indus. Inc., 665 F.2d at 1317 (quoting McComb v. Jacksonville Paper Co., 336 U.S. 187, 192, 69 S.Ct. 497, 93 L.Ed. 599 (1949) (holding that the "record of continuing and persistent violations of the *1138 [statute] would indicate that that kind of a [general] decree was wholly warranted in this case")). Defendants complain that the volume of findings in this case actually make understanding the injunctions more difficult and chill speech because some of the district court's findings present "express prohibitions" whereas others, like the use of white filter paper for cigarettes, "simply reflect the district court's disapproval" of aspects of Defendants' business practices without finding the conduct fraudulent. Defs. Br. 137. This objection answers itself, as the plain terms of the injunctions prohibit only conduct that would constitute a racketeering act or a "material false, misleading, or deceptive statement or representation," not all activities the court mentioned in its findings.

C. Extraterritorial Effect
Paragraph four of the injunction prohibits the use of "any express or implied health message or health descriptor for any cigarette brand." Philip Morris, 449 F.Supp.2d at 938. The government concedes that this prohibition "should not be read to govern overseas activities with no domestic effect." Gov. Br. 215-16. But because paragraph four contains no such limiting language, see Philip Morris, 449 F.Supp.2d at 938, we vacate that provision and remand for the district court to reformulate it so as to exempt foreign activities that have no substantial, direct, and foreseeable domestic effects. See supra Part IV.E.

D. Corrective Statements
As part of the remedial order, the district court ordered Defendants to disseminate "corrective statements" concerning the topics about which they had previously misled consumers. The court will determine the precise content of the statements at a future date after receiving proposals from the parties, but ordered that they must address five topics: (1) the adverse health effects of smoking; (2) the addictiveness of smoking and nicotine; (3) the lack of any significant health benefit from smoking light cigarettes; (4) the manufacturers' manipulation of cigarette design and composition to ensure optimum nicotine delivery; and (5) the adverse health effects of exposure to secondhand smoke. Philip Morris, 449 F.Supp.2d at 938-39. The remedial order sets out schedules for the manufacturer Defendants to follow in disseminating the corrective statements in cigarette package onserts, retail point-of-sale displays, newspapers, television, and their company websites. Id. at 939-41. Defendants object to the corrective statements as a whole on the grounds that they did not receive adequate notice of and opportunity to respond to the government's proposed remedy and that the remedy extends beyond the court's jurisdiction under RICO. Regarding the specific means of disseminating the statements, Defendants argue that cigarette package onserts violate the Labeling Act, that the point-of-sale displays are duplicative and impose severe burdens on retailers, and that requiring Defendants to make corrective statements in various media apart from existing advertising violates the First Amendment.

Notice
Defendants argue that because the government did not disclose its final corrective statements proposal until its post-trial proposed remedial order, the district court denied Defendants due process by ordering a version of that remedy without providing Defendants adequate notice and an opportunity to respond. Although Defendants purport to press this objection in a general fashion "with respect to many other remedies imposed by the district court," they state it with sufficient specificity for our consideration only with regard to corrective statements. Defs. Br. 135. The *1139 exact content of the statements is yet to be determined and so is not before us at this stage.
The sequence of events surrounding the remedies phase of the trial did not deprive Defendants of the process they were due. Defendants received the government's proposed remedies, including a general corrective statements proposal, two months before the remedies phase of the trial began. They participated in a fourteen-day, fully briefed remedies trial, at which thirteen witnesses testified and were subject to cross-examination, including at least one government witness who testified about corrective statements. Philip Morris, 449 F.Supp.2d at 923. In its post-trial proposed remedial order, the government specified the five categories of corrective statements (which correspond to the subjects about which the district court found Defendants committed fraud) and the details of its recommended publication campaign. Defendants responded to the government's proposed order in their own post-trial brief and raised numerous legal objections to the propriety of the corrective statements remedy, which the district court considered and resolved in its final opinion and order. See id. at 921-23. Defendants have not demonstrated any prejudice from this sequence of events. In their offer of proof to the district court they asserted only that if they had known more "specifics" of the government's proposed remedy before the hearing, they would have retained, and might have offered testimony from, one or more experts addressing the proposal. See Defs. Offer of Proof at 9-10. Even on appeal, Defendants suggest no testimony they would have offered, no lines of cross-examination inquiry they would have pursued, and no factual dispute they would have addressed.
This case bears no resemblance to United States v. Microsoft Corp., 253 F.3d 34 (2001), as Defendants attempt to suggest. In Microsoft, the district court ordered the break-up and restructuring of Microsoft into two companies without holding any evidentiary hearing to resolve the numerous disputed fact questions surrounding the remedy. Id. at 101-02. Microsoft submitted two offers of proof identifying serious unresolved issues of fact and included 53 pages of submissions specifying the evidence it would introduce to challenge the government's representations. Id. at 103. Microsoft gives us no reason to believe Defendants in this casewho enjoyed pre-trial notice and a lengthy remedies trial, and have shown no prejudice suffered a denial of due process.

Section 1964
A district court that finds a defendant civilly liable for violating RICO has jurisdiction "to prevent and restrain violations of [RICO] by issuing appropriate orders...." 18 U.S.C. § 1964(a). Congress limited relief under section 1964(a) to forward-looking remedies aimed at preventing and restraining future RICO violations. Disgorgement Opinion, 396 F.3d at 1198, 1200. Earlier in this litigation, we held that the statute does not authorize disgorgement because it is "both aimed at and measured by past conduct": "[i]t is measured by the amount of prior unlawful gains and is awarded without respect to whether the defendant will act unlawfully in the future." Id. at 1198. Defendants argue that corrective statements are similarly "focused on remedying the effects of past conduct," id., because they seek to correct Defendants' campaign of deceptive marketing.
The government urges that the corrective statements are a forward-looking remedy authorized under section 1964(a) because future advertising that "may not contain any statements which are themselves false or deceptive" nevertheless inevitably builds upon Defendants' previous *1140 false statements and, if uncorrected, "continues the deception, albeit implicitly rather than explicitly," rendering those advertisements "part of the continuing deception of the public." Warner-Lambert Co. v. FTC, 562 F.2d 749, 769 (D.C.Cir.1977); see Novartis Corp. v. FTC, 223 F.3d 783, 787 (D.C.Cir.2000). We do not doubt that consumers may "continue to make purchasing decisions based on the false belief" created by a manufacturer's false advertising even when that advertising ceases, Novartis Corp., 223 F.3d at 787 (quoting Warner-Lambert Co., 562 F.2d at 762), but it is less clear whether, and in what circumstances, continuing consumer confusion created by uncorrected but truthful advertising would amount to a knowing fraud. Section 1964(a) authorizes only remedies that prevent and restrain future RICO violations, not all future effects of past RICO violations, Disgorgement Opinion, 396 F.3d at 1198, or all future unseemly business practices.
We need not consider this question, however, because as the district court observed and the intervenors here argue, requiring Defendants to issue corrective statements will "prevent and restrain them from making fraudulent public statements on smoking and health matters in the future." Philip Morris, 449 F.Supp.2d at 926. Defendants will be impaired in making false and misleading assurances about, for instance, smoking-related diseases or the addictiveness of nicotineas the district court found they continue to do, id. at 925-26if they must at the same time communicate the opposite, truthful message about these matters to consumers. Requiring Defendants to reveal the previously hidden truth about their products will prevent and restrain them from disseminating false and misleading statements, thereby violating RICO, in the future.

Package onserts
One of the vehicles for the corrective statements is a cigarette package onsert, which the district court ordered Defendants to "affix to cigarette packaging, either on the outside of or within the outer cellophane wrapping around the package... in the same manner as certain Defendants, such as Philip Morris and Brown & Williamson, have utilized package onserts in the past." Philip Morris, 449 F.Supp.2d at 939. Defendants object that the onserts violate the Federal Cigarette Labeling and Advertising Act ("Labeling Act"), which provides that "[n]o statement relating to smoking and health, other than the statement required by section 1333 of this title, shall be required on any cigarette package." 15 U.S.C. § 1334(a).
The Labeling Act defines a "package" as "a pack, box, carton, or container of any kind in which cigarettes are offered for sale, sold, or otherwise distributed to consumers." Id. § 1332(4). A package onsert is "[a] communication affixed to but separate from an individual cigarette pack and/or carton purchased at retail by consumers, such as a miniature brochure included beneath the outer cellophane wrapping or glued to the outside of the cigarette packaging." Philip Morris, 449 F.Supp.2d at 948; see Schwab v. Philip Morris USA, Inc., 449 F.Supp.2d 992, 1084-85 (E.D.N.Y.2006) (defining onserts as "pamphlets attached to the outside of cartons or packs of cigarettes"), rev'd on other grounds by McLaughlin v. Am. Tobacco Co., 522 F.3d 215 (2d Cir.2008); United States v. Star Scientific, Inc., 205 F.Supp.2d 482, 484 (D.Md.2002) (defining onsert as "a type of external package label").
These definitions show that the corrective statements in an onsert are not "statement[s] ... on [a] package," 15 U.S.C. § 1334(a), but rather statements in *1141 a brochure attached to or included with a package, and thus are not prohibited by the plain language of the Labeling Act. See Philip Morris, 449 F.Supp.2d at 928 n. 89. Congress could have used more expansive language to reach statements in onserts had it chosen to do so, but it chose only to preempt the requiring of alternative statements about smoking and health "on any cigarette package." Moreover, the district court and the parties appear to have recognized the distinction between packages and onserts throughout the trial. See id. at 206 ("Philip Morris has never told its customers on its cigarette packaging or in onserts that it agrees that smoking causes cancer and other diseases in smokers."), 288 ("Philip Morris replaced the pre-existing package labels with onserts."), 424 ("[Brown & Williamson] began a new test market ... using its redesigned packaging and onsert.... Star Scientific ... added an informational `onsert' attached to the package."); Trial Tr., Jan. 10, 2005 (Philip Morris senior vice president distinguishing between cigarette pack and onsert). We therefore conclude that the onsert remedy does not violate the Labeling Act.

Point-of-sale displays
The district court ordered each Defendant with a retail merchandising programwhereby retailers agree to use the manufacturer's in-store advertisingto design countertop and header displays containing the corrective statements and "require retailers who participate in such program" to display them for two years. Philip Morris, 449 F.Supp.2d at 939-40. The freestanding countertop displays must be at least thirty inches high and eighteen inches wide, and retailers must place them on their counters "within the line-of-sight of any customer who is standing in line for the register." Id. at 946. The header displays must be of at least equivalent size to Defendants' other brand advertising headers and placed "in an equivalent position with any other brand advertising header" at the top of the cigarette display case. Id. at 939-40, 947. Under the injunctive order, each Defendant must "suspend from its Retail Merchandising Program for a period of one year any retailer that fails to comply with this provision." Id. at 940.
Retailers affected by this ordernone of whom were involved in the litigation in any waydid not receive notice of this remedy or an opportunity to present evidence or arguments to the district court regarding the impact the injunction would have on their businesses. Nor does it appear that the district court independently considered the impact of this program on affected retailers. In their appellate brief as amicus curiae and in affidavits filed with Defendants' motion for a stay of final judgment pending appeal, the National Association of Convenience Stores represents that this injunction will cost retailers substantial revenue. The convenience stores indicate that countertop space is the most important space within a convenience store, and the loss of one square foot of countertop space can cost the industry $82 million in sales per year. Yet if the retailers choose not to carry the countertop displays, Defendants must suspend them from their retail merchandising program for one year, which one retailer asserted would cost ten to fifteen percent of his convenience stores' annual profits. See Hartman Aff. at 2.
Section 1964(a) explicitly cautions that in crafting an injunctive remedy the court must "mak[e] due provision for the rights of innocent persons." 18 U.S.C. § 1964(a). We believe that the district court exceeded its authority by failing to consider the rights of retailers and crafting an injunction that works a potentially serious detriment to innocent persons not parties to or otherwise heard in the district *1142 court proceedings. Even though not explicitly bound by the terms of an injunction on pain of contempt, third parties may be so adversely affected by an injunction as to render it improper. See, e.g., Cook Inc. v. Boston Scientific Corp., 333 F.3d 737, 744 (7th Cir.2003).
We therefore vacate the order regarding point-of-sale displays and remand for the district court to evaluate and "mak[e] due provision for the rights of innocent persons," either by abandoning this part of the remedial order or by crafting a new version reflecting the rights of third parties. 18 U.S.C. § 1964(a). Of course, any such remedy the district court imposes on remand can only affect contracts entered after the injunctive order issues. See Nat'l Wildlife Fed'n v. Burford, 835 F.2d 305, 315 (D.C.Cir.1987) (explaining an injunction's validity due to the fact that it "does not affect the contractual rights of third parties"). In addition, we agree with Defendants that the injunction appears to order each Defendant separately to require the same retail store to display substantively identical, but separate, signs. The government concedes that, despite the language of the order, the district court could not have intended to require the burden of multiple duplicative displays at each retail store. We therefore direct the district court, if it concludes that some form of a point-of-sale display injunction is still appropriate after considering the rights of third parties and existing contracts, to clarify that its order does not require duplicative displays.

First Amendment
The district court also ordered each Defendant to publish the corrective statements on its corporate website, as a one-time full-page advertisement in thirty-five major newspapers, and as at least ten advertisements on a major television network over the course of one year. Philip Morris, 449 F.Supp.2d at 939-41. The court chose these media in order to "structure a remedy which uses the same vehicles which Defendants have themselves historically used to promulgate false smoking and health messages." Id. at 928. The court concluded compelled corrective advertising is permissible under the commercial speech doctrine. Id. at 926-28.
The First Amendment protects against government infringement on "the right to speak freely and the right to refrain from speaking at all." Wooley v. Maynard, 430 U.S. 705, 714, 97 S.Ct. 1428, 51 L.Ed.2d 752 (1977). This holds true whether applied to individuals, see W. Va. State Bd. of Educ. v. Barnette, 319 U.S. 624, 642, 63 S.Ct. 1178, 87 L.Ed. 1628 (1943), or to companies, see Pac. Gas & Elec. Co. v. Pub. Utils. Com., 475 U.S. 1, 16, 106 S.Ct. 903, 89 L.Ed.2d 1 (1986) ("For corporations as for individuals, the choice to speak includes within it the choice of what not to say."). In limited circumstances, however, courts have upheld the government's ability to dictate the content of mandatory speech. This largely occurs in the commercial context.
Under the commercial speech doctrine, the government's "power to regulate commercial transactions justifies its concomitant power to regulate commercial speech that is `linked inextricably' to those transactions." 44 Liquormart v. Rhode Island, 517 U.S. 484, 499, 116 S.Ct. 1495, 134 L.Ed.2d 711 (1996). Thus, the government may require commercial speech to "appear in such a form, or include such additional information, warnings, and disclaimers, as are necessary to prevent its being deceptive." Va. Bd. of Pharmacy v. Va. Citizens Consumer Council, Inc., 425 U.S. 748, 762, 96 S.Ct. 1817, 48 L.Ed.2d 346 (1976). Because commercial speech receives a lower level of protection under the First Amendment, burdens imposed on it receive a lower level of scrutiny from the *1143 courts. Zauderer v. Office of Disciplinary Counsel of Supreme Court, 471 U.S. 626, 637, 105 S.Ct. 2265, 85 L.Ed.2d 652 (1985); Cent. Hudson Gas & Elec. Corp. v. Pub. Serv. Comm'n, 447 U.S. 557, 562-64, 100 S.Ct. 2343, 65 L.Ed.2d 341 (1980). Although the standard for assessing burdens on commercial speech has varied, Bd. of Trs. v. Fox, 492 U.S. 469, 476-78, 109 S.Ct. 3028, 106 L.Ed.2d 388 (1989) (describing the diverse levels of scrutiny applied in various cases, including Central Hudson, 447 U.S. at 566, 100 S.Ct. 2343, In re R.M. J., 455 U.S. 191, 203, 102 S.Ct. 929, 71 L.Ed.2d 64 (1982), and Zauderer, 471 U.S. at 644, 105 S.Ct. 2265), the Supreme Court's bottom line is clear: the government must affirmatively demonstrate its means are "narrowly tailored" to achieve a substantial government goal, id. at 480, 109 S.Ct. 3028.
Defendants object that the "freestanding" corrective statements violate the First Amendment because they are not connected to existing advertising and, therefore, cannot be considered commercial speech. That being the case, Defendants contend the less rigorous commercial speech standard does not apply. Alternatively, Defendants argue that, even if these statements are commercial speech, the corrective statements do not directly and materially advance a substantial government interest. See Cent. Hudson, 447 U.S. at 566, 100 S.Ct. 2343. Defendants' arguments misunderstand the commercial speech doctrine and misstate the commercial speech standard.
Defendants' first argument, that the stand-alone corrective statements do not fall within the commercial speech doctrine because they are not attached to advertisements, is a red herring. The context of the corrective statements does not dictate the level of scrutiny; rather, the level of scrutiny depends on the nature of the speech that the corrective statements burden. Riley v. Nat'l Fed'n of Blind, 487 U.S. 781, 796, 108 S.Ct. 2667, 101 L.Ed.2d 669 (1988) ("Our lodestars in deciding what level of scrutiny to apply to a compelled statement must be the nature of the speech taken as a whole and the effect of the compelled statement thereon."). Here, the district court clearly imposed these statements as a burden on Defendants' current and future commercial speech. Philip Morris, 449 F.Supp.2d at 926-28 (justifying ordering the freestanding corrective statements under the commercial speech doctrine).
Commercial speech is defined as "expression related solely to the economic interests of the speaker and its audience" or "speech proposing a commercial transaction." Cent. Hudson, 447 U.S. at 561-62, 100 S.Ct. 2343. In addition to information related to proposing a particular transaction, such as price, it can include material representations about the efficacy, safety, and quality of the advertiser's product, and other information asserted for the purpose of persuading the public to purchase the product. See, e.g., Zauderer, 471 U.S. at 637 & n. 7, 639-40, 105 S.Ct. 2265 (information and legal advice about a defective product and the possibility of suing were commercial); Bolger v. Youngs Drug Prods. Corp., 463 U.S. 60, 66-68, 103 S.Ct. 2875, 77 L.Ed.2d 469 (1983) (informational brochures discussing "important public issues such as venereal disease and family planning" distributed by contraceptives manufacturer were commercial); Brown & Williamson Tobacco Corp., 778 F.2d at 38, 43 (claims that cigarettes contained one milligram of tar and were "99% tar free" were commercial); Nat'l Comm'n on Egg Nutrition v. FTC, 570 F.2d 157, 159, 163 (7th Cir.1977) (holding egg trade association's advertisements about the relationship between eggs and heart disease were commercial speech). *1144 Defendants' various claimsdenying the adverse effects of cigarettes and nicotine in relation to health and addictionconstitute commercial speech. Defendants disseminate their fraudulent representations about the safety of their products, both in formats that do and those that do not explicitly propose a particular commercial transaction, in attempts to persuade the public to purchase cigarettes.
The fact that somebut certainly not allof these advertisements involve Defendants as a group joined in advertising their common product, discuss cigarettes generically without specific brand names, or link cigarettes to an issue of public debate, does not change the commercial nature of the speech. Bolger, 463 U.S. at 66 n. 13, 67-68, 103 S.Ct. 2875; Nat'l Comm'n on Egg Nutrition, 570 F.2d at 163. Moreover, the reality that these corrective statements may tangentially burden noncommercial speech does not render the statements unconstitutional. A burden on commercial speech, whether it be suppression or mandatory disclosure, only triggers a higher level of scrutiny if the commercial speech is "inextricably intertwined" with fully protected speech. Riley, 487 U.S. at 796, 108 S.Ct. 2667 ("[S]peech [does not] retain[] its commercial character when it is inextricably intertwined with otherwise fully protected speech."). Here, Defendants' past participation in the public controversy surrounding smoking and health may have been inextricably intertwined with their marketing efforts, but the intentionally fraudulent character of the noncommercial public statements undermines any claim for more exacting scrutiny. See McIntyre, 514 U.S. at 357, 115 S.Ct. 1511. Moreover, because the injunctive order cannot retroactively burden Defendants' past communications, to determine the constitutionality of the corrective statements we must look to the future and evaluate whether the district court's order targeting commercial speech cuts too broad a swath.
The issue of corrective advertising's possible peripheral impact on protected speech does not affect the character of the burdened speech, but rather bears on whether the remedy is sufficiently narrowly tailored to achieve a substantial government interestin this case, preventing Defendants from committing future RICO violations. We have no reason to think it is not. The district court found that, for over fifty years, Defendants violated RICO by making false and fraudulent statements to consumers about their products. Philip Morris, 449 F.Supp.2d at 26-27. The court also found Defendants reasonably likely to commit similar violations in the future, id. at 908-15, and concluded the corrective statements were necessary to counteract these anticipated violations, see id. at 927 ("The injunctive relief sought here is narrowly tailored to prevent Defendants from continuing to disseminate fraudulent public statements and marketing messages by requiring them to issue truthful communications."). Thus, contrary to Defendants' argument, the publication of corrective statements addressing Defendants' false assertions is adequately tailored to preventing Defendants from deceiving consumers.
The district court has not yet determined the content of the corrective statements. Id. at 928. As the validity of its order relies on the commercial nature of the speech it burdens, the court must ensure the corrective disclosures are carefully phrased so they do not impermissibly chill protected speech. Zauderer, 471 U.S. at 651, 105 S.Ct. 2265. Consequently, the court must confine the statements to "purely factual and uncontroversial information," id., geared towards thwarting prospective efforts by Defendants to either directly mislead consumers or capitalize on *1145 their prior deceptions by continuing to advertise in a manner that builds on consumers' existing misperceptions. Warner-Lambert Co., 562 F.2d at 769 (concluding, due to Listerine's fifty year history of false advertisements, "advertising which fails to rebut the prior claims ... [would] inevitably build[] upon those claims; continued advertising continues the deception, albeit implicitly rather than explicitly"). Assuming the corrective advertising once drafted meets these requirements, it is a permissible restraint on Defendants' commercial speech.

E. Intervention
Tobacco-Free Kids Action Fund and five other public health organizations intervened in both the trial and appeal in order to advocate additional remedies against Defendants. Defendants assert that the intervenors are not properly before the court because they do not have standing and do not have the ability to pursue remedies for RICO violations under the statute. Not surprisingly, the intervenors disagree. Before we address the merits of the intervenors' cross-appeal we must resolve the propriety of their intervention.
Section 1964(b) authorizes the Attorney General to "institute proceedings under" section 1964(a) for equitable remedies. 18 U.S.C. § 1964(b). Private parties, on the other hand, may seek relief under section 1964(c), which allows suits for damages. The statutory scheme does not directly provide private parties with a cause of action for equitable remedies. Id. § 1964(c). According to Defendants, the inability to bring an action under section 1964(a) precludes private intervention in a RICO suit instituted by the government under subsection (a) and permitting private intervenors would contravene congressional intent. Id. § 1964(a), (c).
Defendants are wrong. Under Federal Rule of Civil Procedure 24(a)(2), "the question is not whether the applicable law assigns the prospective intervenor a cause of action[, but] [r]ather ... whether the individual may intervene in an already pending cause of action." Jones v. Prince George's County, 348 F.3d 1014, 1018 (D.C.Cir.2003). Therefore, intervention of right only requires "an `interest' in the litigationnot a `cause of action' or `permission to sue.'" Id. (citing FED.R.CIV.P. 24(a)(2)). Section 1964(b) reserves for the government the ability to "institute" a cause of action for equitable remedies, but does not bar a private person with a sufficient interest under Rule 24(a)(2) from intervening. Likewise, section 1964(c) designates that private parties may bring a cause of action to pursue damages for RICO violations, but does not prevent them from intervening in a governmental action seeking to "prevent and restrain" future violations. Even where Congress has explicitly excluded private persons from a particular statutory cause of action they may, if not demonstrably contrary to congressional intent, still intervene if (1) they satisfy standing and Rule 24(a) requirements and (2) their intervention is "limited to the claims of illegality presented by the [government]." Trbovich v. United Mine Workers of Am., 404 U.S. 528, 537, 92 S.Ct. 630, 30 L.Ed.2d 686 (1972) (finding a statute forbidding a particular party from bringing a cause of action may only be read to prohibit intervention by that party if intervention would frustrate Congress's reasons for barring that party from initiating the litigation in the first place). Outside the text of the statute, which is at best silent on this subject, Defendants offer no evidence Congress intended to prevent private organizations from intervening in section 1964(a) actions. Moreover, the intervenors assert no novel "claims of illegality," but merely *1146 seek to expand the remedies sought by the government.
Two considerations are left: whether the intervenors satisfy standing and Rule 24(a) requirements. In this circuit, because an intervenor "participates on equal footing with the original parties to a suit," a prospective intervenor must satisfy Article III standing requirements. Bldg. & Constr. Trades Dep't v. Reich, 40 F.3d 1275, 1282 (D.C.Cir.1994); see also Fund for Animals, Inc. v. Norton, 322 F.3d 728, 732-33 (D.C.Cir.2003). In Lujan v. Defenders of Wildlife, 504 U.S. 555, 112 S.Ct. 2130, 119 L.Ed.2d 351 (1992), the Supreme Court enunciated a three-part test for standing: (1) injury-in-fact, (2) causation, and (3) redressability. Id. at 560-61, 112 S.Ct. 2130; Transp. Workers Union of Am. v. Transp. Sec. Admin., 492 F.3d 471, 474 (D.C.Cir.2007). On appeal, Defendants claim the intervenors fail on the first two prongs: injury and causation. According to Defendants, the intervenors' alleged injuries are "purely conjectural" and no causal connection exists between their injuries and possible ongoing or future RICO violations.
We conclude the intervenors present sufficient injuries directly caused by Defendants' RICO violations. The membership organizations aver, under the umbrella of associational standing, see UAW v. Brock, 477 U.S. 274, 281-82, 106 S.Ct. 2523, 91 L.Ed.2d 228 (1986), their members suffered injury because Defendants exposed their children to predatory and misleading advertisements intended to entice the children to smoke. "[A] person who received `a misrepresentation made unlawful under [statute] has suffered injury in precisely the form the statute was intended to guard against.'" Public Citizen v. FTC, 869 F.2d 1541, 1548 (D.C.Cir. 1989) (quoting Havens Realty Corp. v. Coleman, 455 U.S. 363, 373, 102 S.Ct. 1114, 71 L.Ed.2d 214 (1982)). As we have discussed at length, through their deceptive marketing, Defendants committed various racketeering acts in order to defraud consumers, including acts that violated mail and wire fraud statutes. Intervenor membership organizations, therefore, suffered an injury-in-fact at the hands of Defendants every time Defendants intended to deceive a member or a member's child. As only one intervenor must have standing for us to consider their additional proposed remedy, we need not decide the standing issue as to the remaining intervening public health organizations. McConnell v. FEC, 540 U.S. 93, 233, 124 S.Ct. 619, 157 L.Ed.2d 491 (2003).
Intervenors fulfill the Rule 24(a) requirements if they: (1) submitted a timely application to intervene, (2) "have an interest relating to the property or transaction which is the subject of the action," (3) are "so situated that the disposition of the action may, as a practical matter, impair or impede [their] ability to protect that interest," and (4) have an interest that the existing parties would not adequately represent. Bldg. & Constr. Trades Dep't, 40 F.3d at 1282. The intervenors easily satisfy the first two prongs. Defendants do not contest the timeliness of the intervenors' application. And, by demonstrating Article III standing, the intervenors adduce a sufficient interest. Fund for Animals, 322 F.3d at 735. The latter prongs are also met. We agree with the district court that the intervenors needed to intercede to protect their interests as the government "substantially altered the scope of the remedies it [sought]" and "no longer share[d] the views of Intervenors as to how extensive the appropriate remedies should be." United States v. Philip Morris USA Inc., No. 99-2496, 2005 WL 1830815, at *5 (D.D.C.2005). Accordingly, we conclude intervention was proper.


*1147 F. Cross-Appeal
The government and the intervenors bring a cross-appeal challenging the district court's denial of additional remedies they sought against Defendants. Specifically, they appeal from the district court's refusal of their proposed counter-marketing campaign, national smoking cessation program, youth smoking reduction plan, and monitoring scheme. They also appeal from the denial of their request for disgorgement, which we affirm as the law of the case. See Disgorgement Opinion, 396 F.3d 1190.
We review de novo the district court's legal conclusion that the government's proposed counter-marketing, smoking cessation, and youth smoking reduction remedies were beyond its authority to order. Under section 1964(a), the district court may craft only forward-looking remedies aimed at preventing and restraining future RICO violations. Id. at 1198. Remedies "focused on remedying the effects of past conduct" or "awarded without respect to whether the defendant will act unlawfully in the future" are beyond the court's statutory jurisdiction. Id.
As the government suggests, the proposed counter-marketing and smoker cessation programs are closely related: they share the goal of reducing the number of smokers in America. The former would "requir[e] Defendants to fund a long-term, extensive, culturally-competent public education and counter-marketing campaign... aimed at diluting both the impact of Defendants' fraudulent statements and at undermining the efficacy of Defendants' marketing efforts towards youth." Philip Morris, 449 F.Supp.2d at 936. The district court concluded that the counter-marketing campaign would "serve to reduce the number of youth smokers, reduce the number of addicted adult smokers in the future, and thereby potentially reduce the economic incentives for Defendants to continue their fraud." Id. Similarly, the smoker cessation program would require Defendants to fund a media campaign "to encourage smokers to seek assistance to quit smoking," a "national tobacco quitline network" to provide access to counseling and medication for quitting smoking, and research to improve "tobacco dependence interventions and physician and clinician training and education." Id. at 933. The government and intervenors offer two rationales for these programs.
First, they argue that each future sale of cigarettes to a smoker who became addicted in the past due to Defendants' fraud is a continuing effect of the past fraud, due to the nature of addiction. The government and intervenors urge that, even if the court cannot order recovery of past profits gained by past deception, it can deny Defendants the continuing future profits flowing from their past misconduct; that is, the court may remedy the continuing effects of past illegal conduct because such a remedy is forward-looking and not measured by past conduct. This argument overlooks the explicit instruction of section 1964(a) that district courts may only order remedies "to prevent and restrain violations of [RICO]." 18 U.S.C. § 1964(a). Future cigarette sales, even to addicted smokers, are not by themselves RICO violations. The proposed remedies attempt to prevent and restrain future effects of past RICO violations, not future RICO violations, therefore they are outside the district court's authority under section 1964(a).
Even those courts that would allow some version of disgorgement under section 1964(a) recognize that the statute is limited to preventing future violations and does not extend to future effects flowing from past violations. See, e.g., Richard v. Hoechst Celanese Chem. Group, Inc., 355 F.3d 345, 355 (5th Cir.2003) ("Section 1964(a) establishes that equitable remedies *1148 are available only to prevent ongoing and future conduct."); United States v. Carson, 52 F.3d 1173, 1182 (2d Cir.1995) ("[T]he jurisdictional powers in § 1964(a) serve the goal of foreclosing future violations, and do not afford broader redress."). Nor do the government's examples from antitrust lend support to their argument. See, e.g., Ford Motor Co. v. United States, 405 U.S. 562, 573, 92 S.Ct. 1142, 31 L.Ed.2d 492 (1972) ("The relief in an antitrust case must be effective to redress the violations and to restore competition." (quotation marks omitted)); United States v. E.I. du Pont de Nemours & Co., 353 U.S. 586, 607, 77 S.Ct. 872, 1 L.Ed.2d 1057 (1957) (ordering the district court to determine "the equitable relief necessary and appropriate ... to eliminate the effects of the acquisition offensive to the statute"). The condition of monopolization is itself a violation of the Sherman Act, 15 U.S.C. §§ 2, 3, therefore district courts may order remedies to cure the monopolizing effects of the forbidden anticompetitive combination or acquisition so as to prevent the continuing violation, id. § 4. The same is not true of RICO or the fraud statutes, under which any future violation would have to result from ongoing acts, not ongoing conditions.
The intervenors suggest that remedies aimed at helping addicted smokers quit would "divest" Defendants of the "fruits of [their] ill-gotten gains," which are addicted smokers and the money they continue to pay for Defendants' cigarettes. Turkette, 452 U.S. at 585, 101 S.Ct. 2524 (describing the civil RICO remedies as a whole, including treble damages). This rhetoric simply disguises the same argument about continuing effects of past violations. The very authorities upon which the intervenors rely establish only the statute's authorization to "order any person to divest himself of any interest ... in any enterprise," 18 U.S.C. § 1964(a), by separating the RICO defendant from the RICO enterprise in order to prevent future violations. See, e.g., United States v. Local 560 of Int'l Bhd. of Teamsters, 780 F.2d 267, 295 (3d Cir.1985) (removal of a union's corrupt executive board was an act of divestiture).
Second, the intervenors argue that the proposed counter-marketing and smoking cessation campaigns would eliminate Defendants' incentive to market their products fraudulently by shrinking Defendants' customer base. It may be, as one expert testified, that "remov[ing] from the marketplace a population of consumers and potential consumers of defendants' products, namely children" and addicted smokers (the targets of the counter-marketing and smoking cessation campaigns), would eliminate rather than heighten Defendants' incentive to market to these groups. Bazerman Written Direct Examination at 65. But marketing to these groups is not in itself a RICO violation. Certainly, if Defendants have no incentive to advertise their products then they have no incentive to do so with fraudulent statements, but we reject general deterrence remedies aimed so wide of the statutorily-ordained mark. Disgorgement Opinion, 396 F.3d at 1200 (rejecting disgorgement even though it "may act to `prevent and restrain' future violations by general deterrence insofar as it makes RICO violations unprofitable"). Under the intervenors' theory, any remedy that reduces Defendants' potential customer base in any manner would prevent and restrain RICO violations because Defendants would have less incentive to market their products and therefore potentially market with fraudulent statements. As the Second Circuit observed, this argument goes too far: a remedy "may not be justified simply on the ground that whatever hurts a civil RICO violator necessarily serves to `prevent and restrain' future RICO violations. If this were adequate justification, the phrase `prevent and restrain' would read `prevent, restrain and *1149 discourage,' and would allow any remedy that inflicts pain." Carson, 52 F.3d at 1182. Such a remedy reaches beyond the bounds of section 1964(a), which authorizes the district court to order injunctions to prevent and restrain fraudulent statements about smoking and health and addiction, not to prevent Defendants from marketing and selling their products at all.
We note that in its brief the government offhandedly mentions an alternative narrower smoking cessation program that would be "calculated to address the number of smokers who would become addicted after the judgment, as a result of future fraud," and suggests this program would be a viable option even if we affirm the district court's denial of the original program. Gov. Br. 225. The district court did not address this alternative, and the government does not further describe it or direct us to where we may find it in the record, so we do not consider it.
Only the intervenors appeal from the district court's denial of the government's proposed "youth smoking reduction targets" plan. Under that proposal, the court would require Defendants to reduce youth smoking by six percent each year for seven years, and if Defendants fail to meet an annual target, the court would assess them a $3,000 fine for each youth above the target who continues to smoke, a figure representing the "lifetime proceeds a Defendant could expect to earn from making its brands appealing" to youth. Philip Morris, 449 F.Supp.2d at 933-34. The district court denied this injunction because it was not tailored to prevent and restrain future RICO violations for at least two reasons. First, the RICO violation the court found with relation to youth marketing was not Defendants' "continuing efforts to market to youth but rather their false denials of those efforts." Id. at 932 n. 91. The youth smoking reduction proposal was not aimed at preventing Defendants from denying their youth marketing efforts but rather at restraining Defendants from marketing and selling to youth. Second, the court agreed with expert testimony that the youth smoking reduction plan was an "outcome-based" remedy that "tie[s] financial assessments to the outcome of youth smoking ... rates[, which] may increase or decrease due to input factors beyond Defendants' control." Id. at 934. An injunction that would hold Defendants responsible for outcomes they could not control regardless of modifications in their behavior would not serve to prevent or restrain Defendants from committing future RICO violations.
The intervenors' argument in favor of the youth smoking reduction proposal is based on the incorrect assumption that the underlying RICO violation to be prevented and restrained is Defendants' youth marketing, rather than their false denials of their efforts to market to youth. As noted above, we need not decide whether such denials amounted to RICO violations. Even if they did, the district court correctly concluded that an injunction aimed solely at reducing youth smoking rates does not address the section 1964 goal of preventing and restraining the underlying RICO violation. The intervenors' argument is unavailing.
Finally, the district court denied the government's proposed monitoring scheme pursuant to Cobell v. Norton, 334 F.3d 1128 (D.C.Cir.2003), because the scheme would "require delegation of substantial judicial powers to non-judicial personnel in violation of Article III of the Constitution." Philip Morris, 449 F.Supp.2d at 935. In Cobell, we held that the district court lacked authority to appoint a monitor charged with "wide-ranging extrajudicial duties" to fill "an investigative, quasi-inquisitorial, quasi-prosecutorial role that is unknown to our adversarial legal system." Cobell, 334 F.3d at 1142. Although we *1150 acknowledged that a monitor may report on a defendant's "compliance with the district court's decree and ... help implement that decree," we held that the court could not invest the monitor with authority to direct a defendant "to take or to refrain from taking any specific action to achieve compliance" with the court's order or to adjudicate violations of the order as "a roving federal district court." Id. at 1143 (citations omitted). Our decision did not turn, as intervenors suggest, on the lack of a complex decree for the monitor to enforce. See id.
The government does not challenge the district court's legal conclusion that the government's proposed monitor possessed impermissibly broad powers. Rather, the government argues that the district court should have sua sponte created a modified version of the government's monitoring scheme that would not violate the principles of Cobell. In support, the government merely demonstrates that courts possess authority to appoint monitors (a proposition the district court did not dispute), and argues that a monitor is necessary in this case because of the complexity of the injunction and the intransigence of Defendants. These assertions do not demonstrate that the district court abused its discretion by deciding not to create its own monitoring scheme to replace the government's inappropriate proposal.
We therefore affirm the district court's denial of the government's proposed counter-marketing campaign, smoking cessation program, youth smoking reduction plan, and monitoring scheme.

* * *
For the foregoing reasons, we affirm the district court's judgment of liability in its entirety except as to CTR and TI, with regard to which we vacate the judgment and remand with directions to dismiss them from the suit. We also largely affirm the remedial order, including the denial of additional remedies sought on cross-appeal, and remand to the district court regarding only four discrete issues. First, because we have no factual findings specific to BWH, we cannot determine whether it is reasonably likely to commit future violations; therefore, we remand that issue for further fact finding and clarification. Second, to the extent that it binds all Defendants' subsidiaries, we vacate the remedial order and remand to the district court for proceedings to determine whether inclusion of the subsidiaries, and which ones, satisfies Rule 65(d). Third, we vacate the prohibition on the use of health messages or descriptors and remand for the district court to reformulate that injunction so as to exempt foreign activities that have no substantial, direct, and foreseeable domestic effects. Finally, we also vacate the remedial order as it regards point-of-sale displays and remand for the district court to make due provision for the rights of innocent third parties and clarify that the order, if reinstated in any form, does not require duplicative displays.
