
665 F.3d 560 (2012)
UNITED STATES of America
v.
Christopher G. WRIGHT, Appellant (No. 09-3467)
Ravinder S. Chawla, Appellant (No. 09-3731)
Andrew Teitelman. Appellant (No. 09-3965).
Nos. 09-3467, 09-3731, 09-3965.
United States Court of Appeals, Third Circuit.
Argued September 21, 2011.
Opinion filed: January 4, 2012.
*564 Lisa A. Mathewson, Esquire (Argued), Philadelphia, PA, for Appellant Christopher G. Wright.
Peter Goldberger, Esquire (Argued), Ardmore, PA, for Appellant Ravinder S. Chawla.
Ellen C. Brotman, Esquire (Argued), Montgomery, McCracken, Walker & Rhoads, Philadelphia, PA, for Appellant Andrew Teitelman.
William A. DeStefano, Esquire, Terri A. Pawelski, Esquire, Buchanan Ingersoll & Rooney PC, Philadelphia, PA, for Appellants Ravinder S. Chawla & Andrew Teitelman.
Zane David Memeger, Esquire, United States Attorney, Robert A. Zauzmer, Esquire, Assistant U.S. Attorney, Jennifer Arbittier Williams, Esquire (Argued), Assistant U.S. Attorney, Michael J. Bresnick, Esquire, Office of United States Attorney, Philadelphia, PA, for Appellee.
Before: AMBRO, CHAGARES, and VANASKIE, Circuit Judges.

OPINION OF THE COURT
AMBRO, Circuit Judge.
A jury convicted appellants Christopher G. Wright, Ravinder ("Ravi") S. Chawla, and Andrew Teitelman ("Appellants") of honest services fraud in violation of, inter *565 alia, 18 U.S.C. § 1346, mail fraud (referred to below as "traditional" fraud) in violation of, inter alia, 18 U.S.C. § 1341, and conspiracy to commit these offenses in violation of 18 U.S.C. § 371. After sentencing, the Supreme Court's decision in Skilling v. United States, ___ U.S. ___, 130 S.Ct. 2896, 177 L.Ed.2d 619 (2010), affected the law of honest services fraud. Among other arguments on appeal, Appellants challenge the sufficiency of the evidence and assert that Skilling undermines their convictions. We agree that Skilling requires a new trial on Appellants' honest services fraud convictions and that prejudicial spillover tainted their traditional fraud convictions. We thus vacate and remand.

I. Background
From 2005 through 2007, Wright was Chief of Staff to Philadelphia City Councilman John "Jack" Kelly.[1] Wright was also a realtor. Chawla owned the real estate firm World Acquisition Partners ("World Acquisition"), and Teitelman, an attorney, did most of the firm's legal work. Teitelman was not a World Acquisition employee, but his offices were in its office suite, and most of his work came from World Acquisition. Chawla and Teitelman befriended Wright when Wright had an office in the same building.
This case concerns a series of gifts that Chawla, Teitelman, or both gave Wright and a simultaneous series of official acts that Wright took on behalf of World Acquisition. Wright received a free stint in an apartment, free legal services, and was promised commissions on World Acquisition deals. At the same time, Wright shepherded a bill that Chawla favored through Kelly's office, arranged meetings about a World Acquisition development, and communicated with City of Philadelphia offices for World Acquisition.
More specifically, Wright received three main benefits. First, he lived at least part-time in an apartment (with a free parking space) for 14 months without paying rent. World Acquisition had contracted to buy a building at 2000 Delancey Street in Philadelphia, then sold its right to buy the building to another purchaser. Meanwhile, Wright was in divorce proceedings and struggled with alcohol abuse. Teitelman, concerned for Wright, helped him move into one of the building's vacant units. The parties contest the extent to which Chawla knew about this arrangement. The new purchaser's agent soon discovered Wright, who left the apartment months later after the new purchaser sought to evict him.
Second, Wright received free legal help from Teitelman and his associate. When the Delancey Street building's new owner attempted to evict Wright, Teitelman defended him. Teitelman also took over negotiations with the lawyer for Wright's wife when Wright could no longer afford his previous divorce lawyer. Finally, Teitelman defended Wright in a bank foreclosure against Wright's marital home. For all that work, Teitelman billed Wright but $350, and did so only after Teitelman learned that the FBI was investigating their relationship. As with the apartment, the parties contest Chawla's involvement.
Third, Wright was promised commissions in his capacity as a realtor. He occasionally "brought deals" to World Acquisition in the same manner that any realtor could, but none of those deals succeeded, so Wright never earned anything. On one occasion. World Acquisition granted Wright and his partner the exclusive right to approach a buyer for a $100 million property. Had Wright succeeded in making the sale, he would have earned a *566 commission of $6 million, but that deal also fell through. Chawla offered Wright "liaison work" as well,[2] but Wright declined that offer.
While he was receiving those benefits, Wright took three sets of actions as Councilman Kelly's Chief of Staff that tended to benefit World Acquisition. First, Wright helped Kelly propose and pass a "mechanical parking" ordinance. Philadelphia law required developers planning to install mechanical parking to get a zoning variance, a time-consuming process. At Teitelman's behest, Wright set up a meeting at which Chawla and his partner suggested that Kelly change that law. Kelly, who usually took a pro-development stance, agreed. Chawla and Teitelman prodded Wright to make the bill a priority, and Kelly soon after introduced the bill. The City Council passed it by a vote of 15-0.
Second, Wright helped Chawla oppose an ordinance that would cripple a planned World Acquisition project. Chawla envisioned a large development called "River City" south and west of Philadelphia's Logan Square, where low-rise residences predominate. When the neighborhood association protested, Wright arranged a meeting between Chawla and association leaders. Afterward, Wright wrote Chawla and Teitelman advising that his "role as Jack's Chief of Staff" should be to focus City staff on River City's benefits. Nonetheless, in the face of continued opposition, the City Council passed a building-height restriction that thwarted the River City plans. Kelly joined the 15-0 vote.
Third, Wright worked with other City offices on World Acquisition's behalf. When the Parking Authority was selling a certain property, Wright forwarded public information about its "request for proposal" process to Chawla and Teitelman. Wright also arranged a walkthrough of the property. He obtained public information for World Acquisition from Philadelphia Gas Works through a high-level official rather than through the main call center. Finally, Wright worked with the City's Department of Licenses and Inspections on a certification that the River City property was not encumbered with zoning violations. City Council staff often did so for their constituents, though this certification was unusually complicated.
In 2008, a federal grand jury returned a fourteen-count indictment against Chawla, Teitelman, Wright, and Chawla's brother Hardeep. The indictment charged honest services fraud, traditional fraud, conspiracy to commit both kinds of fraud, and bribery in connection with a federally funded program. After a four-week jury trial, including five days of deliberations, the jury convicted Chawla, Teitelman, and Wright on three counts: (1) conspiracy to commit honest services and traditional fraud (Count One); (2) honest services fraud for the apartment arrangement (Count Ten); and (3) traditional fraud for the apartment arrangement (Count Twelve). The jury further convicted Chawla alone on one honest services count for offering Wright liaison work (Count Three). It acquitted on the other ten counts and acquitted Hardeep Chawla of all counts.
The District Court sentenced Wright to 48 months' imprisonment, Chawla to 30 months, and Teitelman to 24 months, followed in each case by two years of supervised *567 release. It also imposed fines and special assessments on each person. After sentencing, they filed timely appeals to our Court. The District Court had jurisdiction under 18 U.S.C. § 3231, and we have jurisdiction under 28 U.S.C. § 1291.
Appellants challenge their convictions on the grounds that: (1) the evidence was insufficient to convict them on any count; (2) the jury instructions on honest services fraud constitute error after the Supreme Court's intervening decision in Skilling; (3) if the honest services fraud convictions are vacated for any reason, the traditional fraud convictions must be as well due to "prejudicial spillover;" (4) the Government constructively amended the indictment; (5) the District Court allowed inadmissible evidence; and (6) it improperly calculated Appellants' Guidelines sentencing ranges.
We stayed the briefing schedule pending the Supreme Court's decision in Skilling. After that decision, all defendants were released on bail without the Government's objection.

II. Discussion

A. Honest Services Fraud: Sufficiency of the Evidence
"Honest services fraud" has proven hard to define. We recently reviewed its history at length, see United States v. Riley, 621 F.3d 312, 326-27 (3d Cir.2010), so a shorter treatment is sufficient here. The District Court instructed the jury that it could convict for honest services fraud under either a "conflict of interest" theory (whereby it is fraud for a public servant not to disclose a conflict of interest resulting in personal gain) or a "bribery" theory (whereby it is fraud for a public servant to accept benefits in exchange for taking an official action). At the time, this instruction properly stated our law. See United States v. Panarella, 277 F.3d 678, 690 (3d Cir.2002). However, the Supreme Court later construed "honest services fraud" to exclude the conflict-of-interest theory, holding that this interpretation of the statute would render it unconstitutionally vague. Skilling, 130 S.Ct. at 2927-35. The jury's general verdict, encompassing both theories, could thus be defective.
Appellants contend that the evidence was insufficient to convict them on the bribery theory alone, requiring that we vacate their convictions. This contention echoes their motion for a judgment of acquittal under Federal Rule of Criminal Procedure 29, which the District Court denied.
"The burden on a defendant who raises a challenge to the sufficiency of the evidence is extremely high." United States v. Lore, 430 F.3d 190, 203 (3d Cir. 2005) (quoting United States v. Serafini, 233 F.3d 758, 770 (3d Cir.2000)). We must affirm the jury's verdict so long as "there is substantial evidence that, when viewed in the light most favorable to the government, would allow a rational trier of fact to convict." United States v. Lee, 612 F.3d 170, 178 (3d Cir.2010) (quotation marks and citation omitted).
We thus turn to the definition of honest services fraud. The bribery theory, which is the only theory left standing to convict for honest services fraud in our case,[3] "requires a quid pro quo," United States v. Kemp, 500 F.3d 257, 281 (3d Cir.2007), that is, "a specific intent to give or receive something of value in exchange *568 for an official act." United States v. Sun-Diamond Growers of Cal., 526 U.S. 398, 404-05, 119 S.Ct. 1402, 143 L.Ed.2d 576 (1999) (emphasis in original). (The Supreme Court has contrasted bribery with a gratuity, which is "merely a reward for some future act that the public official will take[,] and may already have determined to take[,] or for a past act that he has already taken." Id. at 405, 119 S.Ct. 1402.) The bribery theory does not require that each quid, or item of value, be linked to a specific quo, or official act. Rather, a bribe may come in the form of a "stream of benefits." United States v. Bryant, 655 F.3d 232, 240-41 (3d Cir. 2011). The public official need not even perform the official acts if he stood ready to do so having intended to accept a bribe. Id. Intent is the determinant. "The key to whether a gift constitutes a bribe is whether the parties intended for the benefit to be made in exchange for some official action; [indeed,] the government need not prove that each gift was provided with the intent to prompt a specific official act." Kemp, 500 F.3d at 282.
An honest services fraud prosecution for bribery after Skilling thus requires the factfinder to determine two things. First, it must conclude that the payor provided a benefit to a public official intending that he will thereby take favorable official acts that he would not otherwise take. Second, it must conclude that the official accepted those benefits with the intent to take official acts to benefit the payor. See Bryant, 655 F.3d at 240-41; Kemp, 500 F.3d at 281-82. The intent of both parties may be inferred from circumstantial evidence. "The quid pro quo can be implicit, that is, a conviction can occur if the Government shows that [the official] accepted payments or other consideration with the implied understanding that he would perform or not perform an act in his official capacity `under color of official right.'" United States v. Antico, 275 F.3d 245, 257 (3d Cir.2001).
As noted, the jury convicted all three Appellants on Count One, conspiracy to commit honest services fraud in violation of 18 U.S.C. § 371. "The specific elements of conspiracy to violate federal law are: ... an agreement to commit an offense proscribed by federal law; ... the defendants intentionally joining in the agreement; [and] one of the conspirators committing an overt act ... in furtherance of the conspiracy." United States v. Rigas, 605 F.3d 194, 206 n. 9 (3d Cir.2010) (en banc). In the honest services fraud context, the Government must prove overt acts in furtherance of a quid pro quo, such as mutual and contemporaneous benefits.
There were mutual and contemporaneous benefits in this case. Teitelman provided Wright a free place to live and free legal services. As we discuss below, Chawla likely knew of their arrangement and could have encouraged it. That arrangement supported the convictions of all three Appellants on Count Ten, a specific instance of alleged honest services fraud. Chawla also was undeniably involved in extending Wright his exclusive potential commission, and Teitelman sent the email expressly granting that opportunity. In addition, Chawla sent Wright the email offering him "liaison work," which was the basis for his conviction on Count Three. At the same time, Wright helped Chawla bring mechanical parking to Kelly's attention. Thereafter, Wright made sure that Councilman Kelly's office quickly prepared a bill and had Kelly introduce it. Wright also set up meetings for Chawla to persuade the Logan Square Neighborhood Association to support River City. He did so even though his boss, Kelly, planned to vote for the anti-River City height restriction because Logan Square's councilman *569 supported it. Finally, Wright used his influence and knowledge to work with City agencies on World Acquisition's behalf more effectively than Chawla or Teitelman could.
Intent, which the Government must prove both for conspiracy in Count One and for the specific frauds in Counts Three and Ten, is the more difficult question. Parties to a bribery scheme rarely reduce their intent to words, but the law does not require that. "The official and the payor need not state the quid pro quo in express terms, for otherwise the law's effect could be frustrated by knowing winks and nods. The inducement from the official is criminal ... if it is implied from his words and actions...." Evans v. United States, 504 U.S. 255, 274, 112 S.Ct. 1881, 119 L.Ed.2d 57 (1992) (Kennedy, J., concurring in part and in the judgment). Furthermore, Count One is a conspiracy charge, and "the very nature of the crime of conspiracy is such that it often may be established only by indirect and circumstantial evidence." United States v. Brodie, 403 F.3d 123, 134 (3d Cir.2005). Inferring mental state from circumstantial evidence is among the chief tasks of factfinders. We rely on the good sense of jurors (and, where applicable, trial judges) to distinguish intent from knowledge or recklessness where the direct evidence is necessarily scanty.
In this case, a reasonable jury could find that each Appellant had fraudulent intent. Therefore, Appellants have failed to show that the evidence against them was insufficient, as a jury could find that the Government had proven each of the elements of honest services fraud and conspiracy to commit it. We consider the inferences that a jury could have made about each Appellant in turn.
First, consider Wright. The language of some of his emails could persuade a jury that he intended to be influenced. For example, the request-for-proposal information about the Parking Authority property that Wright provided to Chawla and Teitelman was publicly available. But in advising Chawla of a certain deadline, Wright added that "[t]he party must sign in and this will be [a] public recordit would not be [a] good thing for me to sign for this RFPso you should do it or someone from [World Acquisition] should do [it.]" Regarding River City, Wright emailed Chawla (copying Teitelman) without prompting to offer his help. "[Y]ou need someone to contact and monitor City Planning efforts," Wright wrote. "My role as Jack's Chief of Staff should be to keep City Planning's focus on what [R]iver [C]ity will ... bring to ... Philadelphia's tax base/economy for the next twenty years."
This is the language of collaboration and influence. In the spring of 2007, the date of both emails, Wright was living in the Delancey Street apartment and receiving Teitelman's legal help. Mere simultaneity does not create an exchange, but, coupled with the emails, a jury could infer intent. In addition, the Government presented other evidence that could indicate Wright's intent. In one heated exchange with Kelly in the summer of 2006, Kelly told Wright that he should be paying rent for the apartment and that Wright's relationship with World Acquisition should be "squeaky clean." Though he knew it was an issue, Wright lived in the apartment for a year thereafter without paying rent.
Second, a jury could infer that Chawla knew of and approved the benefits that Wright received. The contract under which Chawla sold his rights to buy 2000 Delancey Street, the site of Wright's free apartment, forbade Chawla from putting new tenants there. Wright's presence before *570 closing would risk the deal's collapse. Yet, sometime around the closing, a friend had told Chawla that Wright was "happy and comfortable" in the apartment. Chawla, rather than being surprised or upset, "was happy about that." Chawla also conceded to Kelly in mid-2007 that "Andy [Teitelman] gives [Wright] free legal advice." Teitelman was Chawla's lawyer working in Chawla's office. As Teitelman was representing Wright in a divorce, a foreclosure, and an eviction, it is plausible that Chawla approved of it. A reasonable jury could combine that knowledge with Chawla's emails to infer fraudulent intent. Chawla told Teitelman to "chase Chris" on the mechanical parking issue, which Teitelman promptly did. And when he learned unfavorable news about River City, Chawla wrote Wright, requesting simply: "Chris: Please call Andy or me asap. Thanks." Shortly thereafter, Wright arranged for Chawla to meet with the Logan Square Neighborhood Association. Finally, in the email on which his Count Three conviction was based, Chawla proposed that Wright handle "liaison work" for World Acquisition, though he declined.
Third, it is plausible that Teitelman intended to help influence Wright. There is no dispute that Teitelman got Wright fourteen free months in an apartment with a parking space in an affluent neighborhood. When the agent of the Delancey Street building's new owner found Wright there, everyone passed the buck to Teitelman, who promised to have Wright moved out when the owner requested. Instead, Teitelman defended Wright in the eviction attempt, drafting the answer to the eviction complaint referred to in Count Ten. And there is no dispute that Teitelman acted as Wright's personal lawyer in other matters when Wright could no longer afford one. Teitelman himself sent many of the emails soliciting official acts from Wright, and he (Teitelman) was copied as a recipient on most others. A jury could infer that Teitelman conferred these benefits on Wright so that he would help the business of Teitelman's main client, Chawla.
Thus, drawing all possible inferences in the Government's favor, a reasonable jury could have found that Chawla and Teitelman conferred benefits on Wright intending to secure his favors, and that Wright accepted those benefits intending to aid Chawla and Teitelman. The evidence was therefore sufficient to convict Appellants of honest services fraud, and conspiracy to commit that fraud, under the bribery theory alone.

B. Honest Services Fraud: Erroneous Jury Instruction
Appellants also challenge their honest services fraud convictions in Counts One, Three, and Ten on the ground that Skilling rendered the District Court's jury instructions erroneous. Both sides agree that the "jury [was] instructed on multiple theories of guilt, one of which is improper." Hedgpeth v. Pulido, 555 U.S. 57, 61, 129 S.Ct. 530, 172 L.Ed.2d 388 (2008) (per curiam). In light of Skilling, the jury should have been instructed on the bribery theory but not the conflict-of-interest theory.
"This determination, however, does not necessarily require reversal of the [honest services fraud] conviction[s];... errors of [this] variety are subject to harmless-error analysis." Skilling, 130 S.Ct. at 2934. We presume that such errors are not harmless "unless it can be `prove[d] beyond a reasonable doubt that the error complained of did not contribute to the verdict obtained.'" United States v. Waller, 654 F.3d 430, 434 (3d Cir.2011) (quoting Chapman v. California, 386 U.S. *571 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967)). That Appellants objected to the District Court's honest services fraud instruction on other grounds suffices to preserve this issue for our review. See Black v. United States, ___ U.S. ___, 130 S.Ct. 2963, 2970, 177 L.Ed.2d 695 (2010) ("[B]y properly objecting to the honest-services jury instructions at trial, Defendants secured their right to challenge those instructions on appeal.").
We do not believe that the Government has proven beyond a reasonable doubt that the jury instruction on the conflict-of-interest theory did not affect the honest services verdict. That theory required nondisclosure of a financial interest that could conflict with a public official's duty to provide honest services. See Panarella, 277 F.3d at 690. There is ample evidence on which the jury could have convicted Appellants under that theory. By contrast, the evidence supporting the bribery theory, while sufficient, is less than the "overwhelming" evidence needed to hold that an error is "harmless beyond a reasonable doubt." United States v. Balter, 91 F.3d 427, 440 (3d Cir.1996).
In particular, the jury may have drawn inferences about Appellants' intent that would not sustain a verdict based on the bribery theory. In the sufficiency-of-evidence context, we must draw all reasonable inferences in the Government's favor. Without that constraint here, we believe that other inferences about Appellants' intent are plausible. As above, we will address the intent of each Appellant in turn.
First, Wright may have intended not to be influenced, but merely to do his job. By reputation and by his own trial testimony, Councilman Kelly favored developers and business interests. He also testified that constituent services advancing his policy goals were part of Wright's job. Wright therefore could not "pick and choose" which developers he would assist. Kelly no less than Chawla encouraged Wright to make mechanical parking a priority in his office. On cross-examination, Kelly approved of Wright's other "official acts" as within the scope of his job. Kelly's legislative assistant also testified that while Chawla and his brother "called a lot," they were among many constituents who did so. The President of the Northeast Philadelphia Chamber of Commerce, for example, testified that Wright went personally to visit with its members and worked with many City departments on their behalf. When Chawla's requests extended beyond "constituent services," as in his offer of liaison work, Wright declined. On this evidence, the jury could have acquitted Wright of honest services fraud under the bribery theory because he lacked the required intent to be influenced.
Second, it is not clear beyond doubt that the jury found Chawla seeking to bribe Wright. The Government presented little evidence that Chawla directed Teitelman's gifts or even that he was closely involved with them. There was no direct evidence that Chawla knew that Wright stayed in the apartment for free until well after Wright had performed the official acts at issue. This is a critical distinction because, were Wright paying, his tenancy could not constitute a gift. The jury thus could have inferred that Chawla knew only that Teitelman had found Wright a place to live. And while Chawla knew of Teitelman's free legal services for Wright, there is no evidence that he asked Teitelman to perform them. Chawla openly admitted knowledge of these legal services when Kelly was asking him about his ties to Wright in a conversation that the FBI instigated and recorded. Moreover, Chawla's brief emails do not necessarily show sinister intent. High-level executives are known for quick missives tapped *572 out on mobile devices between meetings. The jury thus might have concluded that while Chawla knew the possible ramifications of Teitelman's gifts to Wright, he did not intend thereby to influence Wright.
Third, Teitelman's friendship with Wright offers a motive for his generosity other than fraud. The evidence establishes, and the Government does not dispute, that Wright and Teitelman were close friends. It is equally clear that Wright was in dire personal straits at the time. His mother had just died of cancer, he was embroiled in a marital fight and divorce, he was essentially broke, and he was drinking heavily. Teitelman was among Wright's few friends who intervened and helped him enter rehabilitation. Those same friends agreed that Wright should walk to work in Center City Philadelphia rather than drive to and from his brother's home. While friendship is no bar to an honest services fraud conviction (as the parties involved are often friends), these facts show a close friendship. Here, the jury could have found that friendship, not fraud, motivated Teitelman to find the apartment in Center City and to act as Wright's lawyer.
In addition to these alternate inferences about Appellants' intent, the context of the trial suggests that the jury may have convicted based on the erroneous conflict-of-interest instruction. See Virgin Islands v. Martinez, 620 F.3d 321, 338 (3d Cir.2010) ("While many ... cases focus on the quantum of evidence against the defendants, harmless-error analysis must, by necessity, take into account the totality of the circumstances." (citation omitted)). For example, the Government insisted in its opening argument that public disclosure forms exist to ensure that "public service is not being tainted." It also linked the Pennsylvania ethics laws to bribery in its closing arguments. And the jury instructions themselves devoted about eight times more words to the conflict-of-interest theory than they did to the bribery theory.
Considering these plausible alternate inferences about Appellants' intent and a trial environment that emphasized the conflict-of-interest theory, we cannot say that the erroneous instruction did not contribute to the verdict. We therefore vacate Appellants' honest services fraud convictions and remand for a new trial.

C. Traditional Mail Fraud: Sufficiency of the Evidence
Appellants' other convictions were for traditional mail fraud. In addition to charging a conspiracy to commit honest services fraud, Count One charged that Appellants conspired, in violation of 18 U.S.C. § 371, to commit traditional fraud. Count Twelve, the only specific instance of traditional fraud in the indictment, charged that Appellants committed mail fraud in violation of, inter alia, 18 U.S.C. § 1341. The jury convicted on both counts. Appellants challenge these convictions, as they challenged their honest services fraud convictions, on the ground that the evidence was insufficient.
Our standard of review in the sufficiency-of-evidence context, while technically plenary, is stringent. To repeat, we must affirm the jury's verdict so long as "there is substantial evidence that, when viewed in the light most favorable to the government, would allow a rational trier of fact to convict." Lee, 612 F.3d at 178 (quotation marks and citation omitted). This challenge thus "`places a very heavy burden on [the] appellant[s].'" United States v. Dent, 149 F.3d 180, 187 (3d Cir.1998) (citation omitted).
We read § 1341 to contain three elements: "(1) a scheme to defraud; (2) use of the mails to further that scheme; *573 and (3) fraudulent intent." United States v. Jimenez, 513 F.3d 62, 81 (3d Cir.2008) (quotation marks and citation omitted). We have elaborated that "`fraudulent representations, as the term is used in [section] 1341, may be effected by deceitful statements or half-truths or the concealment of material facts and the devising of a scheme for obtaining money or property by such statements or concealments.'" United States v. Olatunji, 872 F.2d 1161, 1167 (3d Cir.1989) (modification in original) (quoting United States v. Allen, 554 F.2d 398, 410 (10th Cir.1977)).
Traditional mail fraud under § 1341 involves defrauding a private party of money or property, whereas honest services fraud under § 1346 involves defrauding the public of an official's "honest services." (Unlike honest services fraud, Skilling did not disturb the law of traditional fraud.) Both Count Ten and Count Twelve were based on the same facts: Wright's occupancy of the Delancey Street apartment and the answer that Teitelman mailed in Wright's eviction case.[4] But whereas Count Ten charged that the scheme defrauded Philadelphia's citizens of Wright's honest services, Count Twelve charged that the scheme defrauded the building's owner, PBRG, of rent payments.
We believe that, under the demanding standard of review applied here, we cannot say the evidence was insufficient to convict Appellants of traditional fraud. We consider each of the three elements of traditional mail fraud in turn.
The first element is that there was a fraudulent scheme. A reasonable jury could have found that Appellants sought to defraud PBRG of Wright's rent. PBRG bought the building to renovate it and convert it to condominiums. For that reason, PBRG's principal, Robert Guttman, testified that he "certainly wanted to know" how many units of the mostly vacant building were occupied. Yet at the closing no one mentioned that Wright had just moved in. That was not for want of opportunity. Guttman had bought his right to purchase the building from Chawla, and Teitelman formed PBRG as an entity for the purpose of Guttman and his brother buying buildings from World Acquisition. Moreover, at closing Guttman was provided with a document that listed Wright's apartment as empty. The Government presented no evidence that Chawla or Teitelman prepared that document. But it would be possible for a jury to infer that, because Chawla had sold PBRG its right to purchase the building, he had to approve the list.
Appellants contend that, far from concealing Wright's presence, as Olatunji requires, they were forthright about it. When PBRG's realtor found Wright while inspecting the building, Wright did not make up a story about his presence there or say that he was paying rent. The Government also does not contest that Wright complained to PBRG's initial building manager about his apartment's plumbing. Ultimately, Appellants argue, any scheme to conceal Wright from PBRG failed, as PBRG served him with an eviction notice early in 2007.
A reasonable jury need not have found these arguments persuasive. Chawla knew that it was important to PBRG that the building be as vacant as possible. A jury could have concluded that Wright's absence on the closing documents constituted concealment of his presence there. It could also conclude that Wright's outreach to building managers was consistent with a scheme to defraud, as those managers *574 may have assumed that PBRG had approved what Wright was doing.
The second element of traditional mail fraud is that the mailing alleged for mail fraud purposesthe answer that Teitelman's associate filed in Wright's eviction casefurthered the alleged fraudulent scheme. Appellants point out that "a mailing cannot ... be considered even incident to an essential part of the scheme[] when it occurs after the scheme has reached fruition." United States v. Yusuf, 536 F.3d 178, 187 (3d Cir.2008). Any scheme to defraud PBRG by concealing Wright's occupancy, Appellants argue, must have ended by the time that Teitelman's associate mailed a public legal document admitting that Wright was there. Therefore, they contend, the sole alleged mailing could not have furthered the scheme.
A reasonable jury could have viewed the nature of the scheme differently, so that it did not end as soon as PBRG became aware of Wright's presence. The indictment alleges that the nature of the scheme was "[t]o continue allowing [Wright] the free use of the Delancey Street Apartment and parking space...." The affirmative misstatement alleged toward that end was the claim, made in the mailed answer, that Wright had PBRG's permission to live in the building. Viewing the scheme in this way, a jury could conclude that the mailed answer furthered the scheme.
The third element is that the defendant(s) knew about the alleged scheme and, therefore, could have had the requisite intent to defraud. Chawla and Wright each claim that, to the extent that any such scheme existed, he did not know about it. Chawla asserts that there was no evidence that he knew of Wright's eviction, though he knew that Wright was in the apartment and that Teitelman was helping him with legal issues. Wright similarly points to the lack of evidence that he knew about his exclusion from the closing documents or about any false statements made on his behalf during his eviction proceedings.
The Government responds with two arguments that a reasonable jury could have found persuasive. First, the evidence was sufficient for the jury to make the necessary inferences. Wright, as Teitelman's client, could have known what documents were being filed on his behalf. Indeed, Wright asked Teitelman to handle the eviction complaint. And Chawla told Kelly in 2007 that he knew that Wright was living in the building and that Wright was tight on money. Second, even if Chawla and Wright did not personally know of or intend a fraud, co-conspirators act as mutual agents for one another. See, e.g., United States v. Pungitore, 910 F.2d 1084, 1147 (3d Cir.1990). As such, each becomes responsible for the acts of the other. On these grounds, a jury could have inferred not only that Wright and Chawla knew about the scheme to defraud but also that they intended it.
Teitelman raises a fourth issue in his brief. He asserts that if Appellants did conceal any information from PBRG, that information was not material, as the law requires. See Neder v. United States, 527 U.S. 1, 16, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999) ("[A] false statement is material if it has `a natural tendency to influence, or [is] capable of influencing, the decision of the decisionmaking body to which it was addressed.'" (quoting United States v. Gaudin, 515 U.S. 506, 509, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995))). Teitelman argues that Wright's presence was not material because it did not impair PBRG's ability to convert the building into condominiums. However, Guttman testified that the presence of any renters or squatters in the building would have been material to him *575 as, in effect, its purchaser. A reasonable jury could have determined, then, that information about Wright's presence might have changed Guttman's mind about the building's value.
Based on the evidence recounted above, a reasonable jury could conclude that Appellants agreed on a scheme to defraud PBRG of payment for Wright's tenancy by concealing his presence, that the answer mailed in Wright's eviction case furthered that scheme, and that all three Appellants knew of the scheme and intended that it succeed. Therefore, a reasonable jury could have convicted Appellants under 18 U.S.C. § 1341 and our interpretations thereof.

D. Traditional Mail Fraud: Prejudicial Spillover
Appellants' traditional fraud convictions may be tainted by "prejudicial spillover" from the honest services fraud convictions that we vacate and remand. When two charges are closely linked and we vacate a conviction on one of them, we must ensure that the error on the vacated charge has not affected the remaining charge. If there has been such prejudicial spillover, we must order a new trial on the remaining charge as well. United States v. Murphy, 323 F.3d 102, 122 (3d Cir. 2003).
We apply a two-step test for prejudicial spillover. First, we ask "whether the jury heard evidence that would have been inadmissible at a trial limited to the remaining valid count[s]." United States v. Cross, 308 F.3d 308, 317 (3d Cir.2002). If all evidence on the discarded counts (here, the honest services fraud counts) would remain admissible at a trial on the remaining valid counts (here, the traditional fraud counts), then our inquiry ends. We would remand for resentencing on the valid counts only.
If some evidence would be inadmissible, then we proceed to the second step. There, we ask whether that evidence (the "spillover evidence") was prejudicial. Id. We answer that question by weighing four factors: "whether (1) the charges are intertwined with each other; (2) the evidence for the remaining counts is sufficiently distinct to support the verdict on these counts; (3) the elimination of the invalid count significantly changed the strategy of the trial; and (4) the prosecution used language of the sort to arouse a jury." Murphy, 323 F.3d at 118 (quotation marks omitted) (citing United States v. Pelullo, 14 F.3d 881, 898-99 (3d Cir.1994)). We evaluate these factors in a light "`somewhat favorable to the defendant.'" Murphy, 323 F.3d at 122 (quoting Pelullo, 14 F.3d at 898). If the otherwise inadmissible evidence was prejudicial, we remand for a new trial on the "tainted" count.
Applying this two-step test, we hold that there was spillover evidence from the honest services convictions to the traditional fraud convictions and that it was prejudicial. As to the first step, much of the evidence at this trial would be inadmissible at a hypothetical trial on traditional mail fraud alone. The bulk of the prosecution concerned Wright's allegedly corrupt relationship with Chawla and Teitelman. Proving that Appellants defrauded PBRG of rent would not require proving that Wright was a public servant, that Chawla and Teitelman sought to influence him, or that he sought to be influenced. Evidence of the latter sort fills most of this case's four-volume appendix.
Specifically, the following evidence likely would be inadmissible at a trial on traditional mail fraud alone: (1) Kelly's testimony about Wright's official duties as his Chief of Staff; (2) the testimony of City *576 agency staff[5] about their interactions with Wright, which the Government alleges were undertaken to aid Chawla and Teitelman; (3) the testimony of Russell Meddin of the Logan Square Neighborhood Association about Wright's work on the River City project; (4) the myriad emails among Appellants about the mechanical parking proposal and River City; (5) any evidence pertaining to a $1,000 check that Chawla's brother Hardeep gave to Wright at a holiday party; and (6) the testimony by the Executive Director of the Pennsylvania State Ethics Commission and the General Counsel to the Philadelphia Board of Ethics regarding Wright's disclosure obligations under state law (which pertained only to the conflict-of-interest theory of honest services fraud). This evidence is essentially irrelevant to the question of whether Appellants schemed to defraud PBRG of rent. See Fed.R.Evid. 401, 402.
The Government counters that the enumerated evidence would be relevant to show Appellants' motive to conceal Wright's tenancy from PBRG. As we explained in Cross, "[t]he existence of an overarching scheme can provide circumstantial evidence of a defendant's guilt by explaining his motive in committing the alleged offense." 308 F.3d at 322-23. However, were motive the sole purpose of this considerable body of evidence, a trial court likely would exclude some of it under Federal Rule of Evidence 403 or 404.[6] The probative value on the question of motive in several hundred pages of testimony and documentary evidence is outweighed by the costs of "needless presentation of cumulative evidence." Also, insofar as the evidence portrays Appellants as corrupt, any probative value on motive could be outweighed by its danger of unfair prejudice. And because the "motive" evidence tends to show one type of fraud (honest services) in a trial about another type (traditional), it may be inadmissible character evidence under Rule 404(b).
For these reasons, acknowledging the generous discretion that these rules vest in district courts, much of the enumerated evidence would be inadmissible at a trial on Count Twelve alone. Here, as in Murphy, "the quantum of evidence ... would not be necessary absent the [honest services fraud] theory." 323 F.3d at 121.
We thus proceed to the second step of the prejudicial spillover inquiry. Weighing the four Pelullo factors, we conclude that the otherwise inadmissible evidence was prejudicial.
First, the traditional fraud charge was intertwined with the honest services fraud charges. The same facts underlay both Count Ten (honest services) and Count Twelve (traditional): Wright's presence in the apartment and the answer that Teitelman's associate filed in the eviction case. As in Pelullo, the charges "described similar, if not identical, methods used in the alleged frauds." 14 F.3d at 898. Furthermore, because Count One charged both an honest services fraud conspiracy and a traditional *577 fraud conspiracy, the jury instructions on that Count intermingled the two theories. The Government points out that, because the jury did not convict on all counts, it must have understood the counts separately. Cf. Lee, 612 F.3d at 181 (holding that charges were not intertwined, in part, because the jury convicted on one but acquitted on the other). But in this case the jury convicted all three Appellants on the two counts most likely to be confused.
Second, there was scant evidence that would support a traditional fraud conviction yet be distinct from the honest services fraud charges. The apartment was the most valuable of the alleged bribes that Wright accepted. Yet without his stint there being rent-freethe crux of the traditional fraud chargethe jury could not characterize it as a bribe or as an impediment to Wright's honest services. Thus little of the traditional fraud evidence is independent of the honest services fraud evidence.
Third, the parties' strategy likely would have differed in a trial on traditional mail fraud alone. We have addressed this factor in much the same way that we address the first part of the prejudicial spillover test. Namely, we assess the extent to which the parties would have called different witnesses and, correspondingly, the extent to which their opening and closing arguments would have differed. See Lee, 612 F.3d at 182-83; Pelullo, 14 F.3d at 898-99. In this case, the parties would not have needed to present evidence or opening and closing arguments about the allegedly corrupt relationships among Wright, Chawla, and Teitelman.
Fourth and finally, the prosecution's language about honest services fraud was "of the sort to arouse a jury." In its opening argument, for example, the Government told the jury that "[t]he Chawla brothers bought big, big properties, but they didn't buy them to ... develop them, no, they... ma[de] a quick profit with no investment in time or rehabilitation." As for Wright, "he was seduced by that money, the free apartment, the potential for future wealth," seduction that eventually "had become a full-blown affair." The closing argument used similar rhetoric that likewise did not pertain to the traditional fraud charge. The Government proclaimed that "Chris Wright was bought and paid for ... to do their personal bidding, to be their personal public servant," and that he "was no longer looking after the good of the City of Philadelphia." This language speaks for itself. It is provocative, and it went well beyond Appellants' motive for allegedly defrauding PBRG.
Having concluded that both parts of the inquiry are satisfied, we hold that there was prejudicial spillover in this case. We therefore vacate Appellants' traditional fraud convictions as well as their honest services fraud convictions, and remand for a new trial.

III. Conclusion
We believe that the evidence was sufficient to convict Appellants on each count. However, the Skilling decision that followed trial made the District Court's instructions on honest services fraud incorrect. Because our law of honest services fraud leaves so much to intent and because intent leaves so much to the jury's ability to make reasonable inferences, we cannot say that this error was harmless. Further, as the evidence of honest services fraud overlapped substantially evidence submitted on traditional fraud, prejudicial spillover tainted Appellants' traditional fraud convictions. We thus vacate all four counts of conviction and remand for a new *578 trial.[7]
NOTES
[1]  Councilman Kelly was not implicated in any of the crimes charged against Appellants.
[2]  In an email about the River City project, discussed below, Wright concluded to Chawla that "I am there if you need me." In his brief reply twelve minutes later, Chawla wrote: "Thanks for your offer.... We will need your help on going forward with this project and would like to retain you as our consultant to handle liaison work. We will discuss when we meet next."
[3]  In addition to bribery, Skilling held that honest services fraud may encompass kickbacks. 130 S.Ct. at 2932 ("Reading [28 U.S.C.] § 1346 to proscribe bribes and kickbacksand nothing moresatisfies Congress' undoubted aim...."). Kickbacks are not at issue here.
[4]  These facts also formed part of the basis for the conspiracy charged in Count One.
[5]  These agency staff included the head of Major Tax Enforcement, the Tax Enforcement Administrator, the Director of Corporate Communications at Philadelphia Gas Works, the Contract Administration Manager for the Philadelphia Parking Authority, and a clerk in the Licenses and Inspections Department.
[6]  Rule 403 provides that "[t]he court may exclude relevant evidence if its probative value is substantially outweighed by a danger of one or more of the following: unfair prejudice, confusing the issues, misleading the jury, undue delay, wasting time, or needlessly presenting cumulative evidence." Rule 404(a)(1) provides that "[e]vidence of a person's character or character trait is not admissible to prove that on a particular occasion the person acted in accordance with the character or trait."
[7]  In this context, we need not reach Appellants' constructive amendment, evidentiary, and sentencing challenges.
