
667 F.3d 122 (2011)
UNITED STATES of America, Appellee,
v.
Viktor KOZENY, David Pinkerton, Defendants,
Frederic Bourke, Jr., Defendant-Appellant,
Landlocked Shipping Co., Dr. Jitka Chvatik, Petitioners.[1]
Docket No. 09-4704-cr(L).
United States Court of Appeals, Second Circuit.
Argued: February 10, 2011.
Decided: December 14, 2011.
*126 Michael E. Tigar, Law Office of Michael E. Tigar, Pittsboro, N.C. (John D. Cline, Law Office of John D. Cline, San Francisco, Cal.; Harold A. Haddon, Saskia A. Jordan, Jason C. Middleton, Haddon, Morgan & Foreman, P.C., Denver, Colo., on the brief), for Defendant-Appellant Frederic Bourke Jr.
Harry A. Chernoff, Assistant United States Attorney for the Southern District of New York (Preet Bharara, United States Attorney for the Southern District of New York, Iris Lan, Andrew L. Fish, Assistant United States Attorneys for the Southern District of New York; Robertson Park, Assistant Chief, Fraud Section, United States Department of Justice, on the brief) New York, NY, for Appellee the United States of America.
Before: POOLER and HALL, Circuit Judges.[2]
POOLER, Circuit Judge:
Azerbaijan reclaimed its independence in 1991 following the collapse of the Soviet Union, gaining control over its rich stores of oil and natural gas. In the mid-1990s, Azerbaijan began privatizing various state assets. The candidates for privatization included the state-owned oil company, SOCAR. The government alleged that in an attempt to capitalize on this opportunity, Viktor Kozeny and Frederic Bourke Jr. conspired with others in a scheme to illegally purchase SOCAR by bribing the Azerbaijani president and other officials. After a jury trial, Bourke was convicted of conspiring to violate the Foreign Corrupt Practices Act ("FCPA"), 15 U.S.C. § 78dd1 et seq., 18 U.S.C. § 371, and the Travel Act, 18 U.S.C. § 1953, and of making false statements in violation of 18 U.S.C. § 1001. The district court denied Bourke's motions for new trial and for judgment of acquittal.
On appeal, Bourke vigorously attacks his conviction on several fronts, including (1) the correctness of the jury instructions given, (2) the sufficiency of the evidence, and (3) the propriety of certain evidentiary *127 rulings made by the district court. For the reasons given below, we affirm.

BACKGROUND
Bourke co-founded the accessory company Dooney & Bourke, and considers himself an inventor, investor and philanthropist. In the mid-1990s, Bourke met Viktor Kozeny. Dubbed the "Pirate of Prague" by Fortune magazine, Kozeny is an international entrepreneur known for shady dealings. In a December 1996 article, Fortune detailed how Kozeny and his partner engaged in massive fraud during the privatization of the state-owned industries in the Czech Republic, including engaging in insider trading, purchasing state secrets and participating in various other unsavory business practices. Testimony at trial established that Bourke was aware of Kozeny's "Pirate of Prague" moniker.
In the late 1990s, Azerbaijan began converting state-controlled industries to private ownership through a voucher-based initiative, similar to the one used in the Czech Republic. Among the assets being considered for privatization was SOCAR, the state-owned Azerbaijani oil company. However, observers considered it unlikely that SOCAR would ever actually be privatized, given its economic importance to the country. As part of the privatization process, the Azerbaijani government issued each citizen a voucher book with four coupons. The coupons, which could be freely traded, were used to bid at auction for shares of state-owned enterprises being privatized. Foreigners seeking to participate in the auctions needed to pair their vouchers with options issued by the State Property Committee ("SPC"), the entity charged with administrating the privatization process. Every coupon needed to be matched with an option, so to bid a complete voucher book a foreigner needed to match the four coupons with four options. Voucher books sold for roughly $12.
In May 1997, Kozeny invited Bourke to travel with him to examine potential investments. Their journey included a stop in Azerbaijan. Kozeny created two entities upon returning from the trip: the Minaret Group, an investment bank; and Oily Rock, an entity formed to purchase and own the privatization vouchers issued by the Azerbaijani government. Kozeny recruited Thomas Farrell to work for the entities, and instructed Farrell and other employees to start purchasing vouchers. The vouchers were purchased using U.S. currency flown in on private jets from Zurich or Moscow. Altogether, about $200 million worth of vouchers were purchased.
Kozeny and Farrell were introduced to Ilham Aliyev, the then president's son and vice-president of SOCAR. Aliyev introduced the two to Nadir Nasibov, chair of the SPC, and his deputy, Barat Nuriyev. Kozeny discussed acquiring SOCAR at auction with Nuriyevan auction that would not be conducted absent a presidential decree. As part of a scheme to purchase SOCAR, Kozeny and Nuriyev agreed that all future purchases of vouchers would be made through Nuriyev and his confederates. Nuriyev told Kozeny purchasing SOCAR would require one million vouchers (four million coupons paired with four million options). Nuriyev also made clear that an "entry fee" would need to be paid to various Azerbaijani officials, including President Aliyev, in the range of $8 to $12 million dollars. The "entry fee" was intended to encourage the president to approve SOCAR's privatization. Kozeny agreed to pay the "fee," with Farrell delivering cash payments to Nuriyev to pass on to the president.
In addition, Nuriyev demanded that two-thirds of Oily Rock's voucher books and options be transferred to Azerbaijani *128 officials. The officials would then be able to receive two-thirds of the profits from SOCAR's eventual privatization without actually investing any money. To make the transfer possible, in September 1997 Kozeny instructed his attorney, Hans Bodmer, to set up a complex corporate structure involving multiple parent and holding companies. In December 1997, Nuriyev told Farrell that Aliyev had doubled the voucher book requirement from one to two million vouchers. At the time Nuriyev had this conversation with Farrell, voucher books had increased in price to approximately $100 each.
This development spurred Kozeny to start seeking out additional investors, an effort he kicked off with a lavish holiday party at his home in Aspen, Colorado. Bourke attended, as did Tom McCloskey, another Aspenite who previously invested in Oily Rock. In January, 1998 Kozeny took a group of potential investors to Azerbaijan, including Bourke and his friend, Robert Evans. The group met with Nuriyev and toured the Minaret Group offices. Carrie Wheeler traveled with the group on behalf of a potential investor. She testified that, "it seemed like the gist of the meeting was to communicate [to] investors that [Kozeny] had a relationship with the government in some way."
Bourke and Evans returned to the Azerbaijani capital, Baku, with Kozeny in February 1998. Bodmerwho traveled separatelytestified that Bourke approached him in Baku and questioned him regarding the Azerbaijanis. Bodmer testified that during this so-called "walk-talk," he told Bourke of the nature of the bribery scheme and the corporate structures created to carry it out. Bodmer conveyed the substance of his conversation with Bourke to Rolf Schmid, an associate at Bodmer's law firm. Schmid memorialized Bodmer's description of the conversation years later in a memorandum:
Ricky Bourke asked Hans Bodmer about the legal structure of Oily Rock and its subsidiaries, the ownership of vouchers and options by the holding companies, etc. Hans Bodmer remembers thatprobably at the beginning of 1998he left together with Ricky Bourke . . . in Baku and went for a walk together with Ricky Bourke. During this walk he briefed Ricky Bourke in detail about the involvement of the Azeri interests . . . the 2/3:1/3 arrangement. . .
After traveling to Baku, Bourke set up Blueport, an investment company incorporated in the British Virgin Islands, and invested $7 million in the company. He also recruited other American investors to invest via Blueport, including former Senator George Mitchell. Over time, Blueport would invest roughly $8 million in Oily Rock. In April 1998, Bourke traveled back to Baku for the official opening of the Minaret offices. Mitchell also traveled to Baku for this event, and met with President Aliyev to discuss Oily Rock's investment. Following his conversation, Mitchell told Bourke and Kozeny that the president intended to go forward with SOCAR's privatization. During this same period, Bourke also asked Farrell several times whether "Viktor [was] giving enough" and "[h]as Viktor given them enough money?"
Bourke made another trip to Baku shortly after the Minaret office opening. When he returned home, Bourke contacted his attorneys to discuss ways to limit his potential FCPA liability. During the call, Bourke raised the issue of bribe payments and investor liability. Bourke's attorneys advised him that being linked to corrupt practices could expose the investors to FCPA liability. Bourke and fellow Oily *129 Rock investor Richard Friedman agreed to form a separate company affiliated with Oily Rock and Minaret. This separate company would shield U.S. investors from liability for any corrupt payments made by the companies and Kozeny. To that end, Oily Rock U.S. Advisors and Minaret U.S. Advisors were formed, and Bourke joined the boards of both on July 1, 1998. Directors of the advisory companies each received one percent of Oily Rock for their participation.
In mid-1998, Kozeny and Bodmer told Bourke that an additional 300,000,000 shares of Oily Rock would be authorized and transferred to the Azeri officials. Bourke told a Minaret employee, Amir Farman-Farma, that "Kozeny had claimed that the dilution was a necessary cost of doing business and that he had issued or sold shares to new partners who would maximize the chances of the deal going through, the privatization being a success."
Bodmer set up a Swiss bank account for several Azeri officialsincluding Nuriyev, his son and another relative, as well as President Aliyev's daughter. From May to September 1998, nearly $7 million in intended bribe payments was wired to these accounts. In addition to the evidence of cash bribes, the government adduced evidence that Bourke and other conspirators arranged and paid for medical care, travel and lodging in the United States for both Nuriyev and his son.
By the end of 1998, Kozeny had abandoned all hope of SOCAR's privatization, and began winding down the investment scheme. The Minaret Group fired most of its employees by the end of January 1999, and drastically reduced the pay of the few who remained. Kozeny told the investors that the vouchers were worthless, good only for "wallpaper." Around the same time, Bourke resigned from the advisory company boards. As time went on, the privatization scheme became an issue in civil litigation by investors in the United Kingdom. Kozeny's attorneys contacted the U.S. Attorney's office in late 2000, and Bourke was subsequently advised he was the subject of an investigation. Bourke entered into a proffer agreement on April 26, 2002. Bourke also waived attorney-client privilege and instructed his attorneys to answer questions from investigators. During his proffer sessions, Bourke was asked specifically about whether Kozeny made corrupt payments, transfers and gifts to Azeri officials, and Bourke denied any such knowledge.
On May 12, 2005, Bourke, Kozeny and David Pinkerton, a managing director for American International Group responsible for its investments in Oily Rock and Minaret, were indicted. Kozeny remains a fugitive in the Bahamas and has never faced trial. The indictment charged Bourke with five counts of violating FCPA, 15 U.S.C. § 78dd-1 et seq.; two counts of violating the Travel Act, 18 U.S.C. § 1952; one count of conspiracy to violate FCPA and the Travel Act, 18 U.S.C. § 371; two counts of money laundering, 18 U.S.C. § 1956; one count of conspiracy to commit money laundering, 18 U.S.C. § 371; and one count of making false statements to FBI agents, 18 U.S.C. § 1001. Bourke moved to dismiss all of the counts of the indictment save the false statement charge on statute of limitations grounds. The district court partially granted his motion, United States v. Kozeny, 493 F.Supp.2d 693 (S.D.N.Y.2007), and this Court affirmed, United States v. Kozeny, 541 F.3d 166 (2d Cir.2008). Bourke ultimately went to trial on three counts: conspiracy to violate FCPA and the Travel Act, conspiracy to launder money, and making false statements to the FBI.
The trial lasted five weeks. At the close of the government's case, Bourke moved *130 pursuant to Federal Rule of Criminal Procedure 29 for a judgment of acquittal, which the district court denied. United States v. Kozeny, 638 F.Supp.2d 348 (S.D.N.Y.2009). After three days of deliberations, the jury convicted Bourke on Count One (FCPA conspiracy) and Count Three (false statements) of the indictment, but acquitted on Count Two (conspiracy to commit money laundering). Bourke moved again for a judgment of acquittal or, in the alternative, a new trial. The district court denied the motion. United States v. Kozeny, 664 F.Supp.2d 369 (S.D.N.Y.2009). This appeal followed.

DISCUSSION
Bourke raises numerous challenges to his conviction. He primarily argues the district court erred in (1) instructing the jury, (2) allowing his conviction to stand without being supported by sufficient evidence, and (3) certain evidentiary rulings. We address each of his arguments in turn.

I. Jury Instructions.
Bourke challenges the jury instructions on four primary grounds. First, he argues the district court erred in refusing to instruct the jury that it needed to agree unanimously on a single overt act committed in furtherance of the conspiracy. Second, he argues the district court improperly charged the jury on conscious avoidance because (1) there was no factual basis for such a charge; and (2) the government waived its reliance on the conscious avoidance theory. Third, he argues the district court erred by failing to instruct the jury that the government needed to prove Bourke acted "corruptly" and "willfully" to sustain a conviction on FCPA conspiracy. Finally, he argues the district court erred in failing to give the jury Bourke's proposed good-faith instruction.
We review claims of error in jury instructions de novo. United States v. Wilkerson, 361 F.3d 717, 732 (2d Cir.2004). "An erroneous instruction, unless harmless, requires a new trial." Anderson v. Branen, 17 F.3d 552, 556 (2d Cir. 1994). An error is harmless if it is "clear beyond a reasonable doubt that a rational jury would have found the defendant guilty absent the error." Neder v. United States, 527 U.S. 1, 18, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999). "[A] defendant who requests an instruction bears the burden of showing that the requested instruction accurately represented the law in every respect and that, viewing as a whole the charge actually given, he was prejudiced." Wilkerson, 361 F.3d at 732 (internal quotation marks omitted).

A. Overt acts.
Bourke seeks to overturn his conviction on the ground that the district court erred in refusing to instruct the jury that it needed to agree unanimously on the specific overt act committed in furtherance of the conspiracy. He relies on the Eighth and Ninth Circuits, arguing both require jury unanimity on a specific overt act. Our reading of the cases finds each stands on its own facts, rather than for the proposition Bourke relies on. In United States v. Haskell, the Eighth Circuit approved a charge instructing the jury that "in order to return a verdict of guilty, you must unanimously agree upon which act was done." 468 F.3d 1064, 1074-75 (8th Cir. 2006). There was no discussion about whether such charge was always required when charging on overt acts, just that the particular charge in question sufficed. Id. The Ninth Circuit in United States v. Jones addressed the issue in a similarly oblique manner. See 712 F.2d 1316, 1322 (9th Cir.1983). A fair reading of both Haskell and Jones suggests that the Eighth and Ninth Circuits were simply *131 approving the jury instructions, rather than undertaking an analysis of whether jurors are, as a rule, required to agree on a particular overt act.
Conversely, the Fifth and the Seventh Circuits hold that the jury need not agree unanimously on the specific overt act committed in furtherance of a conspiracy in order to convict. In United States v. Sutherland, the Fifth Circuit held:
We are convinced that in this case the jury need not specifically have considered and agreed as to which of a large number of potential overt acts of bribery were established by the government. These acts were not distinguished in any significant respect and the evidence as to each is remarkably similar. Therefore this series of alleged acts comprises one "conceptual group" and the jury need not have unanimously agreed as to which was proven.
656 F.2d 1181, 1202 (5th Cir.1981). Similarly, in United States v. Griggs, the Seventh Circuit found the jury did not need to unanimously agree on a particular overt act to convict on conspiracy:
The law distinguishes between the elements of a crime, as to which the jury must be unanimous, and the means by which the crime is committed. If the jurors in our case disagreed about which of the overt acts charged were committed, that was less momentous than failing to agree on what crime the defendant had committed.
569 F.3d 341, 343 (7th Cir.2009) (citations omitted).
We have not yet decided the issue on direct review. However, in United States v. Shaoul, we considered the issue under a plain error review. 41 F.3d 811, 817 (2d Cir.1994). In Shaoul, defendant argued, for the first time on appeal, that the district court erred when it failed to instruct the jury that it needed to unanimously agree on which overt acts took place in furtherance of the conspiracy. Id. The district court gave a general unanimity instruction, to wit, that "[t]o report a verdict, it should be unanimous." Id. Applying a plain error review, we found that even if the jurors had to agree on which particular act the defendant committed, "the district court was required only to instruct the jury generally about its duty to return a unanimous verdict." Id. at 819.
In Richardson v. United States, the Supreme Court examined whether a jury must agree unanimously about which specific violations were committed as part of the "continuing series of violations" that make up a continuing criminal enterprise under 21 U.S.C. § 848(c). 526 U.S. 813, 815, 119 S.Ct. 1707, 143 L.Ed.2d 985 (1999). The Court held that the jury must agree that a defendant committed each of the violations comprising the "continuing series." Id. While a jury "cannot convict unless it finds that the Government has proved each element" of the charged crime, the jury "need not always decide unanimously which of several possible sets of underlying brute facts make up a particular element." Id. at 817, 119 S.Ct. 1707. The Richardson Court aptly described the distinction between a brute fact and an element of the crime:
Where, for example, an element of robbery is force or the threat of force, some jurors might conclude that the defendant used a knife to create the threat; others might conclude he used a gun. But that disagreementa disagreement about meanswould not matter as long as all 12 jurors unanimously concluded that the Government had proved the necessary related element, namely, that the defendant had threatened force.
Id.
We agree with the district court's rationale, and hold that the jury *132 need not agree on a single overt act to sustain a conspiracy conviction. As the district court noted, the overt act taken in furtherance of the conspiracy need not be a crime. See Braverman v. United States, 317 U.S. 49, 53, 63 S.Ct. 99, 87 L.Ed. 23 (1942) ("The overt act, without proof of which a charge of conspiracy cannot be submitted to the jury, may be that of only a single one of the conspirators and need not be itself a crime"). "[A]n indictment need not specify which overt act, among several named, was the means by which a crime was committed." Schad v. Arizona, 501 U.S. 624, 631, 111 S.Ct. 2491, 115 L.Ed.2d 555 (1991). Indeed, the government may plead one set of overt acts in the indictment and prove a different set of overt acts at trial without prejudice to the defendant. United States v. Kaplan, 490 F.3d 110, 129 (2d Cir.2007). We conclude, therefore, that although proof of at least one overt act is necessary to prove an element of the crime, which overt act among multiple such acts supports proof of a conspiracy conviction is a brute fact and not itself element of the crime. The jury need not reach unanimous agreement on which particular overt act was committed in furtherance of the conspiracy.

B. Conscious avoidance.
The district court instructed the jury on conscious avoidance as part of its charge on the substantive FCPA violation (Count One):
The FCPA provides that a person's state of mind is knowing with respect to conduct, a circumstance, or a result if, and I'm quoting from the statute, the FCPA, if such person is aware that such person is engaging in such conduct; that such circumstance exist [sic] or that such result substantially is certain to occur, or such person has a firm belief that such circumstances exist or that such result is substantially certain to occur. That's the end of the quote.
When knowledge of existence of a particular fact is an element of the offense, such knowledge may be established when a person is aware of a high probability of its existence, and consciously and intentionally avoided confirming that fact. Knowledge may be proven in this manner if, but only if, the person suspects the fact, realized its high probability, but refrained from obtaining the final confirmation because he wanted to be able to deny knowledge.
On the other hand, knowledge is not established in this manner if the person merely failed to learn the fact through negligence or if the person actually believed that the transaction was legal.
"A conscious avoidance instruction permits a jury to find that a defendant had culpable knowledge of a fact when the evidence shows that the defendant intentionally avoided confirming the fact." United States v. Ferrarini, 219 F.3d 145, 154 (2d Cir.2000). The jury may be instructed on conscious avoidance only where "(1) the defendant asserts the lack of some specific aspect of knowledge required for conviction, and (2) the appropriate factual predicate for the charge exists, i.e., the evidence is such that a rational juror may reach the conclusion beyond a reasonable doubt that the defendant was aware of a high probability of the fact in dispute and consciously avoided confirming that fact." Id. (internal quotation marks, alterations and citation omitted). Without either of those factors, as we explained in Ferrarini:
[A] jury could be given a conscious avoidance instruction in a case where there was only equivocal evidence that the defendant had actual knowledge and where there was no evidence that the defendant deliberately avoided learning *133 the truth. Under those circumstances, a jury might conclude that no actual knowledge existed but might nonetheless convict, if it believed that the defendant had not tried hard enough to learn the truth.
Id. at 157.
Bourke first argues that the conscious avoidance charge lacks a factual predicate. We disagree. While the government's primary theory at trial was that he had actual knowledge of the bribery scheme, there is ample evidence to support a conviction based on the alternate theory of conscious avoidance. The testimony at trial demonstrated that Bourke was aware of how pervasive corruption was in Azerbaijan generally. Bourke knew of Kozeny's reputation as the "Pirate of Prague." Bourke created the American advisory companies to shield himself and other American investors from potential liability from payments made in violation of FCPA, and joined the boards of the American companies instead of joining the Oily Rock board. In so doing, Bourke enabled himself to participate in the investment without acquiring actual knowledge of Oily Rock's undertakings.
The strongest evidence demonstrating that Bourke willfully avoided learning whether corrupt payments were made came from tape recordings of a May 18, 1999 phone conference with Bourke, fellow investor Friedman and their attorneys, during which Bourke voiced concerns about whether Kozeny and company were paying bribes:
I mean, they're talking about doing a deal in Iran. . . . Maybe they . . . bribed them, . . . with . . . ten million bucks. I, I mean, I'm not saying that's what they're going to do, but suppose they do that.
Later in the conversation, Bourke remarks:
I don't know how you conduct business in Kazakhstan or Georgia or Iran, or Azerbaijan, and if they're bribing officials and that comes out . . . Let's say. . . one of the guys at Minaret says to you, Dick, you know, we know we're going to get this deal. We've taken care of this minister of finance, or this minister of this or that. What are you going to do with that information?
He goes on to say:
What happens if they break a law in . . . Kazakhstan, or they bribe somebody in Kazakhstan and we're at dinner and . . . one of the guys says, `Well, you know, we paid some guy ten million bucks to get this now.' I don't know, you know, if somebody says that to you, I'm not part of it . . . I didn't endorse it. But let's say [ ] they tell you that. You got knowledge of it. What do you do with that? . . . I'm just saying to you in general. . . do you think business is done at arm's length in this part of the world.
Finally, Bourke's attorney testified that he advised Bourke that if Bourke thought there might be bribes paid, Bourke could not just look the other way. Taken together, a rational juror could conclude that Bourke deliberately avoided confirming his suspicions that Kozeny and his cohorts may be paying bribes.
Of course, this same evidence may also be used to infer that Bourke actually knew about the crimes. See United States v. Svoboda, 347 F.3d 471, 480 (2d Cir. 2003). Relying on Ferrarini, 219 F.3d at 157, Bourke argues that the conscious avoidance charge was given in error because the government argued Bourke actually knew of the bribes. We disagree. In Svoboda, we held that:
the same evidence that will raise an inference that the defendant had actual knowledge of the illegal conduct ordinarily *134 will also raise the inference that the defendant was subjectively aware of a high probability of the existence of illegal conduct. Moreover, [conscious avoidance] may be established where, a defendant's involvement in the criminal offense may have been so overwhelmingly suspicious that the defendant's failure to question the suspicious circumstances establishes the defendant's purposeful contrivance to avoid guilty knowledge.
347 F.3d at 480 (citation, emphasis and internal quotation marks omitted); see also United States v. Carlo, 507 F.3d 799, 802 (2d Cir.2007) ("The conscious avoidance charge was appropriate because [defendant] asserted that he did not know that his statements were false and the government presented an adequate factual predicate for the charge."); United States v. Aina-Marshall, 336 F.3d 167, 171 (2d Cir.2003) (approving conscious avoidance charge where defendant "admitted possession of contraband but . . . denied knowledge of its nature," because "the defendant herself has directly put in issue whether the circumstances were such as to alert her to a high probability that the goods were contraband and what steps she took to learn of the extent of that danger").
It is not uncommon for a finding of conscious avoidance to be supported primarily by circumstantial evidence. Indeed, the very nature of conscious avoidance makes it unlikely that the record will contain directly incriminating statements. Just as it is rare to find direct record evidence of an employer stating, "I am not going to give you a raise because you are a woman," it is highly unlikely a defendant will provide direct record evidence of conscious avoidance by saying, "Stop! I think you are about to discuss a crime and I want to be able to deny I know anything about it!" Here, the evidence adduced by the government at trial suffices to support the giving of a conscience avoidance charge.
Finally, Bourke argues that the conscious avoidance charge improperly allowed the jury to convict him based on negligence, rather than based on evidence that he avoided learning the truth. As detailed above, the record contains ample evidence that Bourke had serious concerns about the legality of Kozeny's business practices and worked to avoid learning exactly what Kozeny was doing. Bourke also argues that the risk of the jury convicting on negligence was heightened here because the district court erroneously admitted the testimony of Wheeler and James Rossman, the attorney also conducting due diligence for Texas Pacific Group ("TPG"). At one time, TPG considered investing with Kozeny, but decided against it. Rossman and Wheeler testified regarding the due diligence they undertook on Oily Rock. Rossman testified that as part of his due diligence, he traveled to Switzerland to meet with Bodmer, and that Bodmer provided Rossman with documents related to the Oily Rock investment. Bodmer also discussed the involvement of the Azeri investors with Rossman. Based on his conversations with Bodmer, and his knowledge of Kozeny's reputation gleaned from news articles, Rossman advised TPG that Oily Rock "was a dumb investment," with "a significant risk because of the lack of information about the other shareholders, [and because] there could be a FCPA issue."
We find no grounds supporting the proposition that Wheeler and Rossman's testimony, coupled with the jury charge, allowed Bourke to be convicted based on negligence. The government offered the testimony to demonstrate that others with access to the same sources of information available to Bourke were able to figure out Kozeny's scheme and avoid participating. *135 It was entirely proper for the government to argue that Bourke refrained from asking his attorneys to undertake the same due diligence done by Rossman and Wheeler because Bourke was consciously avoiding learning about the bribes. This is distinguishable from United States v. Kaplan, 490 F.3d 110. Bourke relies on Kaplan for the proposition that a court abuses its discretion when it admits testimony about a third party's knowledge of fraud where "the Government failed to offer evidence that would explain how [the] defendant. . . would have obtained the third parties' knowledge of the criminal scheme." Id. at 121. Here, Bourke went to Azerbaijan on the same trip as Wheeler, and like Rossman had access to Bodmer. This is the type of explanation Kaplan contemplates. Id. ("Evidence of others' knowledge would have been highly relevant had it been supplemented by evidence supporting the conclusion that such knowledge was communicated to [the defendant], or that [the defendant] had been exposed to the same sources from which these others derived their knowledge of the fraud.").
Finally, the district court specifically charged the jury not to convict based on negligence. There is no reason to suspect that the jury ignored that instruction.

C. Insufficiency of the mens rea charge.
Bourke argues that the district court erred by failing to instruct the jury that it must find he acted "corruptly" and "willfully," because that is the mens rea necessary to sustain a conviction on a substantive FCPA offense. In giving the charge on conspiracy, the district court instructed the jury that:
[T]he government must prove beyond a reasonable doubt that the defendant knew that he was a member of an operation or a conspiracy that committed or was going to commit a crime, and that his action of joining such an operation or conspiracy was not due to carelessness, negligence or mistake.
Unlawful means simply contrary to the law. The defendant need not have known that he was breaking any particular law or any particular rule. He need only have been aware of the generally unlawful nature of his acts.
An act is done knowingly and willfully if it is done deliberately and voluntarily, that is, the defendant's act or acts must have been the product of his conscious objective, rather than the product of a mistake or accident or mere negligence or some other innocent reason.
Earlier, when charging on the conspiracy FCPA count, the district court instructed the jury as to the elements of a substantive FCPA offense:
The third element, corruptly and willfully: The third element of a violation of the FCPA is that the person intended to act corruptly and willfully. A person acts corruptly if he acts voluntarily and intentionally, with an improper motive of accomplishing either an unlawful result or a lawful result by some unlawful method or means. The term "corruptly" is intended to connote that the offer, payment, and promise was intended to influence an official to misuse his official position.
A person acts willfully if he acts deliberately and with the intent to do something that the law forbids, that is, with a bad purpose to disobey or disregard the law. The person need not be aware of the specific law and rule that his conduct may be violating, but he must act with the intent to do something that the law forbids.
The district court prefaced its instruction on the substantive elements with:

*136 The substantive offensethat is, the substantive offense of violating the FCPAhas seven elements, which I will define for you. You should note that the government need not prove each of the following elements in order to prove that the defendant engaged in a conspiracy to violate the FCPA. I am instructing you on the elements only that they will aid you in your determination as to whether the government has sustained its proof, burden of proof, with respect to this count.
We need not decide if Bourke properly preserved this issue for appellate review, because we find the charge proper under either a de novo or plain error standard. Bourke relies on United States v. Feola, 420 U.S. 671, 686, 95 S.Ct. 1255, 43 L.Ed.2d 541 (1975), for the proposition that "in order to sustain a judgment of conviction on a charge of conspiracy to violate a federal statute, the Government must prove at least the degree of criminal intent necessary for the substantive offense itself." Bourke maintains that Feola requires the government to prove at least the specific mens rea for the underlying substantive offense, and the district court erred in not so instructing the jury. In Feola, the Supreme Court considered whether, in order to convict for conspiracy to assault federal officers, the government had to prove that the defendants knew the victims were federal officers. Id. at 684, 95 S.Ct. 1255. The Supreme Court answered in the negative. Id. It went on to hold that "where a substantive offense embodies only a requirement of mens rea as to each of its elements, the general federal conspiracy statute requires no more." Id. at 692, 95 S.Ct. 1255.
Here, the district court instructed the jury to make the necessary findings. The district court instructed the jury that to convict, it must find that he knew of the conspiracy's object, and that Bourke intended for that object to be accomplished. The district court further instructed the jury that one possible object of the conspiracy was to violate FCPA, and to violate FCPA one must act "corruptly" and "willfully." Thus, the district court properly instructed the jury that it must find Bourke knowingly entered a conspiracy that had the object of corruptly and willfully bribing foreign officials and that Bourke intended to aid in achieving this object. Moreover, the jury charge that Bourke urged the district court to adopt would require the jury to find Bourke willfully and corruptly joined a conspiracy to willfully and corruptly bribe foreign government officialsan absurd result unsupported by law. We find no error.

D. Proposed good faith instructions.
"A defendant is entitled to a jury charge which reflects his defense." United States v. Doyle, 130 F.3d 523, 540 (2d Cir.1997). "A conviction will not be overturned for refusal to give a requested charge, however, unless that instruction is legally correct, represents a theory of defense with basis in the record that would lead to acquittal, and the theory is not effectively presented elsewhere in the charge." Id. (internal quotation marks omitted).
Bourke argues the district court erred in not giving the jury a separate good faith instruction with respect to FCPA and false statement counts. Even assuming arguendo that Bourke's proposed instruction was legally correct with an adequate basis in the record, his argument fails because the theory was effectively presented elsewhere in the charge. The district court instructed the jury that the government did not meet its burden if the defendant "merely failed to learn the fact through negligence or if the person *137 actually believed that the transaction was legal." It also charged that "the government must prove beyond a reasonable doubt that the defendant knew that he was a member of an operation or conspiracy that committed or was going to commit a crime, and that his action of joining such an operation or conspiracy was not due to carelessness, negligence or mistake." The jury was told that it "must first find that [Bourke] knowingly joined in the unlawful agreement or plan." The jurors were instructed that "knowingly" meant "deliberately and voluntarily," and could not be a "mistake or accident or mere negligence or some other innocent reason."
The instructions given here were strikingly similar to the ones given in Doyle. There, we found that:
The indictment charged, and the court instructed, that knowledge and willfulness concerning the ultimate destination of the equipment is an element of the offense that the Government was required to prove beyond a reasonable doubt. It was not error for the court to refuse to charge that the Government had the burden to prove bad faith, when it had already charged that the Government had to prove willfulness and that good faith was a defense to the willfulness element.
130 F.3d at 540-41. The failure to give a specific good faith charge does not require a reversal.

II. Evidentiary Rulings.
We review decisions to admit or exclude evidence for abuse of discretion. United States v. Massino, 546 F.3d 123, 128 (2d Cir.2008). In evaluating whether testimony should have been excluded based on Fed.R.Evid. 403, we have explained that:
Federal Rule of Evidence 403 provides for the exclusion of otherwise relevant evidence if its probative value is substantially outweighed by the danger of unfair prejudice. We uphold Rule 403 rulings unless the district court has abused its discretion. So long as the district court has conscientiously balanced the proffered evidence's probative value with the risk for prejudice, its conclusion will be disturbed only if it is arbitrary or irrational. In light of the deferential nature of our review, appellate courts reviewing a district court's evaluation of evidence under Federal Rule of Evidence 403 generally maximize its probative value and minimize its prejudicial effect.
Id. at 132 (citations, brackets, and internal quotation marks omitted).
Bourke challenges a number of the district court's evidentiary rulings, including the decision to admit testimony from Wheeler and Rossman. For the reasons discussed above, we find no abuse of discretion in admitting their testimony.

A. Proposed testimony of Bruce Dresner.
Bourke argues the district court abused its discretion in not permitting him to introduce the testimony of Bruce Dresner, vice president for investments at Columbia University. Columbia also invested in Oily Rock through Omega Advisors, a hedge fund. Dresner oversaw that investment. Bourke sought to admit the testimony to serve as a benchmark for the type of due diligence undertaken by others, and to demonstrate that others also asked questions about potential FCPA liability. The district court precluded Dresner's testimony as irrelevanta holding well within its discretion. Dresner invested in the hedge fund Omega Advisors, not directly in Oily Rock, which necessarily required different due diligence. Dresner did not travel to Azerbaijan, and did not *138 meet Kozeny, Farrell or Bodmer. Further, the fact that Dresner also asked questions about FCPA liability does not make Bourke's questions less indicative of guilt. As the district court aptly noted, the statements Bourke made regarding FCPA on the recorded call could only be evaluated in the context of that call.

B. Cross-examination of Farrell.
Bourke also challenges the district court's refusal of his request to cross-examine Farrell regarding certain matters discussed under seal. The seal was imposed to protect confidential investigations. For the reasons set forth by the district court at the May 21, 2009, conference, we find no abuse of discretion.

C. The Schmid memorandum.
At trial, the government was permitted to introduce a portion of a memorandum written for Bodmer by his associate, Rolf Schmid, that included an account of Bodmer's February 1998 conversation with Bourke about the corrupt scheme. Bodmer testified that while in Baku with Bourke, Bodmer told Bourke about the particulars of the corrupt arrangements, including that the Azeri government officials would receive two-thirds of the vouchers in an arrangement that would allow the Azeri officials to incur no risk. The defense called Bodmer's recollection of this conversation into question because Bodmer had trouble remembering exactly when the conversation took place. The government then sought to salvage Bodmer's testimony by having Schmid testify that Bodmer had told Schmid of his conversation with Bourke, and memorialized that conversation in a memo. The government sought to admit that portion of the memo referencing the conversation as a prior consistent statement of Schmid under Federal Rule of Evidence 801(d)(1)(B).
While he objected to its admission below, on appeal, Bourke does not argue that the portion of the memo introduced at trial was inadmissible. Instead, he argues the entire memo ought to have been admitted into evidence, under both the rule of completeness and as a prior inconsistent statement of Bodmer. We are skeptical that the portions of the memo introduced by the government at trial were admissible. However, any error in that regard was harmless. Further, we find no abuse of discretion in the district court's decision not to admit the entirety of the memo. The memo was prepared by Schmid in response to a request for information by lawyers suing Kozeny over the collapse of the privatization scheme. Schmid was charged with drafting the response. The admitted portion of the memo states:
Ricky Bourke asked Hans Bodmer about the legal structure of Oily Rock and its subsidiaries, the ownership of vouchers and options by the holding companies etc. Hans Bodmer remembers thatprobably at the beginning of 1998he left together with Ricky Bourke in Baku and went for a walk together with Ricky Bourke. During this walk he briefed Ricky Bourke in detail about the involvement of the Azeri Interests by way of the credit facility agreements, the 2/3:1/3 arrangement . . .
Bourke argues that while this portion of the memo seemingly supports Bodmer's trial testimony about the walk-talk, the redacted portion contradicts Bodmer's testimony. The redacted portion states in relevant part:
At the time [Bodmer's law firm] drafted the credit facility agreements it was our understanding that the credit facility agreements should be the basis for an arm's length transaction. If Viktor Kozeny *139 and/or the Azeri interests had other intentions [it] is unknown to us.
In another portion, the memo states:
Neither Hans Bodmer nor any one else [at the firm] has specific knowledge of corrupt payments. Whether there is such an agreement between Viktor Kozeny and Barat Nuriyev is not known to [the firm] and if such payments were in fact discussed Hans Bodmer did not attend such meetings.
Under the rule of completeness, "[w]hen a writing or recorded statement or part thereof is introduced by a party, an adverse party may require the introduction at the time of any other part or any other writing or recorded statement which ought in fairness to be considered contemporaneously with it." Fed.R.Evid. 106 [2010]. Omitted portions of the "statement must be placed in evidence if necessary to explain the admitted portion, to place the admitted portion in context, to avoid misleading the jury, or to ensure fair and impartial understanding of the admitted portion." United States v. Johnson, 507 F.3d 793, 796 (2d Cir.2007) (quotation marks omitted). "The completeness doctrine does not, however, require the admission of portions of a statement that are neither explanatory of nor relevant to the admitted passages." Id. (quotation marks omitted).
The district court did not abuse its discretion in declining to admit the entirety of the memo. Schmid testified that the parts of the memo discussing the legality of the transactions were based on his own understanding and opinions, and that he did not consult Bodmer in drafting the memorandum. Schmid's legal opinions were therefore irrelevant. Importantly, the memo was offered to corroborate Schmid's testimony that Bodmer had told him he discussed the two-thirds/one-third split with Bourke. The memo was offered as a prior consistent statement of Schmid, not of Bodmer. Thus, the rule of completeness does not require that the entire memo be admitted, because Schmid's legal analysis, recollection and understandings are not relevant.

III. Sufficiency of the Evidence.
Bourke challenges his conviction on the false statements count (Count III) on the ground that the verdict is not supported by sufficient evidence. A defendant challenging the sufficiency of the evidence bears a heavy burden, because the reviewing court is required to draw all permissible inferences in favor of the government and resolve all issues of credibility in favor of the jury verdict. United States v. Desena, 287 F.3d 170, 176-77 (2d Cir.2002). We must affirm the conviction if "any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979) (emphasis omitted). While circumstantial evidence may support a conviction, the conviction cannot "rest on mere speculation or conjecture." United States v. Pinckney, 85 F.3d 4, 7 (2d Cir. 1996).
Count Three charges that Bourke falsely stated during four proffer statements with the FBI that he was unaware that Kozeny made corrupt payments, transfers and gifts to the Azeri officials. The FBI agent who interviewed Bourke testified that when Bourke was asked if he learned of any personal favors or gifts between Kozeny and the Azeri officials Bourke replied, "I was unaware. I'm still unaware of any transfers of anything." When asked if he had any reason to believe Kozeny had paid bribes or made corrupt payments, Bourke said, "No." The government adduced statements from Bodmer and Farrell that contradicted Bourke's statements to the FBI. Specifically, Bodmer *140 testified that Bourke had approached him in February 1998 about an "arrangement" with the Azeri officials, and that Bodmer had then explained to Bourke how the Azeri officials were to receive a two-thirds share of the vouchers without assuming any risk, and without payment.
Bodmer's testimony regarding the timing of his conversation with Bourke in Baku was the subject of extensive cross-examination. Documentary evidence demonstrated that at least one of the conversations with Bourke that Bodmer testified to could not have taken place on the date Bodmer believed it did, and the government so stipulated. While Bodmer's testimony regarding the date of the conversation was questioned by the defense, that does not mean a reasonable juror could not conclude that the conversation took place on a different date. Indeed, both Bodmer and Farrell testified regarding conversations with Bourke by April 1998 about payments to the Azeri government officials, and both were extensively cross-examined on the issue. Bourke argues that the only reasonable inference from Bodmer and Farrell's failure to accurately identify the date the conversations took place is that the conversations never took place. However, drawing all inferences in favor of the government, as we must, a reasonable juror could have concluded that the conversations took place and that the witnesses simply got the dates wrong. Thus, there is sufficient evidence to sustain the conviction on Count Three.

CONCLUSION
We have examined the remainder of Bourke's arguments and we find them to be without merit. For the reasons given above, we affirm his conviction.
NOTES
[1]  The Clerk of the Court is directed to amend the official caption as shown.
[2]  The Honorable Joseph F. Bianco, United States District Court for the Eastern District of New York, sitting by designation, took no part in the consideration of this matter. The two remaining members of the panel, who are in agreement, have determined this matter. See 28 U.S.C. § 46(d); 2d Cir. Internal Operating Procedure E(b); United States v. Desimone, 140 F.3d 457, 458-59 (2d Cir. 1998).
