This appeal arises from a six-week trial in which the Government charged that Enron and Merrill Lynch employees engaged in a conspiracy and scheme to defraud Enron and its shareholders by “parking” an Enron asset — an equity interest in three power-generating barges moored off the coast of Nigeria — with Merrill for six months for the purpose of artificially enhancing Enron’s 1999 end-of-year earnings report. Merrill agreed to invest $7 million to purchase equity in the barges so that Enron could record $12 million in earnings and meet its forecasts. The Government contended, however, that the sale was a sham because Enron executives orally promised Merrill a flat fee of $250,000 and a guaranteed 15% annual rate of return over the six-month period of Merrill’s investment; Enron executives allegedly promised that Enron or an affiliate would buyback Merrill’s interest in the barges if no third party could be found. Such a buyback agreement, the Government contended, rendered Merrill’s interest in the barges risk-free, meaning that Enron’s accounting of the deal as a sale rather than a lease was false. The jury agreed and convicted the appellants of conspiracy and wire fraud. Additionally, appellant Brown was convicted of perjury and obstruction of justice. For the reasons stated below, we reverse the conspiracy and wire-fraud convictions of each of the Defendants on the legal ground that the government’s theory of fraud relating to the deprivation of honest services — one of three theories of fraud charged in the Indictment — is flawed. We further vacate appellant Fuhs’s conviction on the ground that the evidence is insufficient to support his conviction. Finally, we affirm appellant Brown’s convictions of perjury and obstruction of justice.
I
The trial below involved six Defendants. Sheila Kahanek, an accountant by training and a Senior Director in Enron’s Asia/Pacific/Africa/China (“APACHI”) energy division, was acquitted of all charges against her. Daniel Boyle, an Enron Vice President of Global Finance, was convicted on all counts against him and does not appeal. The following four Merrill Lynch executives (the “Defendants”) were convicted on *514all counts against them and appear before us on appeal: Jim Brown, the head of Merrill’s Strategic Asset and Lease Finance Group in New York City; William Fuhs, a Vice President under Brown in the New York office; Daniel Bayly, the head of Merrill’s Global Investment Banking division; and Robert Furst, a Merrill executive answering directly to Bayly, responsible for generating business from Enron.
A
The Nigerian barges at the heart of this case were held by Enron’s APACHI energy division. At the close of 1999, APACHI was pressured to monetize or sell assets in order to show a gain and meet earnings targets that, in turn, would allow Enron as a whole to meet the company’s forecasted earnings for the final quarter of 1999. Various attempts at selling APACHI’s primary asset, the barges, to an industry buyer were made in the final months of 1999, but each prospective deal collapsed. In early December 1999, Enron executives discussed the need for an “emergency alternative.” When executives were informed that the barges would not be sold by year’s end, they responded that a “friend of Enron,” Merrill Lynch, might be able to buy the barges and “help Enron out.”
In late December, Enron approached Merrill about buying the barges. Boyle discussed the deal with Furst, Merrill’s Enron relationship manager. Furst communicated with others at Merrill, including Bayly, Brown, and Schuyler Tilney, the head of banking in Merrill’s Houston office. Furst explained that Enron’s then-Treasurer, Jeff McMahon, “asked Merrill to purchase $7 [million] of equity in a special purpose vehicle that will allow Enron to book $10 [million] of earnings. The transaction must close by 12/31/99. Enron is viewing this transaction as a bridge to permanent equity and they believe [Merrill’s] hold will be for less than six months. The investment would have a 22.5% return.” Furst emphasized the importance of fostering an ongoing business relationship with Enron and that the deal offered Merrill a chance to differentiate itself from other investment banks. When Furst explained the deal to Katherine Zrike, chief counsel for Merrill’s Global Investment Banking, Zrike noted her concern due to the year-end nature of the deal, its unique quality, and a lack of due diligence.1
Furst and Brown communicated by fax regarding the deal, and Brown noted his concerns: “Enron credit/performance risk,” a lack of “repurchase oblig. from Enron,” and the “reputational risk” of “aid[ing]/abet[ting] Enron income stmt, manipulation.” Brown also communicated his concerns to Fuhs, who in turn communicated the risks, including the risk of aiding Em-on with “income manipulation,” to Tina Trinkle, an analyst. Due to these concerns, the short timeline, and a lack of information about the deal, some Merrill employees, including Trinkle, thought the deal would not go through.
According to the Government, the barge deal proceeded because Enron agreed that either it or an affiliate would repurchase the barges from Merrill if a third-party buyer could not be found and that Enron would pay a fixed rate of return for the duration of Merrill’s hold of the interest in the barges. Ben Glisan, a colleague of *515Boyle’s and a Government witness, testified that multiple sources informed him of Enron’s oral guarantee that Merrill would be taken out of the transaction within six months for a set return on the investment.
On December 22, Bayly, Brown, Furst and others (excluding Fuhs and any lawyers) participated in a conference call about the deal (the “Trinkle call”). Furst and Tilney explained that Enron needed to sell the barges by year-end in order to book additional earnings in 1999 and that someone at Enron indicated that Enron would agree to take Merrill out at a fixed rate of return. Bayly asked for a written assurance to support Enron’s promise, and someone responded that a writing was not possible because such an assurance would prevent Enron from receiving the accounting treatment it sought with the deal. But either Furst or Tilney responded that Enron had given its strongest verbal assurances that Merrill would not own the barges after June 30. That same day, Brown and Fuhs received an e-mail from Furst’s office in Dallas, describing some of the material terms of the deal including that Bayly would confirm Enron’s promise with senior Enron management. In a later meeting with Furst that day, Zrike warned that for Enron to show the sale as a profit on its books, Merrill would have to own the barges outright without any buyback agreement. Furst stated that the agreement contemplated only Enron’s attempt to remarket the barges. Zrike restated her concerns in afternoon meetings with Bayly on December 22, where the Government alleges Bayly had a duty, under Merrill’s policy, to disclose his awareness of Enron’s buyback promise to Zrike but failed to do so. At the end of the day on December 22, Furst e-mailed Boyle to announce the conference call between Bayly and Enron management — Andrew Fas-tow, McMahon, and Boyle — for 9:30 the next morning.
According to Government witness Eric Boyt, an accountant for APACHI, both Fastow and Boyle said that during the conference call, Fastow promised that Merrill would not own the barges for longer than six months and that if Enron could not facilitate a buyer, it would “guarantee a 15 percent buyback within six months.” In this vein, Boyle authored an e-mail explaining the transaction as follows: “[Merrill’s] decision to purchase the equity was based solely on personal assurances by Enron senior management to [Merrill] that the transaction would not go beyond June 30, 2000.” Although Brown was not on the December 23 conference call,.the Government alleges that he understood Fastow’s promise on Enron’s behalf; this allegation is supported by Brown’s later e-mail of March 2001, describing a similar, prospective deal: “I would support an unsecured deal provided we had total verbal assurances from [the company’s C.E.O. or C.F.O.].... We had a similar precedent with Enron last year, and we had Fastow get on the phone with Bayly and lawyers and promise to pay us back no matter what. Deal was approved and all went well.”
Following this call, the initial draft of the “engagement letter” for the deal, including reference to Enron’s oral buyback promise, was circulated. On December 28, Boyle sent out a revised version of the engagement letter, with “strike-through” indicating proposed removal of the language about the annual rate of return and that Merrill’s interest would be subsequently sold or repurchased by Enron or an Enron affiliate. Another draft, with the oral promises redacted entirely, was circulated shortly thereafter and signed by Brown and Fastow.
At the end of 1999, Enron recorded the barge deal and booked from it $12,563,000 *516in earnings. The Government argues this booking was a false entry because Merrill’s investment was never at risk in the light of the guaranteed buyback, advisory fee, and fixed rate of return. These oral but material terms, according to the Government’s witnesses, required that the deal be booked as a loan rather than as a sale.
The Government further asserted that the parties’ conduct, between the end of 1999 and June 2000, was consistent with Enron’s oral promise to buy back the parked barges from Merrill: Enron wired a $250,000 “advisory fee” to a Merrill account at Citibank even though Brown testified that Merrill did not provide advisory services; Merrill did not monitor Enron’s attempts to remarket the barges during the interim period; efforts to remarket the barges on APACHI’s behalf were motivated by a desire to preclude Enron from having to repurchase them from Merrill; Enron contacted Furst seeking an extension of the deadline; and Merrill drafted for Furst’s signature a letter to Enron demanding that Enron purchase the barges by June 30 for $7,510,976.65, a number that was consistent with the terms of the oral guarantee. Before the letter left Merrill, however, Fuhs contacted Furst and told him that Enron had lined up a buyer, an entity called LJM2.2 LJM2 served as a temporary warehouse for Enron assets, according to Glisan’s testimony, and was not wholly independent from Enron.
Merrill and LJM2 closed the deal for the resale on June 29, 2000, when LJM2 paid Merrill $7,525,000 for its interest in the barges.3 That figure represented exactly six-months’ return at a rate of 15% annually. Including the $250,000 “advisory fee” received at the end of 1999, Merrill made $775,000 on its investment in the barges. At the close of the deal, Fuhs e-mailed Brown and Furst to inform them that the money had been paid to Merrill and referred to the fact that Brown and Furst (along with Bayly) were investors in LJM2 and as such still bore an interest in the barges.
B
The Government charged all six Defendants with one count of conspiracy and two counts of wire fraud. The conspiracy count alleged a conspiracy under 18 U.S.C. § 371 to commit wire fraud in violation of § 1343 (the “money or property” charge) and § 1346 (the “honest services” charge), and to falsify Enron’s books and records in violation of 15 U.S.C. § 78m(b)(2), (b)(5) and 78ff, and 17 C.F.R. § 240.13b2-1 (the “books and records” charge). The substantive wire fraud counts were based upon two interstate transmissions between Houston and New York. The Government also charged Brown with perjury before a Grand Jury in violation of 18 U.S.C. §§ 1623 and 3551, and with obstruction of a Grand Jury investigation in violation of 18 U.S.C. §§ 1503 and 3551.
*517The six Defendants were tried together by jury over six weeks. At the close of the Government’s case in chief, each Defendant moved for a judgment of acquittal under Rule 29(a), claiming that the Government’s evidence was insufficient to sustain a conviction on any count of the Indictment. The district court reserved ruling on the motions under Rule 29(b). Boyle and the appealing Defendants were convicted of the conspiracy and wire fraud counts; Kahanek was acquitted. Brown was additionally convicted on the perjury and obstruction counts. The Defendants renewed their motions for acquittal, and the court denied the motions in the light of “substantial evidence justifying an inference of guilt with respect to each.” Brown was sentenced to 46 months’ imprisonment; Bayly was sentenced to 30 months’ imprisonment; and Furst and Fuhs were each sentenced to 37 months’ imprisonment.
II
The Defendants raise numerous issues on appeal. The Defendants’ broadest attack on their convictions suggests that, even if the Government proved all the allegations in the Indictment, the alleged scheme would not run afoul of the wire fraud statutes — there was no deprivation of Enron’s intangible right to the honest services of its employees, and there was no scheme to defraud Enron and its shareholders of money or property. The Defendants also claim that the crime of conspiracy does not apply to the falsification of a corporation’s books and records because of explicit statutory language to that effect. 15 U.S.C § 78m(b)(2), (b)(5) and 78ff. The Defendants raise numerous further claims regarding 1) jury instructions on the theory of the defense, good faith, and the materiality requirement of the books-and-records charge; 2) evidentiary and related rulings, most notably, admission into evidence of an inculpatory e-mail by Brown, allowance of testimony as to Furst’s belief that the barge deal included an Enron guarantee, exclusion of an expert witness on accounting standards, failure of the court to order disclosure of allegedly exculpatory evidence in the form of details of Fastow’s interview with the FBI, and exclusion of impeachment evidence in the form of contradictory statements by Fas-tow; 3) the denial of their individual motions for acquittal and the sufficiency of the evidence supporting their convictions; and 4) the calculation of their sentences. Brown additionally appeals the legal and factual sufficiency of the evidence supporting his convictions for perjury and obstruction of justice, and Fuhs additionally alleges prosecutorial misconduct in the form of a repudiation of a stipulation pertaining only to him.
Because we hold that the honest-services theory of wire fraud does not extend to the circumstances as contended by the Government, we vacate the conspiracy and wire-fraud convictions. We therefore do not reach the remaining issues, with the exception of the denial of the Defendants’ motions for acquittal, which we reverse only as to Fuhs, and Brown’s appeal of his separate perjury and obstruction convictions, which we affirm.
III
A
We begin with the Defendants’ broad attack on the legal sufficiency of the Government’s assertion of criminal liability. We review the legal sufficiency of an Indictment de novo. United States v. Caldwell, 302 F.3d 399, 407 (5th Cir.2002).4
*518The Indictment charged the Defendants with one count of conspiracy and two substantive counts of wire fraud. The conspiracy count alleged a conspiracy to violate two different statutes. The first statute is the wire-fraud statute, 18 U.S.C. § 1343, which reads:
Whoever, having devised or intending to devise any scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises, transmits or causes to be transmitted by means of wire, radio, or television communication in interstate or foreign commerce, any writings, signs, signals, pictures, or sounds for the purpose of executing such scheme or artifice, shall be fined under this title or imprisoned not more than 20 years, or both. If the violation affects a financial institution, such person shall be fined not more than $1,000,000 or imprisoned not more than 30 years, or both.
Following the Supreme Court’s decision in McNally v. United States, 483 U.S. 350, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987), that § 1343 only protects “money or property” and not an employer’s or the public’s right to the honest services of employees and public officials, Congress added § 1346, which reads:
For the purposes of this chapter, the term “scheme or artifice to defraud” includes a scheme or artifice to deprive another of the intangible right of honest services.
Thus, the conspiracy count recited two objects of the alleged conspiracy to commit wire fraud, namely, the fraudulent deprivation of Enron’s intangible right to the honest services of its employees, and the fraudulent deprivation of Enron’s money or property. The second criminal statute is 15 U.S.C. § 78ff, which punishes
[a]ny person who willfully violates any provision of this chapter (other than section 78dd-1 of this title), or any rule or regulation thereunder the violation of which is made unlawful or the observance of which is required under the terms of this chapter, or any person who willfully and knowingly makes, or causes to be made, any statement in any application, report, or document required to be filed under this chapter or any rule or regulation thereunder....
Thus, the conspiracy count alleged violation of the requirements set forth in 15 U.S.C. § 78m(b)(2),(5) and 17 C.F.R. § 240.13b2-1.5
Because the jury was not asked to indicate the basis for its verdict, the Government must prove all three theories in order for us to affirm the convictions. Yates v. United States, 354 U.S. 298, 77 S.Ct. 1064, 1 L.Ed.2d 1356 (1957). The Defendants argue that the Government has proved none of the three theories it alleges in the Indictment.
B
Wire fraud is (1) the formation of a scheme or artifice to defraud, and (2) use of the wires in furtherance of the scheme. See Pereira v. United States, 347 U.S. 1, 8, 74 S.Ct. 358, 98 L.Ed. 435 (1954); United *519States v. Caldwell, 302 F.3d 399, 406 (5th Cir.2002). Violation of the wire-fraud statute requires the specific intent to defraud, i.e., a “conscious knowing intent to defraud,” United States v. Reyes, 239 F.3d 722, 736 (5th Cir.2001); however, specific intent to defraud need not be charged in the Indictment.
Honest-services wire fraud is wire fraud in which the scheme or artifice to defraud “deprive[s] another of the intangible right of honest services.” 18 U.S.C. § 1346. This provision can be understood only in the light of the long history of the mail- and wire-fraud statutes, which were intentionally written broadly to protect the mail and, later, the wires from being used to initiate fraudulent schemes. See McNally, 483 U.S. at 356, 107 S.Ct. 2875. Over time, the lower courts came to construe the fraud statutes to protect not just money and property but also intangible rights such as the right to privacy,6 and the right to honest services of employees and public officials. In McNally, however, the Supreme Court excised the protection of intangible rights from the scope of §§ 1341 and 1343, holding that the statutes as written protected only money and property. The Court explained that the 1909 amendment adding “or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises” was meant to confirm that liability covered not just fraudulent misstatements about existing facts but also fraudulent promises and representations about the future. Congress’s use of the disjunctive in specifying “obtaining money or property” as an object of the fraud was not meant to expand the criminal statute beyond the protection of money and property. Id. at 358-60, 107 S.Ct. 2875. Congress responded by passing § 1346, which reads in its entirety, “A ‘scheme or artifice to defraud’ includes a scheme or artifice to deprive another of the intangible right of honest services.” 18 U.S.C. § 1346. As we and other courts have held, § 1346 was clearly meant specifically to overturn McNally, at least with respect to the particular intangible right named in the statute, i.e., the right to honest services. See United States v. Brumley, 116 F.3d 728, 733 (5th Cir.1997) (en banc); United States v. Rybicki 354 F.3d 124, 134, 136-37 (2d Cir.2003). Thus, the meaning of honest services — given that the statute provides no perimeters — is to be found in the pre-McNally case law. Brumley, 116 F.3d at 733; Rybicki, 354 F.3d at 136-37.
We have previously undertaken the task of considering the pre-McNally case law. Thus, we have written, “ ‘Honest services’ are services owed to an employer under state law,” including fiduciary duties defined by the employer-employee relationship. Caldwell, 302 F.3d at 409; Brumley, 116 F.3d at 734. In order that not every breach of fiduciary duty owed by an employee to an employer constitute an illegal fraud, we have required some detriment to the employer. United States v. Ballard, 663 F.2d 534, 540 (5th Cir.1981). Ballard, however, implies that breach of the duty to disclose material information is a sufficient detriment to the employer because the materiality requirement, added to the false disclosure or nondisclosure of information, contemplates that the undisclosed information would have led a reasonable employer to change its business conduct. Id. at 541; see also Rybicki, 354 F.3d at 145.7 Here, the Government al*520leged not only the harm inherent in the failure to disclose material information— that the barge transaction presented no risk to Merrill because of the oral side deal — but also concrete harms to Enron in the form of fees paid to Merrill to effect the deal and compensation bonuses paid to Enron employees that depended on the completion of the barge deal.
The Seventh Circuit has additionally held that honest-services fraud requires some personal benefit accruing to the duty-breaching employee. United States v. Bloom, 149 F.3d 649 (7th Cir.1998). Here, those same bonuses would likely constitute such a personal benefit accruing to the Enron employees taking part in the alleged scheme.
Thus, the Government presents a very plausible, even strong, case for a criminal deprivation of honest services, alleging a fiduciary breach — the failure to disclose the full truth about the barge transaction — that resulted in both a personal benefit (increased bonus) to the duty-breaching Enron employees and detriments (but also benefits) to the corporation itself.8
Nevertheless, the Defendants put forth an equally plausible argument that the limiting statements we have expressed in our past cases do not demarcate the exact outer-most boundaries of honest services. Instead, those limiting statements represent only minimal distinctions we have had occasion to declare, and thus they do not exhaust the constraints that are appropriate to recognize. Thus, for example, we noted in Brumley that “the boundaries of ‘intangible rights’ may be difficult to discern, but that does not mean that it is difficult to determine whether Brumley in particular violated them.” Brumley, 116 F.3d at 733. If we are not to lapse into defining a common law crime, the outer boundary of this facially vague criminal statute must be determined from the factual circumstances supporting affirmed convictions, not by negative implication from the few constraints mentioned in disparate cases.9 In essence, the Defendants argue that between the core of cases affirming honest-services fraud convictions and the shell of cases reversing them, there is a gap, a lacuna, a vacuum, a no-man’s land, a demilitarized zone, in which this case awkwardly sits alone.
Appraising this argument requires a study of the case law to understand what behavior justifies criminal liability. We begin by noting that the Government urges the broadest reading by relying on the barest reiteration of the few constraints we have previously acknowledged, even going so far as to argue that no detriment aside from the fiduciary breach *521itself is necessary because “it is sufficient for the government to show that the defendants violated a duty imposed by state law____ The plain text of Section 1346 ... does not require any detriment ... beyond proof that the scheme or artifice to defraud 'deprive[d] another of the intangible right of honest services.’ ” Given our repeated admonition that “not every breach of fiduciary duty works a criminal fraud,” see Ballard, 663 F.2d at 540 (quoting United States v. George, 477 F.2d 508, 512 (7th Cir.1973)), we consider such a broad theory of liability with caution.10
Turning to the case law, we are guided by the leading opinion on honest-services fraud, the Second Circuit en banc decision in Rybicki, supra. Rybicki concluded, and we agree, that cases upholding convictions arguably falling under the honest services rubric can be generally categorized in terms of either bribery and kickbacks or self-dealing. The great weight of cases are clear examples of such behavior.11 The Second Circuit formulated the following rule based on its analysis:
[A] scheme or artifice to deprive another of the intangible right to honest services in section 1346, when applied to private actors, means a scheme or artifice ... to enable an officer or employee of a private entity ... purporting to act for and in the interests of his or her employer ... secretly to act in his or her or the defendant’s own interests instead ....
Rybicki, 354 F.3d at 141-42.12 Our circuit’s analysis has not been much different from Rybicki’s, although perhaps we have couched our language more broadly in terms of an understood divergence, rather than a secret conflict, of interests. Thus, in Brumley, although we recognized that bribery and self-dealing are the paradigmatic cases of honest-services fraud, we wrote:
“honest services fraud” contemplates that in rendering some particular service or services, the defendant was conscious of the fact that his actions were something less than in the best interests of the employer — or that he consciously contemplated or intended such actions. For example, something close to bribery.
Brumley, 116 F.3d at 734.
While it may be argued that the Defendants here were conscious of the fact *522that their actions were “something less than in the best interests of the employer,” at least long term, that argument relies on the presumption, inherent in the Government’s insistent argument, that a fiduciary breach is itself a sufficient reflection of interest divergence. But that view encompasses every knowing fiduciary breach, and we meet again our oft-mentioned chariness of making every knowing fiduciary breach a federal crime. What makes this case exceptional is that, in typical bribery and self-dealing cases, there is usually no question that the defendant understood the benefit to him resulting from his misconduct to be at odds with the employer’s expectations. This case, in which Enron employees breached a fiduciary duty in pursuit of what they understood to be a corporate goal, presents a situation in which the dishonest conduct is disassociated from bribery or self-dealing and indeed associated with and concomitant to the employer’s own immediate interest.
Here, the private and personal benefit, i.e. increased personal bonuses, that allegedly diverged from the corporate interest was itself a promise of the corporation. According to the Government, Enron itself created an incentive structure tying employee compensation to the attainment of corporate earnings targets. In other words, this case presents a situation in which the employer itself created among its employees an understanding of its interest that, however benighted that understanding, was thought to be furthered by a scheme involving a fiduciary breach; in essence, all were driven by the concern that Enron would suffer absent the scheme. Given that the only personal benefit or incentive originated with Enron itself — not from a third party as in the case of bribery or kickbacks, nor from one’s own business affairs outside the fiduciary relationship as in the case of self-dealing— Enron’s legitimate interests were not so clearly distinguishable from the corporate goals communicated to the Defendants (via their compensation incentives) that the Defendants should have recognized, based on the nature of our past case law, that the “employee services” taken to achieve those corporate goals constituted a criminal breach of duty to Enron. We therefore conclude that the scheme as alleged falls outside the scope of honest-services fraud.
We do not presume that it is in a corporation’s legitimate interests ever to misstate earnings — it is not. However, where an employer intentionally aligns the interests of the employee with a specified corporate goal, where the employee perceives his pursuit of that goal as mutually benefitting him and his employer, and where the employee’s conduct is consistent with that perception of the mutual interest, such conduct is beyond the reach of the honest-services theory of fraud as it has hitherto been applied.13 Therefore, the *523Government must turn to other statutes, or even the wire fraud statutes absent the component of honest services, to punish this character of wrongdoing.
This opinion should not be read to suggest that no dishonest, fraudulent, wrongful, or criminal act has occurred. We hold only that the alleged conduct is not a federal crime under the honest-services theory of fraud specifically. Given our repeated exhortation against expanding federal criminal jurisdiction beyond specific federal statutes to the defining of common-law crimes, we resist the incremental expansion of a statute that is vague and amorphous on its face and depends for its constitutionality on the clarity divined from a jumble of disparate cases. Instead, we apply the rule of lenity and opt for the narrower, reasonable interpretation that here excludes the Defendants’ conduct. See McNally, 483 U.S. at 360, 107 S.Ct. 2875.
In sum, the convictions of each of the Defendants for conspiracy and wire fraud cannot be upheld on the basis of the honest-services theory and must be vacated per Yates, supra. We therefore need not address the viability of the Government’s remaining theories of criminal liability (the money-or-property and books-and-records charges). Nor need we speak to the procedural errors alleged by the Defendants. Instead, we turn to two remaining issues; the Defendants’ motions for acquittal and Brown’s conviction for perjury and obstruction of justice.
IV
A
We first consider the District Court’s denial of Fuhs’s Motion for Judgment of Acquittal, which Fuhs submitted at the close of the Government’s case-in-chief. Fuhs contends that the evidence in the Government’s case-in-chief is insufficient to support a conviction.
Review for sufficiency where, as here, the motion was renewed at the close of the evidence is de novo, meaning that “ ‘we determine whether ... a rational jury could have found the essential elements of the offense beyond a reasonable doubt.’ United States v. Dean, 59 F.3d 1479, 1484 (5th Cir.1995).” United States v. Alarcon, 261 F.3d 416, 421 (5th Cir.2001). As Fuhs notes, because the District Court reserved ruling on the motion, appellate review is limited to the evidence presented in the Government’s case-in-chief. United States v. Rhodes, 631 F.2d 43, 44-45 (5th Cir.1980). Thus, we ought not consider the Government’s rebuttal ev*524idence alleging that Fuhs lied on the witness stand and that he may have edited, or even authored, a key document — the Appropriation Request (Govt. Exhibit 850.1) — in the prosecution’s case against all the Defendants.
The Government’s case-in-chief against Fuhs consisted entirely of documents and e-mails, plus excerpts from Fuhs’s statements before the SEC from 2002. The Government admits that none of its witnesses testified about Fuhs’s knowing participation in the alleged scheme and that Fuhs was absent from the critical calls and meetings that allegedly put the Merrill Defendants on notice of Enron’s intention to account improperly for the barge transaction. Thus, the Government relies solely on the documentary evidence to assert Fuhs’s knowledge of the oral buyback promise and his intent to participate in the scheme to conceal that promise for the purpose of effecting a misaccounting of the overall deal.
We find that the documentary evidence fails to sustain the Government’s burden of proof beyond a reasonable doubt. Much of the Government’s evidence consists of emails or memos not written or initiated by Fuhs, not directly addressed to him, and in some cases not even copied to him. They neither recognize a secret oral side deal nor imply that the addressees of the correspondence knew of such a secret deal. While they may support the assertion that Fuhs knew Merrill wanted a buyback agreement to protect its investment, and that it was at one point understood to be part of the deal by Fuhs’s subordinate Geoffrey Wilson, the principal documents relied upon by the Government simply do not sustain the inference that Fuhs had knowledge of an oral guarantee that was to be kept out of the written agreement and kept secret in (because it conflicted with) the accounting of the deal.
Fuhs’s list of transactional risks was only a transcription of Brown’s list to be passed along to analysts and executives. It reveals nothing regarding Fuhs’s understanding of Enron’s intent to misrepresent the transaction. The list does not reveal the existence of a secret buyback promise or an intent to defraud; in fact, the absence of a promise securing Merrill’s investment is noted. Brown’s suggestion, passed on by Fuhs, that Merrill might face reputational risk for aiding income manipulation does not imply the specific understanding that such income manipulation was to be effected by deception and fraudulent accounting. The Government’s claim that “Fuhs would soon find out, if Brown had not already told him, that Enron was ‘selling’ the barges only so that it could book $12 million in earnings by the end of 1999,” is neither here nor there — selling an asset quickly to book earnings by a certain date is not, by itself, fraudulent.
The Government, however, asserts that certain other documents, especially a series of revisions of the engagement letter representing the transaction, show Fuhs’s knowledge of an intent to further a fraudulent accounting of the deal. The Government’s inferences are deficient for two reasons. First, the revisions of the engagement letter and other pre-deal memos received by Fuhs suggest no more than an understanding that a buyback agreement was desired by Merrill and was at some point, but not ultimately, a part of the proposed deal. It is an unacceptable stretch to conclude from these documents that Fuhs had knowledge that the transaction ultimately included an oral promise to be kept secret from the lawyers and accountants in order to effect a fraudulent accounting. The fact that Fuhs forwarded to Merrill lawyers a black-lined version of the edited engagement letter in which mention of a buy*525back was redacted is only damning to Fuhs if one assumes he was aware that the buyback guarantee remained part of the deal. But the documents do not establish, nor does any other evidence establish, that Fuhs knew the buyback obligation survived the redaction such that the absence of references would suggest concealment. The Government cannot simply assume the linchpin of its case against Fuhs; yet it repeatedly frames documents as inculpatory by presuming that Fuhs knew of the oral promise and concluding that he willfully concealed the promise in furtherance of the deception. Second, whatever understanding these documents do reveal, such understanding is principally that of the primary communicants of the correspondence, namely, Wilson, Furst, and Boyle. The fact that Fuhs is copied on a stream of e-mails documenting the transaction is far from sufficient to support inferences that he knew of the details of an oral side agreement that survived the removal of written references to it.
The Government also produced evidence stemming from six months after the initial transaction, when Merrill was getting rid of its purported equity interest. Fuhs wrote that he had spoken to Boyle and that Enron had lined up a new buyer to purchase Merrill’s interest “for the agreed upon amount outlined in the previously forwarded memo.” This e-mail fails to prove anything other than that Fuhs became aware of Enron’s procurement of a third-party buyer to take Merrill out of its purported equity interest. Even when taken together with the remainder of the evidence against Fuhs, the e-mail demonstrates neither the knowledge of a secret repurchase obligation owed by Enron nor the specific intent to defraud by the concealment of that obligation. Nor does Fuhs’s jocose reply, “only if i can guarantee a make-whole at par + return in case of civil unrest/war,” to Brown’s query, “wanna buy a barge?”, after Merrill had sold its stake but Brown was still exposed because of his involvement in LJM2, add much evidence of the requisite knowledge and the specific intent of Fuhs to defraud in the purchase of the barge six months earlier.
As counsel for Fuhs noted at oral argument, if we begin with the assumption that Fuhs is guilty, the documents can be read to support that assumption. But if we begin with the proper presumption that Fuhs is not guilty until proven guilty beyond a reasonable doubt, we must conclude that the evidence is insufficient to prove beyond a reasonable doubt that Fuhs had the knowledge and intent to enter into the fraudulent scheme alleged by the Government.
Ultimately, we do not have to conclude that Fuhs was an innocent in the deal to relieve Enron of the barges. We only conclude that at the close of its case, the Government had failed to support its charges against Fuhs with sufficient evidence of guilty knowledge, as charged in the Indictment, to survive his motion for judgment of acquittal.
B
Regarding the other Defendants’ motions for acquittal, we have reviewed the record and are satisfied that the Government’s evidence was not so patently deficient that a judgment of acquittal was required as a matter of law.
V
We turn finally to Brown’s convictions for perjury and obstruction of justice. These charges stem from testimony Brown gave to the grand jury investigating the barge transaction in the fall of 2002. The Government charged that Brown’s testi*526mony concerning the agreement between Enron and Merrill was perjurious and ultimately constituted obstruction of justice. The jury agreed and convicted Brown under 18 U.S.C. § 1623 of one count of perjury, and under 18 U.S.C. § 1503 of one count of obstruction of justice. We affirm these convictions.
A
18 U.S.C. § 1623 defines perjury as “knowingly mak[ing] a false material declaration” to a grand jury. The Government charged Brown with one count of perjury, contending that Brown knew or understood that Enron promised to remove Merrill from the barge deal by June 30, and that Brown perjuriously denied under oath any such knowledge or understanding.14 The Indictment quotes the following testimony by Brown as constituting perjury (the underlining is in the original and indicates the portions alleged to be false):15
*527Q: Do you have any understanding of why Enron would believe it was obligated to Merrill to get them out of the deal on or before June 30th?
A: It’s inconsistent with my understanding of what the transaction tvas.
Q: ... Again, do you have any information as to a promise to Merrill that it would be taken out by sale to another investor by June 2000?
A: In — no, I don’t — the short answer is no, I’m not aware of the promise. I’m aware of a discussion between Merrill Lynch and Enron on or around the time of the transaction, and I did not think it was a promise though.
Q: So you don’t have any understanding as to why there would be a reference [in the Merrill Lynch document] to a promise that Merrill would be taken out by a sale to another investor by June of 2000?
A: No.
Brown makes three primary arguments: first, that he testified truthfully as to his subjective understanding of the barge deal; second, that the questions posed to him before the grand jury were too “vague and ambiguous” to support a perjury conviction; and third, that any misrepresentations by Brown were not material and thus cannot sustain a conviction under 18 U.S.C. § 1623. Each of these arguments is properly characterized as an attack on the sufficiency of the evi*528dence.16 Consequently, “[w]e ask whether a rational trier of fact could have found that the evidence established the elements of the offense beyond a reasonable doubt.” United States v. Holmes, 406 F.3d 337, 351 (5th Cir.2005).
First, Brown argues that the evidence presented is insufficient to support a reasonable juror’s finding that his testimony was untruthful. We disagree. Along with other circumstantial evidence of Brown’s knowledge of the details of the transaction, the Government presented the following:
1. Brown was approached in late December 1999 by Furst, who explained that Enron Treasurer Jeff McMahon “asked Merrill to purchase $7 [million] of equity in a special purpose vehicle that would allow Enron to book $10 [million] of earnings”, and that the transaction “must close by 12/31/99”. Furst further explained to Brown that “Enron is viewing this transaction as a bridge to permanent equity and they believe [Merrill’s] hold will be for less than six months”.
2. Brown was a part of a conference call on December 22, 1999 (the Trinkle call) in which Brown, Bayly, Furst and others, all Merrill Lynch employees, but excluding lawyers, discussed Enron’s need to close the deal to achieve needed revenue goals. Further, it was noted that Enron told Merrill that it would help find a third party buyer and that, if a third party buyer was not secured by June 30, 2000, Enron would repurchase the barges from Merrill. At some point during the call, Bayly asked whether a written assurance of Enron’s promise was available, and someone responded that a writing was not possible because such an assurance would prevent Enron from receiving the accounting treatment it was seeking from the deal.
3. Three versions of the engagement letter were circulated among Brown and others, the final draft being executed by Brown on behalf of Merrill. The initial draft of the engagement letter included reference to Enron’s buyback guarantee. On December 28, Boyle sent out a second draft of the letter with “strike-through” indicating the proposed removal of all references to the buyback guarantee. The final executed version of the engagement letter contained no reference to the buyback guarantee.
4. Finally, Brown’s own e-mail in March 2001, more than a year prior to his grand jury testimony, plainly stated that “we had Fastow get on the phone with Bayly and lawyers and promise to pay us back no matter what.”17 (Emphasis added.)
*529Based on this proof, a reasonable jury could have found that the evidence was sufficient to conclude that Brown’s answers were untruthful. Brown further argues that his testimony was not actually false, as he never denied knowledge of some “understanding” or “comfort” between Enron and Merrill as to the buyback; rather, he merely denied knowledge of a “promise” of such a side-deal. This distinction and the spin placed on selective and hyper-technical word choice provides no refuge from the jury’s verdict. “[I]f after conviction the defendant offers ‘a contrived hypertechnical or lame interpretation of his answer’ ... the jury’s decision must be left undisturbed.” Bell, 623 F.2d at 1136 (quoting United States v. Clifford, 426 F.Supp. 696, 704 (E.D.N.Y.1976) (citations omitted)). Based on this proof, a reasonable jury could have found that the evidence was sufficient to conclude that Brown knew that oral agreements had been made and that Brown’s answers before the grand jury were untruthful.
Second, Brown argues that the grand jury questions were “fundamentally ambiguous”. Our review of this testimony convinces us that the questions posed adequately conform with the principle that “[pjrecise questioning is imperative as a predicate for the offense of perjury,” Bronston v. United States, 409 U.S. 352, 358, 93 S.Ct. 595, 34 L.Ed.2d 568 (1973). There is no indication that Brown struggled to understand or actually misunderstood the meaning of the questions. Brown’s answers were carefully responsive to the questions posed. Brown’s caution in his word choice, using words like “comfort” and “best efforts,” rather than “assurance,” “promise,” or “guarantee,” indicates he was keenly aware of the thrust of the prosecutor’s questions.
Finally, Brown’s third argument challenging the materiality of his answers is two-fold: First, he contends that any knowing misrepresentations that he may have made were not material to the grand jury investigation; second, he argues that the refusal of the District Court to admit the entirety of his grand jury testimony was error, because consideration of that evidence would have prevented the jury from believing his testimony to be material. Materiality under § 1623 requires only that the defendant’s statements “[had] a ‘natural tendency to influence, or [were] capable of influencing, the decision of the decisionmaking body to which it is addressed.’ ” United States v. Gaudin, 515 U.S. 506, 509, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995) (quoting Kungys v. United States, 485 U.S. 759, 770, 108 S.Ct. 1537, 99 L.Ed.2d 839 (1988)); see also Abrams, 568 F.2d at 421 (same). The Government does not have to demonstrate that the grand jury was actually hindered in any way by the falsehood. See Abrams, 568 F.2d at 421 (“Actual impediment of the investigation is not required.... Grand jurors are capable of judging credibility and they are free to disbelieve a witness and persevere in an investigation without immunizing a perjurer.”). The central issue before the grand jury at the time of Brown’s testimony was whether there was an oral buyback guarantee between Enron and Merrill and if there was such an agreement, who was culpable. Any testimony by Brown relating to the existence of the agreement, or his knowledge or understanding about that agreement, was necessarily material to the inquiry of the *530grand jury.18 Brown’s argument to the contrary is meritless.
Brown’s second argument as to materiality is that the District Court erroneously excluded his entire grand jury testimony. This evidentiary ruling is reviewed for an abuse of discretion. United States v. Walker, 410 F.3d 754, 757 (5th Cir.2005) (citing United States v. Phillips, 219 F.3d 404, 409 (5th Cir.2000)). Brown contends that it was impossible for the trial jury to determine if his statements were perjurious without seeing the context in which they were given. The District Court reviewed Brown’s proffered testimony and declined to admit it, finding that “the questions ... and answers” contained therein “are not genuinely in question,” and concluding that the testimony was not relevant and would lead to jury confusion. We have reviewed the record, including the proffered testimony, and find no abuse of discretion by the District Court.
For the reasons given, we find no reason to upset the jury verdict and accordingly, affirm Brown’s conviction for perjury before a grand jury.
B
Brown next argues that even if the perjury conviction must be sustained, there is no basis for the verdict on obstruction of justice. Obstruction of justice is defined in 18 U.S.C. § 1503(a) as “corruptly ... endeavoring] to influence, obstruct, or impede ... the due administration of justice”. 18 U.S.C. § 1503(a) (1996). This clause “clearly forbids all corrupt endeavors to obstruct or impede the due administration of justice.” United States v. Williams, 874 F.2d 968, 977 (5th Cir.1989) (emphasis in the original). Brown contends, however, that where false testimony alone is the basis for the offense, “it still must be shown to have the effect of impeding justice.” Brown essentially argues that perjury and obstruction are separable and distinct offenses; consequently, the mere fact that one perjures himself does not mean that he has obstructed justice.19 Thus, the obstruction conviction must be reversed because “[t]he government introduced no evidence ... [to] establish that Brown’s testimony had any effect (actual, natural, or probable) on the Grand Jury proceeding.”
Brown’s argument is reasoned and appealing. Nevertheless, our precedent makes clear that material false testimony regarding one’s knowledge of the subject matter of a grand jury investigation has an effect beyond its falsity; it also impedes the investigation of the grand jury. In both United States v. Griffin, 589 F.2d 200 (5th Cir.1979), and Williams, the defendants testified falsely to a grand jury by giving “evasive answer[s]” and “denials of knowledge” relating to the subject of the *531grand jury inquiry. In both cases, the defendants, like Brown, argued that their § 1503 convictions must be reversed as the Government had not presented independent evidence that these falsehoods actually impeded the grand jury. Writing for this Court, respectively, both Judges Wisdom and Garwood rejected those contentions, finding that “the denials of knowledge had the effect of closing off entirely the avenues of inquiry being pursued, namely, what appellants knew about the subject under investigation.” Williams, 874 F.2d at 981 (emphasis added); see also Griffin, 589 F.2d at 204. As explicated by Judge Wisdom, “[b]y falsely denying knowledge of events and individuals when questioned about them, [the defendant] hindered the grand jury’s attempts to gather evidence [of the alleged scheme] as effectively as if he refused to answer the question at all.” Griffin, 589 F.2d at 204. Consequently, the “testimony had the effect of impeding justice.”20 Id.
Brown attempts to distinguish his case, arguing that he testified of his own free will, that he answered every question, and that he never directly denied knowledge of the Fastow conversation. Consequently, he cannot be found to have obstructed the grand jury. Brown’s argument, however, presupposes that his “voluntary” and “complete” testimony was true — a presupposition rejected by the jury’s conviction of perjury. Given our precedent, we see no principled reason that justifies different treatment of Brown’s untruthful testimony and denials of knowledge; as much as the defendants in Griffin and Williams, Brown “closed off entirely the avenue being pursued,” namely, his knowledge or understanding of what actually occurred. We are bound by the precedent of this Circuit, and under that precedent, no other proof of impediment is required to demonstrate obstruction under § 1503. Williams, 874 F.2d 968; Griffin, 589 F.2d 200.21
Given the evidence presented by the government that Brown’s testimony was false, and the jury’s apparent acceptance of that evidence, Brown’s perjurious testimony had the effect of “closing off entirely the avenue[] of inquiry being pursued.” Williams, 874 F.2d at 981. Consequently, Brown’s testimony was corruptly attempting to influence the administration of justice in violation of § 1503. As such, we affirm Brown’s conviction for obstruction of justice.
VI
We sum up as follows: The convictions of each of the Defendants for conspiracy and wire fraud are VACATED; the District Court’s denial of Fuhs’s motion for judgment of acquittal is REVERSED and his convictions are VACATED; and the conviction and sentences of Brown on charges of perjury and obstruction of justice are AFFIRMED.
REVERSED in part; VACATED in part; and AFFIRMED in part.
. On December 1, 1999, Merrill reissued its policy, warning of problematic end-of-year transactions by clients seeking to show gains or losses prior to the end of the year. "Clients wishing to effect a sale and then reestablish a position must be advised that there can be no prearrangement as to the availability of the financial instrument or the specific purchase price, if and when the client decides to reestablish the position.”
. Brown, Bayly, Furst, and other Merrill employees invested in a Merrill partnership which in turn invested in LJM2. Brown invested $32,500 of the $400 million LJM2 fund; Furst and Bayly each invested $130,000.
. In turn, the plan was for LJM2 to also flip the interest in the barges after the end of 2000 so that Enron would not have to show that the profits earned in 1999 were "unwound.” In return for Enron’s use of LJM2’s balance sheet in this manner, Enron was to pay LJM2 a flat $350,000 fee and a 15% annual rate of return for the period it held the barges, and ensure that LJM2 would be taken out of the investment by January 15, 2001. An industry buyer, an energy company, ultimately bought the barges during the period LJM2 held the barges; tellingly, this ultimate buyer conducted purchase negotiations with APACHI, not with LJM2 which held the barges in name.
. The Government notes some confusion as to whether the Defendants’ argument challenges *518the legal sufficiency of the Indictment or the sufficiency of the jury instructions. If the latter, the Defendants' failure to object during the charge conference would render our standard of review one for plain error. However, it is clear the Defendants mount a facial challenge to the Indictment, and the Government accepts the propriety of de novo review.
. "No person shall directly or indirectly, falsify or cause to be falsified, any book, record or account subject to Section 13(b)(2)(A) of the Securities Exchange Act." 17 C.F.R. § 240.13b2-1.
. See, e.g., United States v. Condolon, 600 F.2d 7 (4th Cir.1979); United States v. Louderman, 576 F.2d 1383 (9th Cir.1978).
. The Government must allege materiality in the Indictment, but failure to do so is not fatal “if the facts alleged in the Indictment warrant *520an inference of materiality.” Caldwell, 302 F.3d at 409.
. The Government's contention that Enron suffered a detriment is not trouble-free. The breach in question resulted in an increase in Enron’s stock price, an immediate benefit Enron specifically sought. The Defendants indeed argue explicitly that their actions ben-efitted the company for this very reason. Certainly, from a practical and short-term perspective, this is true. The Government claims that the detriment was Enron's spending money (in the form of fees paid to Merrill and bonuses paid to employees) for the "sole purpose of misleading shareholders and the investing public.” This theory is not fully convincing absent the implicit claim that this specific deal led to Enron’s unraveling, a causal connection for which there is no substantiated support. Nevertheless, we will assume for purposes of this opinion that the alleged detriment satisfies that element of honest-services fraud.
. Put another way, the Defendants argue that the scope of honest-services fraud is defined by the set of cases in which convictions have been upheld, not by the complement of the set of cases in which convictions have been reversed.
. It is also worth noting that the Government’s argument is somewhat circular, relying as it does on the statutory text’s use of the term “honest services.” As already stated, the statute itself provides not a hint of the definition of the term; instead, it is the case law that establishes the meaning of the vague and amorphous phrase.
. See Rybicki, 354 F.3d at 139-44. For brib-ery/kickback cases, see United States v. Schwartz, 785 F.2d 673 (9th Cir.1986); United States v. Price, 788 F.2d 234 (4th Cir.1986); United States v. George, 477 F.2d 508 (7th Cir.1973); United States v. Conner, 752 F.2d 566 (11th Cir.1985); United States v. Bryza, 522 F.2d 414 (7th Cir.1975); United States v. Hasenstab, 575 F.2d 1035 (2d. Cir.1978); United States v. Lemire, 720 F.2d 1327 (D.C.Cir.1983); United States v. Bohonus, 628 F.2d 1167 (9th Cir.1980); United States v. Boffa, 688 F.2d 919 (3d Cir.1982). For examples of self-dealing cases, see Ballard; Epstein v. United States, 174 F.2d 754 (6th Cir.1949); United States v. McCracken, 581 F.2d 719 (8th Cir.1978); United States v. Von Barta, 635 F.2d 999 (2d Cir.1980).
.Note that the Second Circuit dissenters dissented not from the narrowness of the construction but from the decision to uphold the statute at all. They would have struck down honest-services fraud as facially vague, emphasizing that " 'the average citizen ... must be forewarned and given notice that certain conduct may subject him to federal prosecution.’ ” 354 F.3d at 159 (Jacobs, Circuit Judge, dissenting) (quoting Brumley, 116 F.3d at 745-46 (Jolly and DeMoss, Circuit Judges, dissenting)).
. The Government cites one precedent that lies outside the bulk of the honest-services case law and addresses a situation arguably similar to the instant case. In United States v. Gray, 96 F.3d 769 (5th Cir.1996), university basketball coaches were convicted of mail and wire fraud for fraudulently establishing the academic eligibility of transfer students recruited to play on the basketball team. The court, relying on Ballard's suggestion that a non-disclosure of material information is itself sufficient harm to the employer, rejected the defendants' argument that their actions furthered the fortunes of the basketball team and of the university and were therefore not within the purview of fraud statutes.
The Government argues, quite plausibly, that Gray is similar enough to this case to dispose of the Defendants’ challenge, because the principal argument of the Defendants is that they believed their actions would benefit Enron. But Gray is distinguishable both factually and legally. Gray is dissimilar to this case in part because the opinion recognizes nothing akin to Enron’s corporate incentive policy coupled with senior executive support *523for the deal (the deal was sanctioned by Fas-tow, Enron's Chief Financial Officer), which together created an understanding that Enron had a corporate interest in, and was a willing beneficial^ of, the scheme. The opinion in Gray presents only the coaches' own belief that their scheme benefitted the university; no one or any authority outside the cadre of coaches encouraged, approved, or even knew of the wrongdoing. Moreover, the Gray court did not appear to have before it the limiting arguments presented here based on Rybicki (decided years after Gray). Thus, without attempting to call into question the result in Gray, we limit it to its facts, since applying the wire fraud statute here, even if it requires no new explicit statement of law, would expand honest-services fraud to reach all manner of accounting fraud and securities fraud, which have not generally been prosecuted as honest-services fraud and are heavily regulated under other statutes. The Government, in fact, would go even further; it plainly stated at oral argument its position, explicitly based on Gray, that the honest-services charge would reach the Defendants' conduct even absent an oral buyback agreement. The Government's desire to build on Gray crystalizes the danger we face of defining an ever-expanding and ever-evolving federal common-law crime.
. Specifically, the Indictment alleges that "[w]hile under oath, Defendant BROWN testified falsely as to a material matter by stating, among other things, that he did not know of any oral promise between Enron and Merrill Lynch relating to the barge transaction.”
. The portion of the testimony from which the excerpts in the Indictment were taken is as follows:
Q: Do you see where it [e-mail from Boyle, Grand Jury Exhibit 11] says, "To be clear, Ene. (Enron) is obligated to get Merrill out of the deal on or about June 30th?”
A: Yes, sir.
Q: Do you have any understanding of why Enron would believe it was obligated to Merrill to get them out of the deal on or before June 30th?
A: It is inconsistent with my understanding of what the transaction was.
Q: ... And the question to you is do you have any understanding as to whether — how or why — Enron would believe that it was — it understood that it was required ... to get Merrill Lynch out of the deal by June 30th?
A: I did not understand — you know, my understanding of the transaction was that they were not required to get us out of the transaction, but we made it clear to them that we wanted to be out of it by June 30th.
Q: Now, do you see in this E-mail [still discussing Grand Jury exhibit 11] where it says, "And someone should be working on a backstop, as you will not be able to extend Merrill, and I understand that there are accounting ramifications if Enron repurchases”?
Now, do you have any understanding about whether or not Merrill could extend past June 30th?
A: I don’t know anything about that.
Q: Okay. And under — if it was a true sale and if Merrill purchases something, there would be no extension needed. I mean Merrill has the asset and until somebody comes along and buys it, they have it; correct?
A: Correct.
Q: Now, do you see in this document [LJM-2 document, Grand Jury Exhibit 18] ... in the first sentence where it says, "Enron sold barges to Merrill Lynch in December of 1999, promising that Merrill would be taken out by sale to another investor by June 2000.”
Again, do you have any information as to a promise to Merrill that it would be taken out by sale to another investor by June 2000?
A: In — no, I don't — the short answer is no, I’m not aware of the promise. I’m aware of a discussion between Merrill Lynch and Enron on or around the time of the transaction, and I did not think it was a promise though.
Q: So you don't have any understanding as to why there would be a reference to a promise that Merrill would be taken out by sale to another investor by June of 2000?
A: No.
Q: [Discussing America’s Credit Flash Report for the week ending 12/23/99, Grand Jury Exhibit 9] And let me now *527direct your attention to the paragraph on the Nigerian barge project.
Now, do you see where it says ..., "IBK [Merrill] was supportive based on Enron relationship, approximately $40 million in annual revenues, and assurances from Enron management that we will be taken out of our $7 million investment within the next three to six months.”
Does that accord with your understanding of the transaction?
A: No. I thought we had received comfort from Enron that we would be taken out of the transaction within six months or would get that comfort.
If assurance is synonymous with guarantee, that is not my understanding.
If assurance is interpreted to be more along the lines of strong comforts or use of best efforts, that is my understanding.
Q: [Discussing the Merrill appropriation request for the Enron/Merrill barge transaction, Grand Jury exhibit 7] ... Do you see where it says, "Take out,” where it says, "project starl/finish,” and it says, "Needs to close by 12/31/99”? And I’d for now like to focus on the part where it says, "Take out by June 30th, 2000.”
A: Yes, sir.
Q: Does that comport with your understanding of the transaction, that the finish of the project was June 30th of 2000 when there would be a take out?
A: You know, “take out” could mean that the anticipated time frame of the investment runs through that period, or in my mind it could, or it could mean some sort of legal take out. So I really' — I can’t draw a conclusion from just those words.
Q: Do you see where it says "maturity”?
A: Yes.
Q: And its says "less than 6 months”?
A: Yes.
Q: Do you have any understanding why it would say "less than six months” if the terms of the agreement are open-ended?
A: Well, I’d be speculating but I would assume that that would reflect — at least my understanding or whoever wrote this's understanding, that the anticipated hold period was less than six months.
Q: But if the contract between the parties is an open-ended investment, why does the maturity just say less than six month[s] when the terms of the contract bring Merrill Lynch well beyond six months?
A: I don’t know.
. Brown mischaracterizes his challenges as a legal sufficiency challenge, which we would review de novo. It is clear, however, that Brown’s challenge is to the sufficiency of die evidence. See, e.g., United States v. Abrams, 568 F.2d 411, 417 (5th Cir.1978) (holding that when examining a jury’s determination that the defendant “gave false testimony”, "[t]he applicable standard of review is not whether we think the evidence sufficient but whether a reasonable jury could so conclude beyond a reasonable doubt.”); United States v. Bell, 623 F.2d 1132, 1136 (5th Cir.1980) ("the prevailing view is that the defendant's understanding of the question is a matter for the jury to decide”); United States v. Gaudin, 515 U.S. 506, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995) (holding that materiality is an element of perjury and thus a question for the consideration of the jury).
. Brown, who was not a party to the “Fas-tow call,” argues that the e-mail is inadmissible hearsay and that it is unreliable and fails to provide evidence that his grand jury testimony was false. However, the e-mail is admissible as non-hearsay under Federal Rule of Evidence 801(c) to reveal Brown’s state of mind, i.e., his belief that the side deal had been entered into and confirmed by Fastow. Additionally, although Brown argues that any knowledge he had of the call was based on *529hearsay, the e-mail is admissible against him under Rule 801(d)(2)(A) as an admission by a party opponent. Despite Brown's contentions to the contrary, a reasonable jury could consider such an admission reliable and reject Brown’s proffered explanation that the e-mail was an exaggeration of "the strength of the promise [made by Fastow].... ”
. The materiality requirement of § 1623 has been satisfied in cases where the false testimony was "relevant to any subsidiary issue or [wa]s capable of supplying a link to the main issue under consideration.” United States v. Griffin, 589 F.2d 200, 207 (5th Cir.1979) (noting that "[t]he testimony need not be directed to the primary subject under investigation”). Consequently, it appears that even if Brown's falsehood was relevant only as to his participation in the buyback agreement (and was not, as Brown argues, material to the existence of the buyback itself) the materiality requirement of § 1623 is still satisfied.
. We acknowledge this argument is well reasoned and persuasive. However, under the precedent of this circuit, as discussed infra, false testimony as to one’s knowledge relating to the subject of a grand jury inquiry does in fact establish obstruction; not because the perjury ipso facto establishes obstruction, but because the perjurious testimony has the effect of "closing off entirely the avenue[] of inquiry being pursued.” Williams, 874 F.2d at 981.
. Because the testimony in Griffin and Williams did in fact impede the grand jury, both cases declined to determine whether perjury before a grand jury "ipso facto constitutes a violation of section 1503,” see Griffin, 589 F.2d at 204; Williams 874 F.2d at 980.
. Brown repeatedly cites In re Michael, 326 U.S. 224, 66 S.Ct. 78, 90 L.Ed. 30 (1945), for the proposition that an obstruction conviction based on perjury alone cannot stand. However, Griffin squarely rejected that argument. 985 F.2d at 205-06. See also Williams, 874 F.2d at 979.