Nos. 95-5299 and 95-5326 are affirmed, and Nos. 95-5324 and 95-5325 are affirmed in part and reversed in part by published opinion. Judge MOTZ wrote the opinion, in which Judge NIEMEYER joined. Judge WILLIAMS wrote a concurring opinion.
OPINION
DIANA GRIBBON MOTZ, Circuit Judge:These consolidated appeals arise out of a complex enterprise involving the transfer of funds from the United States to Pakistan. In connection with that enterprise, appellants, Mohammed Ismail, Shakeel Ahmad, Mian Tauqir Ahmed, and Mohammad Bashir, were charged in a fifty-one count indictment and convicted of most of the crimes charged, including structuring financial transactions to evade currency reporting requirements, conspiracy to make false statements to the United States Customs Service, and tax fraud. Appellants raise numerous issues on appeal, most of which are meritless. However, because the Government failed to offer evidence sufficient to prove that Shakeel Ahmad and Mian Tauqir Ahmed willfully violated the antistructuring laws or that Shakeel Ahmad knowingly made a material false statement in a matter within the jurisdiction of a federal agency, we must reverse the convictions and vacate the sentences imposed in connection with those offenses. We affirm in all other respects.
I.
A.
Shakeel Ahmad, a Pakistani national, emigrated to the United States on January 25, 1986, using a visa in the name of Javed Iqbal. He subsequently obtained a driver’s license and social security card, also in the name of Javed Iqbal. In addition to working as a Washington, D.C. taxi driver, Ahmad operated a business whereby he transferred the funds of other Pakistanis in the United States back to their families in Pakistan. Approximately fifty Pakistanis living in New York and Washington, D.C. regularly provided Ahmad with money that they wished to send to Pakistan. They utilized his services because other options, such as wire transfers through the Bank of Pakistan or direct mailing of checks or money orders, were either too expensive or too slow, and because Ah*53mad offered a better exchange rate than was otherwise available. For his services, Ahmad kept one Pakistani rupee for every U.S. dollar transferred.
Also participating in this business were Ahmad’s brothers, Mian Tauqir Ahmed, and Zamir Ahmed, a/k/a Choudrey Hussein, who is not an appellant herein but is a fugitive. Shakeel Ahmad and Zamir Ahmed shared an apartment in Alexandria, Virginia where they received shipments of cash, checks, and money orders from various Pakistanis, usually by express mail. They deposited this money into cheeking accounts at the Van Dorn Street branch of First Virginia Bank, an FDIC insured institution. Bank officials knew that the three men, who were signatories on three First Virginia accounts, were brothers, but knew them as Javed Iqbal, Tauqir Ahmed, and Choudrey Hussein.
On September 25, 1989, when Ahmad deposited $18,400 into one of the three accounts, Jenny Fadoul, the Branch Manager at First Virginia, informed Ahmad that she would have to file a Currency Transaction Report (CTR) because the deposit exceeded $10,000. She also told him that she did not have to file CTRs for deposits under $10,000, but that she could file a CTR for such a deposit. Ahmad proceeded with the $18,400 transaction anyway, and Fadoul filed a CTR. After Ahmad’s conversation with Fadoul regarding the CTRs, all of the brothers’ subsequent cash deposits were in amounts less than $10,000.
On a later occasion, Jenny Fadoul again explained to the brothers the circumstances triggering the filing of a CTR. Some time around late April, 1992, Zamir Ahmed attempted to make two deposits of $9,800 each into two separate accounts. After checking with the bank’s main office, Fadoul informed Zamir Ahmed that she would have to file a CTR if one individual made the transaction, even though it involved two different accounts. Zamir Ahmed told her “no report,” so Fadoul said that they would have to refuse the transaction. Because Zamir Ahmed did not speak English very well, they called Ahmad at home so that Fadoul could explain the situation. Fadoul explained to Ahmad that if one person tried to make two transactions totalling over $10,000, she would have to file a CTR, but if the deposits were made by two people into the two accounts, she would not have to file a CTR. At no time did Fadoul ever tell any of the brothers that structuring deposits so as to avoid the bank’s reporting requirements was illegal.
Over a four year period, the brothers deposited cash, checks, and money orders into their accounts as often as four times a week. The deposits were regularly in amounts greater than $9,000 but less than $10,000. From January 1, 1990 to October 25, 1993, the brothers deposited $5.6 million in cash, cashier’s cheeks, and wire transfers into their First Virginia accounts.
As noted above, one of the reasons the brothers were successful in their currency transfer business was that they offered a better exchange rate from dollars to rupees than did other currency transfer options. Certain features of Pakistani trade law enabled them to do so. Pakistani law requires manufacturers to collect the full invoice price of exported goods in foreign currency, within 120 days of shipment. In cases where the buyer of the goods cannot pay in full within the 120 days, or wants to pay on an installment basis, the exporting company may obtain a “bridge loan” from a currency exchanger so that it can satisfy this requirement. To obtain these bridge loans, the exporters pay an exchange rate higher than the official rate. Additionally, in order to encourage exports, the Pakistani government rebates to Pakistani manufacturers a percentage of their gross exports. This percentage has fluctuated between 12% and 30%. It is this rebate that enables the exporters to afford the higher exchange rate paid to currency exchangers supplying bridge loans.
In order to obtain a competitive exchange rate to attract customers to their currency exchange business, the brothers supplied bridge loans to many different companies using the money received from Pakistanis living in the United States. Rather than repaying the brothers directly, the Pakistani companies repaid the bridge loans by distributing rupees to the family members of Ahmad’s clients in accordance with Ahmad’s *54faxed instructions, at a better exchange rate than the official rate. In addition, the brothers were able to reduce the costs of transferring money to Pakistan by “bundling” many different transfers into one transaction, thus saving on the per-transaction fee charged for wire transfers.
B.
The second part of this case involves the brothers and a company called Falcon Instruments, of which appellants Mohammed Ismail and Mohammad Bashir were President and quality control manager, respectively. Though the brothers dealt with many different Pakistani companies, it is only through their relationship with Falcon that they were charged with making false statements to the U.S. Customs Service.
Falcon Instruments is a reseller of surgical instruments that imports large quantities of inventory from Pakistan for sale in the United States. During the relevant time period, the importation of surgical equipment was duty-free. Like the brothers, Falcon maintained an account at First Virginia Bank. With the help of financing from the brothers, Ismail and Bashir implemented the following plan. Falcon would order surgical supplies from Pakistani exporters, who would ship the products ordered, but list on the invoice a purchase price usually twice the actual market value of the products. After receiving the shipment, Falcon would send a letter to the manufacturer requesting a “discount” on the invoice price. The “discount” requested was generally the difference between the inflated invoice price and the price at which the Pakistani company would make a small profit on the goods. The brothers would deposit into Falcon’s account an amount equal to the discount received from the Pakistani company. Falcon would then wire to the exporter, through the Bank of Pakistan, the full amount of the invoice. The Pakistani exporter would keep the amount due, the “discounted” price for the goods shipped, and would distribute Ahmad’s portion to his clients’ families, according to faxed instructions.
During the period covered by the indictment, the brothers transferred approximately $1.3 million to families in Pakistan through the arrangement with Falcon. As part of this plan, Falcon caused Customs brokerage agents at Dulles Airport to list the inflated invoice price as the “transaction value” of the imported goods on Customs forms.
C.
In early 1993, an IRS/Customs task force received information from First Virginia Bank that Shakeel Ahmad was moving large amounts of money through a checking account in the name of Javed Iqbal. As part of its investigation, the task force obtained copies of the brothers’ bank records.
The task force also discovered that the brothers received packages by express mail almost daily. Investigators obtained a warrant to seize and inspect the contents of some of these packages. One package so seized was found to contain a $9,700 cashier’s cheek and $10,700 in cash. The investigators photocopied the cashier’s check and the cash, recorded the serial number of each bill, and returned the originals to the express mail package, which was resealed and delivered to the brothers. A comparison of the recorded serial numbers with First Virginia’s records revealed that the $10,700 cash was broken up and deposited into the brothers’ accounts in several smaller deposits.
Examining Ahmad’s bank records, the task force noticed a large number of deposits to Falcon’s bank accounts. The task force contacted Ismail and Bashir, and when they hesitated to cooperate in the investigation, Falcon’s business records were seized. Examination of these records revealed to investigators the elaborate plan engaged in by Falcon, the brothers, and Falcon’s suppliers.
Task force investigators reviewed Falcon’s corporate tax returns for the years in question, which an accountant had prepared and Ismail had signed. According to IRS calculations, Falcon’s 1991 tax return understated its tax liability by $186,302.31, and the 1992 return understated its tax liability by $188,-760.40.
D.
This evidence was produced at a three day bench trial, which resulted in convictions on *55the majority of the charges contained in the indictment.
The court found Shakeel Ahmad guilty of one count of conspiracy to structure transactions to evade currency reporting requirements, in violation of 18 U.S.C. § 371; eleven counts of structuring transactions to evade currency reporting requirements, in violation of 31 U.S.C. § 5324(a)(3); one count of making a false material statement in a matter within the jurisdiction of the Federal Deposit Insurance Corporation, in violation of 18 U.S.C. § 1001; one count of conspiracy to defraud the United States Customs Service, in violation of 18 U.S.C. § 371; and fifteen counts of making false statements to the United States Customs Service, in violation of 18 U.S.C. § 542. Because he was found guilty of the structuring offenses, Ahmad was also ordered to forfeit approximately $185,-000 pursuant to 18 U.S.C. § 982.
The court found Mian Tauqir Ahmed guilty of one count of conspiracy to structure transactions to evade currency reporting requirements; one count of conspiracy to defraud the United States Customs Service; and ten counts of making false statements to the United States Customs Service.
The court found Mohammed Ismail guilty of one count of conspiracy to defraud the United States Customs Service; fifteen counts of making false statements to the Customs Service; and two counts of willfully subscribing false tax returns in violation of 26 U.S.C. § 7206(1).
Mohammad Bashir was convicted of one count of conspiracy to defraud the United States Customs Service; and fifteen counts of making false statements to the Customs Service.
Appellants raise numerous arguments on appeal. After review of the record and consideration of the parties’ briefs and arguments, we conclude that several of these arguments are entirely meritless. The district court did not err in refusing to dismiss fifteen counts of the indictment because those counts charged violations of 18 U.S.C. § 541 rather than the more specific 18 U.S.C. § 542. The Government offered sufficient evidence to prove Ismail violated 26 U.S.C. § 7206, and the court properly sentenced Ismail. Four of appellants’ claims, however, require close examination.
II.
Appellants’ strongest arguments concern the sufficiency of the evidence supporting the convictions of Ahmad and Ahmed for conspiring to violate the antistructuring law, and Ahmad’s convictions for violating the anti-structuring law and for providing a material false statement in a matter within the jurisdiction of an agency of the United States. Ahmad and Ahmed claim that we must reverse these convictions because the Government failed to present sufficient evidence to prove the necessary elements beyond a reasonable doubt.
To determine if the prosecution has met its burden in this direct appeal from a bench-trial verdict, we apply a well recognized standard of review, examining whether “there is substantial evidence, taking the view most favorable to the government,” to support the conviction. Glasser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942); United States v. Bales, 813 F.2d 1289, 1293 (4th Cir.1987). See also United States v. Bashaw, 982 F.2d 168, 171 (6th Cir.1992) (“when a defendant is convicted after a bench trial, the test is “whether the evidence is sufficient to justify the trial judge, as trier of facts, in concluding beyond a reasonable doubt that the defendant was guilty.’”) (quoting United States v. Niver, 689 F.2d 520, 529 (5th Cir.1982)). Although the United States may rely on inferences and circumstantial evidence, it “nevertheless must establish proof of each element” of the crime “beyond a reasonable doubt.” United States v. Burgos, 94 F.3d 849, 858 (4th Cir.1996) (en banc). As Judge Williams recently explained for the en banc court, “[t]o require less of the Government would eviscerate its burden to prove all elements of a crime beyond a reasonable doubt and relieve it of its burden of vigilance in prosecuting crimes — thereby violating bedrock principles of our Anglo-American jurisprudence.” Id. (citing In re Winship, 397 U.S. 358, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970)).
*56With these principles in mind, we examine the evidence offered to prove that Ahmad and Ahmed conspired to violate the anti-structuring law, and that Ahmad willfully violated the antistructuring law and made a material false statement in a matter within the jurisdiction of the FDIC.
A.
Federal law requires banks and other financial institutions to file a currency transaction report (CTR) with the Secretary of the Treasury for any cash transaction exceeding $10,000. 31 U.S.C. § 5313 (1994). A related provision forbids structuring a transaction for the purpose of evading a financial institution’s requirement to file CTRs. 31 U.S.C. § 5324 (1994). The district court found Ahmad guilty of conspiracy to violate § 5324 and of several substantive counts of violating the antistrueturing provision. The court found Ahmed guilty of a single count of conspiring to violate § 5324. At the time they were convicted, only persons “willfully violating” § 5324 were subject to criminal penalties. 31 U.S.C. § 5322 (1994).
Prior to 1994, this circuit, like most others, held that a willful violation of the antistruc-turing law meant “no more than that the [defendant] knows what he is doing. It does not mean that in addition he must suppose he is breaking the law.” United States v. Rogers, 962 F.2d 342, 344 (4th Cir.1992) (citation omitted); see also United States v. McNamara, 74 F.3d 514, 515 n. 2 (4th Cir.1996) (listing eases from nine other circuits in accord with our holding in Rogers).
In Ratzlaf v. United States, 510 U.S. 135, 114 S.Ct. 655, 126 L.Ed.2d 615 (1994), the Supreme Court rejected this view. The Court squarely held that “[t]o establish that a defendant ‘willfully violat[ed]’ the antistrue-turing law, the Government must prove that the defendant acted with knowledge that his conduct was unlawful.” Id. at 137, 114 S.Ct. at 657; see also United States v. Rogers, 18 F.3d 265, 268 (4th Cir.1994) (holding that jury instruction that did not require prosecution to prove defendant knew he was “breaking the law” was plain error and required reversal in light of Ratzlaf).
Requiring proof that a defendant knew that structuring violates the law admittedly places a difficult burden on the Government. See Ratzlaf, 510 U.S. at 159-62, 114 S.Ct. at 669-70 (Blackmun, J., dissenting). Nevertheless, Ratzlaf clearly requires this. Congress, however, promptly recognized this difficulty and, within months of the Ratzlaf opinion, eased the government’s burden by enacting legislation that removes the “willfulness” requirement with respect to the crime of structuring. Pub.L. No. 103-325 § 411, 108 Stat. 2160, 2253 (1994), codified at 31 U.S.C.A § 5322(a) (Supp.1996). Thus, in the future, the Government will not have to prove that defendants knew that structuring is illegal to establish a violation of § 5324.
However, when the case at hand was tried, this was the Government’s burden. The evidence the Government presented in this case—e.g., bank official Jenny Fadoul’s explanations to the brothers that she would have to file reports with the IRS for cash deposits of $10,000 or more, Ahmed’s “no report” remark, and the brothers’ frequent cash deposits of amounts just under $10,-000—undoubtedly proved that the brothers knew the bank was required to report cash transactions over $10,000 and that they intended to keep their deposits under that amount to avoid the reports. But the question before us is whether this evidence of structuring activity also proves, beyond a reasonable doubt, that appellants knew that structuring violated the law and thus that they willfully violated the antistructuring provision.
An identical question was presented to the Ratzlaf Court, ie. whether evidence that “a defendant’s purpose to circumvent a bank’s reporting obligation suffices to sustain a conviction for ‘willfully violating’ the antistruc-turing provision.” 510 U.S. at 137, 114 S.Ct. at 657. The Court answered in the negative: “We hold that the ‘willfulness’ requirement mandates something more.” Id. (emphasis added). It explained that by subjecting only those who “willfully” violate § 5324 to criminal penalties, Congress signaled “its intent to require for conviction proof that the defendant knew not only of the bank’s duty to *57report cash transactions in excess of $10,000, but also of his duty not to avoid triggering such a report.” Id. 146-47, 114 S.Ct. at 662.
Immediately after Ratzlaf was decided, two courts suggested that evidence of structuring itself, if the defendant goes to great lengths to hide the structuring, can provide the “something more,” which Ratzlaf held necessary to prove willfulness. See United States v. Marder, 48 F.3d 564, 574 (1st Cir.) (dicta), cert. denied, — U.S. -, 115 S.Ct. 1441, 131 L.Ed.2d 320 (1995); United States v. Walker, 25 F.3d 540, 543, 548 n. 8 (7th Cir.), cert. denied, — U.S. -, 115 S.Ct. 371, 130 L.Ed.2d 323 (1994) and — U.S. -, 115 S.Ct. 531, 130 L.Ed.2d 434 (1994). In these eases, the defendants structured their transactions through elaborate schemes — using different branches of different banks and enlisting other people to make the deposits. Marder, 48 F.3d at 574; Walker, 25 F.3d at 543, 548 n. 8. The Walker court concluded that together with an unspecified “mass of other evidence,” this evidence indicated that the defendant attempted to conceal his structuring and was sufficient to prove defendant’s knowledge that structuring violated the law, Walker, 25 F.3d at 548 n. 8; the Marder court similarly indicated, in dicta, that extensive evidence of concealment was sufficient to establish a willful violation. Marder, 48 F.3d at 574. We need not here determine if evidence of elaborate efforts to conceal structuring is probative of knowledge that structuring violates the law because, even if it is, there is no evidence that Ahmad and Ahmed made such efforts to conceal their structuring activity.1
To the extent that Marder and Walker suggest that evidence of structuring itself is sufficient to prove that a defendant knew structuring violated the law, we believe they are inconsistent with Ratzlaf Like the District of Columbia Circuit, in light of Ratzlaf, we cannot agree that evidence of structuring alone can provide the basis for an inference, proving beyond a reasonable doubt, that a defendant knew that structuring violated the law. See United States v. Wynn, 61 F.3d 921, 928 (D.C.Cir.), cert. denied, — U.S. -, 116 S.Ct. 578, 133 L.Ed.2d 501 (1995).
Ratzlaf expressly rejected the argument “that § 5324 violators, by their very conduct, exhibit a purpose to do wrong.” 510 U.S. at 143, 114 S.Ct. at 660. The Ratzlaf Court pointed out that structuring a financial transaction is not an “inevitably nefarious” activity. Id. at 144, 114 S.Ct. at 661. Law abiding citizens frequently structure transactions to avoid a report, regulation, or tax without violating the law. Id. See Helvering v. Gregory, 69 F.2d 809, 810 (2d Cir.1934) (L.Hand, J.) (“Anyone may so arrange his affairs that his taxes shall be as low as possible; he is not bound to choose that pattern which will best pay the Treasury; there is not even a patriotic duty to increase one’s taxes”), aff'd, 293 U.S. 465, 55 S.Ct. 266, 79 L.Ed. 596 (1935). In fact, as recently as ten years ago, although federal law required financial institutions to report cash transactions in excess of $10,000, the law permitted structuring one’s cash transactions to avoid these reports; not until 1987 did Congress make it a crime to willfully structure transactions to avoid the reporting requirements. Compare 31 U.S.C. §§ 5313, 5322 (1982) with 31 U.S.C. § 5324 (Supp. IV 1986).
Thus, although a defendant’s knowledge that structuring violates the law can certainly be inferred from conduct, Ratzlaf, 510 U.S. at 149 n. 19, 114 S.Ct. at 663 n. 19, the conduct that provides this inference cannot *58consist simply of the act of structuring itself. As Judge Buckley explained:
The Supreme Court explicitly based Ratzlaf on the proposition that, while ignorance of the law generally is no excuse, Congress may decree otherwise and has done so by requiring proof of “willfulness” before the imposition of criminal penalties for structuring activity. Permitting a violation of the law — i e., structuring — alone to serve as sufficient evidence of knowledge of the law would effectively merge the two elements and deprive Congress of this privilege. The jury, of course, may infer knowledge of the law from circumstantial evidence, but for the willfulness requirement to be more than “essentially ... surplusage,” that evidence must suggest knowledge of the antistructuring law as distinct from knowledge of financial institutions’ reporting requirements.
Wynn, 61 F.3d at 928 (citations omitted, alteration in Wynn).
In the wake of Ratzlaf, other courts have sustained convictions for willful violations of the antistructuring law only when the prosecution has presented “something more” than evidence of structuring itself. Specifically, in addition to the structuring itself, courts have relied on evidence of a defendant’s general consciousness that he acted illegally or evidence that a defendant had some special status or expertise from which a jury could reasonably infer that he knew structuring was illegal. See, e.g., United States v. Simon, 85 F.3d 906, 909-10 (2d Cir.1996) (in addition to evidence of structuring, defendant, as a stockbroker, was familiar with the reporting requirements and, in fact, was required to file CTRs in his business); United States v. Hurley, 63 F.3d 1, 16 (1st Cir.1995) (knowledge that structuring violated the law demonstrated by evidence that defendants were generally conscious that their conduct was illegal, i.e., evidence that they knew drug money was involved, that “the break-downs of the cash were designed to disguise proceeds,” and that one defendant indicated in a “recorded statement ... that he knew” his conduct “was criminal”), cert. denied, — U.S. -, 116 S.Ct. 1322, 134 L.Ed.2d 474 (1996); United States v. Tipton, 56 F.3d 1009, 1013 (9th Cir.1995) (in addition to evidence of structuring, defendants, as bank officials, were familiar with CTR reporting requirements and made numerous inculpato-ry admissions to which co-conspirator testified), cert. denied, — U.S. -, 116 S.Ct. 773, 133 L.Ed.2d 725 (1996); United States v. Vazquez, 53 F.3d 1216, 1225 (11th Cir.1995) (because defendant testified at trial that he “knew he was doing something illegal” evidence sufficed to prove knowledge that structuring violated the law).
Moreover, two circuits have expressly held that evidence of structuring activity by itself — no matter how many deposits were made or how much cash was involved — is insufficient to prove knowledge that structuring violated the law. Wynn, 61 F.3d at 927-28 (“abundant evidence” of structuring itself insufficient to demonstrate knowledge that structuring violated the law); Vazquez, 53 F.3d at 1216 (“ample” evidence of structuring failed to prove defendant knew structuring was illegal, only defendant’s testimony as to knowledge of illegality allowed finding of willfulness).
In this case, the Government introduced no evidence that appellants, like the stockbroker in Simon, 85 F.3d at 910, or bank officials in Tipton, 56 F.3d at 1013, had special expertise with CTRs from which a jury could infer that they knew structuring violated the law. Cf. United States v. Diamond, 788 F.2d 1025, 1029 (4th Cir.1986) (certified public accountant’s “education and professional experience suggesting an extraordinary sophistication with respect to tax matters” could support inference that his violation of tax laws was willful).
Nor did the Government present any evidence, like that in Hurley, 63 F.3d at 16, that appellants were “generally conscious” that their conduct was illegal. The bank manager, Jenny Fadoul, testified that she never told any of the brothers that structuring violated the law. Indeed, when Fadoul explained the reporting requirements to the brothers upon Ahmed’s attempt to make two deposits of $9,800 into separate accounts, she expressly informed them that she would not have to file a report if two people made deposits under $10,000 into separate ac*59counts, but did not go on to say that to so divide deposits violated the law. When Fa-doul informed the brothers that she would have to file reports of cash deposits in excess of $10,000, they attempted to arrange their affairs to avoid such reports in the future, but they did not switch banks or even reduce the $18,400 deposit triggering Fadoul’s statement — and her filing of the CTR. Certainly, appellants did not admit that they knew their conduct was “illegal.” Cf. Vazquez, 53 F.3d at 1225; Hurley, 63 F.3d at 16.2 Instructive as to the importance of such evidence is the Eleventh Circuit’s recent decision in United States v. Vazquez, 53 F.3d at 1216.
In Vazquez, after a bank manager informed the defendant of the reporting requirements for cash transactions over $10,-000, the defendant switched banks. Id. at 1225. The defendant often had other persons make deposits for him. Id. During one six-month period, he deposited more than $1.4 million in cash, making “multiple deposits only minutes apart and with different branches during the same day,” with all checks in amounts less than $10,000. Id. Yet the Eleventh Circuit held this evidence was insufficient to prove that the defendant knew structuring violated the law and had willfully structured the transactions. The court explained that although this evidence demonstrates “that the defendant wanted to evade the bank’s reporting requirements ... [it] is not adequate to show that [he] knew the law prohibited him from doing so.” Id. It was only because the defendant testified at trial that he knew he was “doing something illegal” that the court found the evidence sufficient to sustain a conviction of willful structuring. Id. at 1226.
Ratzlaf controls here and requires the Government to prove not only that appellants structured or conspired to structure transactions to avoid First Virginia’s reporting requirements, but also that they did so with the knowledge that their conduct violated the law. The Government failed to meet that burden.3 Consequently, we reverse the convictions of Ahmad and Ahmed under Count 1 of the indictment, and Ahmad’s convictions under Counts 3-13. Additionally, we must reverse those portions of Ahmad’s criminal forfeiture conviction under Count 51 of the indictment that were predicated on his substantive structuring convictions.
B.
Ahmad also maintains that the Government offered insufficient evidence to prove that he knowingly made a false material statement in a matter within the jurisdiction of the Federal Deposit Insurance Corporation (FDIC), in violation of 18 U.S.C. § 1001. For this reason, he asserts that his conviction for a single count (Count 14) of violating that statute should be reversed.
Section 1001 provides that:
Whoever, in any matter within the jurisdiction of any department or agency of the United States knowingly and willfully falsifies, conceals or covers up by any trick, scheme, or device a material fact, or makes any false, fictitious or fraudulent statements or representations, or makes or uses any false writing or document knowing the same to contain any false, fictitious or fraudulent statement or entry, shall be *60[guilty of an offense against the United States].
18 U.S.C. § 1001.
To prove a violation of § 1001, the Government must establish that “(1) the defendant made a false statement to a governmental agency or concealed a fact from it or used a false document knowing it to be false, (2) the defendant acted ‘knowingly or willfully,’ and (3) the false statement or concealed fact was material to a matter within the jurisdiction of the agency.” United States v. Arch Trading Co., 987 F.2d 1087, 1095 (4th Cir.1993) (citation omitted).
Ahmad’s challenge focuses on the third element. Ahmad concedes that, although his bank signature card contains his correct address, he provided the bank with a false name, Javed Iqbal, and a false social security number (he used the name, “Javed Iqbal,” to obtain a visa, social security number, and driver’s license and to open the bank account when he entered the country in 1986). Ahmad maintains, however, that because the Government faded to prove that the false name and social security number were material to a matter within the jurisdiction of the FDIC, it faded to prove he violated § 1001.
A fact about a matter within an agency’s jurisdiction is material under § 1001 if it “has a natural tendency to influence agency action or is capable of influencing agency action.” Id. (quoting United States v. Norris, 749 F.2d 1116, 1122 (4th Cir.1984), cert. denied, 471 U.S. 1065, 105 S.Ct. 2139, 85 L.Ed.2d 496 (1985)); see also United States v. Gaudin, — U.S. -, -, 115 S.Ct. 2310, 2313, 132 L.Ed.2d 444 (1995). “[T]here is no requirement that the false statement [aetuady] influence or effect the decision making process of a department of the United States government.” Arch Trading, 987 F.2d at 1095 (quoting Norris, alterations in Arch Trading).
The district court found that Ahmad’s use of a false name and social security number “[was] within the jurisdiction of the Agency, the FDIC, it was a false statement upon which the bank relied and I find that to be in the jurisdiction of the FDIC.” The court made no finding or express ruling with regard to materiality. We note that in January of 1995 when the court tried this case, materiality, under circuit precedent, was a question of law. See United States v. David, 83 F.3d 638, 640 (4th Cir.1996). Accordingly, the court may have regarded its legal conclusion as to the materiality of Ahmad’s statement as implicit.
In any event, in June, 1995, five months after Ahmad was convicted, a unanimous Supreme Court held that materiality under § 1001 presents a factual question that must be proven to the factfinder beyond a reasonable doubt. See Gaudin, — U.S. at -, 115 S.Ct. at 2320. We review Ahmad’s conviction under Gaudin because “a new rule for the conduct of criminal prosecutions is to be applied retroactively to all cases ... pending on direct review ..., with no exception for cases in which the new rule constitutes a ‘clear break’ with the past.” Griffith v. Kentucky, 479 U.S. 314, 328, 107 S.Ct. 708, 716, 93 L.Ed.2d 649 (1987).
Here, however, the result would be the same whether the determination as to materiality is treated as a question of fact or law. This is so because even when the determination of materiality under § 1001 was “a conclusion of law,” it had to be “fully supported by the evidence, direct or circumstantial.” See United States v. LeMaster, 54 F.3d 1224, 1230 (6th Cir.1995), cert. denied, — U.S. -, 116 S.Ct. 701, 133 L.Ed.2d 657 (1996). Providing a false name or social security number certainly could, in a given situation, be material, but at trial in this case, the Government presented no evidence of the materiality of these statements to a matter within the jurisdiction of the FDIC. Accordingly, there was absolutely no factual basis upon which the court, pre-Gau-din, could have rested the legal conclusion that Ahmad’s statements to First Virginia were material to a matter within the FDIC jurisdiction. Indeed, the district court, as a matter of law, should have granted Ahmad’s motion for judgment of acquittal on the § 1001 count.
We reach this conclusion only after a painstaking review of the extensive trial record. The Government charged the four ap*61pellants with multiple crimes, which, in addition to the numerous structuring offenses, included one count of conspiring to defraud the Customs Service, fifteen counts of making false statements to the Customs Service, four counts of tax violations, and fifteen counts of money laundering. (The district court dismissed the money laundering counts for lack of evidence at the end of the Government’s ease.) The Government’s proof involved the testimony of more than a dozen witnesses and admission of over 300 exhibits.
Perhaps the single count of violating § 1001 was simply lost in this blizzard of other charges and evidence. Perhaps the Government intended to charge Ahmad with a § 1001 offense for making a false material statement in a matter within the jurisdiction of the Secretary of the Treasury, or the Internal Revenue Service to whom the CTRs were sent. Whatever the reason, the Government offered no evidence that Ahmad’s use of a false name and social security number on a bank signature card had a “natural tendency to influence” or was “capable of influencing” the FDIC. Arch Trading, 987 F.2d at 1095.
In fact, the only evidence in the record at all relevant to the § 1001 count is a Certificate of Proof of Insured Status and its attachments, establishing that First Virginia was a FDIC member institution during the relevant time period. This exhibit was admitted as a “self-authenticating document,” and the Government elicited no testimony whatsoever as to its significance. While the certificate may establish that Ahmad’s statements were made in a matter “within the jurisdiction of an agency of the United States,” a question we need not resolve here, it proves nothing about the materiality of the false information on the bank signature card.
Tellingly, the United States does not maintain that the FDIC certificate establishes the materiality of the false name and social security number. Nor does the Government claim that it presented any evidence of materiality at trial. Rather, the Government’s sole argument is that materiality is somehow established by reference, on appeal, to Congress’ pronouncement in 12 U.S.C. § 1829b that “adequate records maintained by insured depository institutions have a high degree of usefulness in criminal, tax, and regulatory investigations and proceedings,” and Congress’ further finding that “records kept by banks of the identity of persons maintaining ... accounts therein, have been of particular value in this respect.” 12 U.S.C. § 1829b(a)(1) (1994).
This argument fails. First, § 1829b’s general statement of legislative purpose does not establish the materiality of the false name or social security number on the bank signature card because § 1829b provides no link between these misstatements and “a matter within the jurisdiction” of the FDIC. Judge Easterbrook’s discussion of the evidence proffered in another § 1001 case involving the FDIC demonstrates this deficiency. See United States v. Kwiat, 817 F.2d 440, 445 (7th Cir.), cert. denied, 484 U.S. 924, 108 S.Ct. 284, 98 L.Ed.2d 245 (1987). There, an FDIC employee testified at trial that the agency sometimes referred to a particular HUD form to obtain information; on appeal the Government argued that a false statement on this HUD form “which helped conceal fiduciary fraud, was capable of influencing the decision of’ the FDIC. Id. (quoting the Government’s brief). But because “no witness at trial said this” and the FDIC employee “never linked” the FDIC’s procedures with the defendant’s misstatement, the Seventh Circuit found the evidence insufficient to establish that the particular false statement the defendant made on the HUD form was capable of influencing FDIC action. This same rationale requires rejection of the Government’s assertion that the § 1829b’s stated statutory purpose proves the materiality of the statements at issue here.
Moreover, the Government advances its claim that § 1829b provides evidence of materiality for the first time on appeal. The Government never proffered the statute as evidence to the district court. The Government never asked the district court to take judicial notice of the statute. Ahmad’s counsel specifically pointed out the total lack of *62evidence of materiality.4 Yet, even in the face of this statement, the Government failed to argue that § 1829b provided a basis for finding the false information on the bank signature card material, or indeed to offer any argument as to why Ahmad’s statement constituted a material misstatement in a matter within the jurisdiction of the FDIC. In sum, the Government has offered no evidence (and at trial did not even offer any argument) to establish that Ahmad’s misstatement was material to a matter within the jurisdiction of the FDIC.
Because the Government failed to present any evidence as to materiality, Ahmad’s conviction for violating § 1001 (Count 14) must be reversed.
III.
Appellants’ remaining arguments involve their convictions for violating 18 U.S.C. § 542 by overstating, on U.S. Customs documents, the value of imported merchandise.
Prior to 1980, the “value” of imported merchandise, for Customs purposes, was determined by reference to the market value of the goods in the country of manufacture. After 1980, value has been calculated in terms of “transaction value,” defined as “the price actually paid or payable for the merchandise.” 19 U.S.C. § 1401a(b)(1). “Price actually paid or payable” is further defined as “the total payment (whether direct or indirect, and exclusive of any costs, charges, or expenses incurred for transportation, insurance, and related services incident to the international shipment of merchandise ... ) made, or to be made, for imported merchandise by the buyer to, or for the benefit of, the seller.” 19 U.S.C. § 1401a(b)(4)(A). At trial, appellants relied on two eases to support their position that the invoices accurately reflected the transaction value of the goods imported.
In the first, Moss v. United States, 714 F.Supp. 1223 (Ct. Int’l Trade 1989), aff'd, 896 F.2d 535 (Fed.Cir.1990), the courts determined that the “buying commission” paid to a buying agent, included in the invoice price of the goods, constituted part of the goods’ transaction value, even though the commission was not technically payment “for the merchandise.” 896 F.2d at 539, 714 F.Supp. at 1227-28. That the payment of a buying commission benefited the buyer was held not to “detract from” the fact that the payment was “for the benefit of the seller” within the meaning of § 1401a. 896 F.2d at 539, 714 F.Supp. at 1228.
In the other case, Generra Sportswear Co. v. United States, 905 F.2d 377 (Fed.Cir.1990), an American importer purchased goods from a Hong Kong company. In order to ship the goods out of Hong Kong, the manufacturer had to purchase transfer quotas. The court held that the transaction price for the goods included the price the buyer’s agent paid to reimburse the manufacturer for the quotas. Id. at 379-80. The court held:
As long as the quota payment was made to the seller in exchange for merchandise sold for export to the United States, the payment properly may be included in the transaction value, even if the payment represents something other than the per se value of the goods. The focus is on the actual transaction between the buyer and the seller; if quota payments were transferred by the buyer to the seller, they are part of the transaction value.
Id. at 380.
A.
On appeal, appellants again rely on these two cases to bolster their argument that the inflated prices, appearing on the invoices and paid by Falcon, reflect the *63transaction value of the goods imported. These cases and § 1401a certainly stand for the proposition that transaction value may include more than the “actual price” of the merchandise. Nevertheless, the plain language of the statute clearly requires transaction value to relate to the acquisition of the merchandise — the transaction value is “the price actually paid or payable for the merchandise.” 19 U.S.C. § 1401a (emphasis added). Thus, in Moss, payment of the “commission” facilitated the buyer’s acquisition of the merchandise, and in Generra, purchase of the quotas was necessary to allow the purchase of the goods. In this ease, the amount by which appellants inflated the price of the surgical equipment did not in any way assist in Falcon’s acquisition of the equipment. Consequently, the invoice prices did not reflect the true transaction values.
Appellants argue that the inflated prices were a “condition imposed by” the Pakistani exporters. See Brief of Appellants at 37; Reply Brief at 14-15. If this were the ease, then the invoice prices would reflect the cost of acquiring the merchandise, and would qualify as the transaction values. There is, however, no evidence in the record to support this conclusion.
Although the Pakistani exporters derived some benefit from the inflated invoices, in the form of higher rebates from the Pakistani government, the evidence supports the conclusion that appellants initiated the inflated invoice scheme. For example, the Government introduced into evidence a letter on Falcon’s letterhead to a Pakistani exporter, signed by Ismail, referring to the pending end of the duty-free treatment of surgical supplies. The letter states that no “shipment will be acceptable which is overinvoiced and dispatched without any notice.” Ismail’s statement is totally at odds with a scenario in which the exporters controlled the relationship and insisted on the overinvoicing policy.
Alternatively, appellants rely on 19 U.S.C. § 1401a(b)(4)(B), which provides that in calculating the transaction value, customs officials should disregard any “rebate or decrease in price made or effected after the importation date.” In this ease, because the additional charges on the invoice were never part of the “price” of the goods, they do not qualify under § 1401a(b)(4)(B) as “rebates” or decreases in the purchase price. Moreover, the district court found that the actual purchase prices (and the inflated prices) were agreed upon before shipment. Thus, the reductions were not “made or otherwise effected between the buyer and the seller after the date of the importation of the merchandise into the United States.” 19 U.S.C. § 1401a(b)(4)(B) (emphasis added). Consequently, the invoice prices did not reflect the transaction value of the merchandise as defined by 19 U.S.C. § 1401a.
In sum, appellants’ use of the inflated invoice prices on Customs forms violated 18 U.S.C. § 542.
B.
Ahmad and Ahmed argue that the Government failed to offer sufficient evidence to support their numerous convictions for conspiring in and aiding and abetting Bashir and Ismail’s violations of § 542. Specifically, they argue that even assuming Ismail and Bashir made false statements to Customs, no evidence established that Ahmad and Ahmed knew about or participated in this scheme.
Contrary to these assertions, sufficient evidence supported their convictions for conspiracy and aiding and abetting Bashir’s and Ismail’s fraud on the Customs Service. This evidence of Ahmad’s and Ahmed’s participation includes records indicating that between February, 1991 and February, 1993, Ahmad and Ahmed transferred approximately $470,000 from their accounts into Falcon Instruments’ account. On several occasions, the amounts transferred exactly equalled the amounts of the “discounts” extended to Falcon by Pakistani exporters.
Furthermore, testimony at trial indicated that Ahmad once attempted to make a wire transfer on behalf of Falcon Instruments, and informed bank manager, Jenny Fadoul, that he was part of Falcon. When Fadoul refused to complete the transfer without some documentation of Ahmad’s relationship to the company, Ahmad simply substituted *64his own name for Falcon’s as the sender of the funds, and went ahead with the transfer to the originally intended recipient. On another occasion, Ismail informed a First Virginia employee that Ahmad was a relative of Ismail’s and affiliated with Falcon Instruments. Additionally, a signature card pertaining to Falcon’s account at First Virginia shows that Ahmed was once a signatory on the account, listed as “operations manager,” although he was later removed from the account and replaced by Bashir.
Thus, the Government clearly produced sufficient evidence to sustain the convictions of Ahmad and Ahmed for conspiracy and aiding and abetting in the scheme to make false statements to the Customs Service.
IV.
For the foregoing reasons, we reverse Ahmad’s convictions on Counts 1, 3-13, 14, and 51 and Ahmed’s conviction on Count 1. We affirm in all other respects.
Nos. 95-5299 and 95-5326 — AFFIRMED.
Nos. 95-5324 and 95-5325 — AFFIRMED IN PART, AND REVERSED IN PART.
. Unlike the defendants in Marder and Walker, the brothers themselves, not surrogates, made the deposits, usually in the same branch of a single bank. They did not even attempt to deal with different tellers. In fact, on many occasions the brothers dealt directly with the branch manager, Jenny Fadoul, the very person who had informed them of the reporting requirements in the first place. Ms. Fadoul even testified that on occasion, Ahmed “would come up to my desk and we would talk." Additionally, she testified that the brothers were familiar figures at the bank, and never acted surreptitiously when they came to make deposits. Although Ahmad was known to bank officials as Javed Iqbal, this was the name he had used in 1986 — almost four years before any structuring activity — to obtain a visa, a social security card, and a driver’s license, as well as to open his bank account; this was also the name he used in his currency exchange business, and thus any checks he deposited in connection with that business were made payable to Javed Iqbal; there is no evidence that he assumed this name to hide his structuring activity.
. The Government's argument — that Ahmad's post-arrest comments, including his statement that he never possessed more than $10,000 "in conducting currency transactions” proved he knew structuring violated the law — is meritless. If by this statement Ahmad meant that, after Fadoul advised him of the CTR requirement, he never brought $10,000 into the bank for deposit, the comment is literally correct. Moreover, even if this statement and others indicated an attempt to deny structuring, the fact that Ahmad attempted to deny structuring after being told that he was arrested for such conduct is minimally probative as to whether he knew structuring was illegal at the time he did it. Ratzlaf requires evidence that a defendant knew structuring violated the law when performing the structuring acts, not after his arrest for those acts. In conjunction with the abundant evidence that Ahmad did little to conceal the structuring at the time he did it (e.g. Fadoul's testimony that the brothers' structuring was clear "without a doubt”), Ahmad’s denial of structuring after learning that he had been arrested for it is insufficient to prove a willful violation beyond reasonable doubt.
. In view of this holding, we need not reach appellants’ alternative argument that the structuring convictions must be reversed because the indictment failed to allege specifically that appellants knew that structuring violated the law.
. Ahmad’s counsel argued:
Further, there's no evidence it was material. A statement is material when it has a natural tendency to influence action by the Government or is capable of doing so. And the Government has got the burden, just like putting the FDCI [sic] insurance certificate into evidence, they've got the burden of coming forward with some evidence as to how this is material to what the Government is doing or to what the FDIC is doing. They didn’t even ask the Court to take any judicial notice of anything. The record is devoid of any evidence as to how this was capable of influencing the Government or affecting any Government operation.
(emphasis added).