
520 F.3d 504 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Stephen P. MILLER, Defendant-Appellant.
No. 06-11078.
United States Court of Appeals, Fifth Circuit.
March 18, 2008.
*505 *506 *507 Marc Woodson Barta (argued), Dallas, TX, Vicki H. Lamberson, Asst. U.S. Atty., Amarillo, TX, Nancy E. Larson, Asst. U.S. Atty., Fort Worth, TX, for U.S.
Charles Howard Portz (argued), Portz & Portz, Houston, TX, for Miller.
Before HIGGINBOTHAM, DAVIS and SMITH, Circuit Judges.
PATRICK E. HIGGINBOTHAM, Circuit Judge:
A jury found Stephen Miller guilty of tax evasion in violation of 26 U.S.C. § 7201. Miller challenges the sufficiency of the evidence, as well as a number of the district court's evidentiary rulings. He also contends that the indictment was duplicitous. Finally, Miller raises a claim of Brady error. We affirm.

I
The jury could have concluded from the evidence the following. During the 1990s, Stephen Miller accumulated large tax deficiencies. According to the Government, Miller had tax liabilities  including deficiencies, penalties, and interests  of more than $2 million. Miller was associated with Charles Matich, a "financial planner." *508 Matich helped wealthy individuals like Miller decrease their tax exposure by moving their funds overseas. Matich's business came to an end when the Government seized his records in 2000 and then charged him with conspiracy to impede income tax collection and personal tax evasion. Matich pled guilty.
Miller had over $1 million in an Individual Retirement Account (IRA). Rather than satisfy his tax obligations, and fearful that the IRS might seize the funds, Miller and Matich concocted a scheme to protect the funds. In January 1999, Miller began transferring money from his IRA overseas to a shell company called Euromex Leasing Limited, which Miller had previously formed and Matich then controlled. Miller transferred approximately $600,000 under the guise of repaying a loan to Euromex. Matich arranged to have Euromex send Miller a "demand payment letter." After Miller had "repaid" the loan, Euromex sent Miller a letter saying his debt was satisfied. After Miller had "repaid" the loan, he continued transferring money from his IRA overseas to accounts controlled by Matich. He transferred more than $1 million from his IRA in 1999, and he did report the IRA withdrawals on his tax return. Unbeknownst to Miller until later, however, the money he transferred disappeared.
On March 25, 2000, the IRS received a Form 656 Offer in Compromise from Miller, in which he proposed settling his tax liabilities for $7,500. On the Offer form, Miller checked the box for "Doubt as to Collectibility  `I have insufficient assets and income to pay the full amount.'" Miller offered the following explanation: "At my age and unavailability of assets, I do not feel that I, nor my spouse, will live long enough to ever be able to pay the liabilities and additional taxes assessed on our account." The IRS requested more information. Miller submitted a Form 433-A, which stated that he had a checking account worth $15,000 and an IRA with a balance of $25,000; Miller did not list any foreign accounts. The IRS again requested more information, and specifically asked about the money withdrawn from his IRA. Miller responded that he used the funds to repay the Euromex loan, and further explained, "I have no idea what happened to the proceeds. I assume the funds were repaid to the lenders of the funds." Miller repeated the story again in a subsequent correspondence with the IRS:
I repaid those loans back to a Euromex Leasing corporation formed in the Isle of Mann which had invested in some disastrous investments in Mexico in which I lost $1,000,000 and was personally responsible for. . . . These funds represented return of principal and interest on funds borrowed. I have absolutely no idea what the present officers of that corporation have done with those proceeds. I do not have these funds nor do I have access to them.
Subsequent to the submission of the Offer, Matich, who was working with the Government, called Miller. Investigators recorded the conversation. A fair interpretation of the call is that Miller transferred the money to shield it from the IRS, believed the money was still his, and wanted it back. The call indicated that Miller was only then learning that his money was gone. Miller and Matich also discussed how they could characterize their various transactions if questioned.
Miller was charged with one count of tax evasion in violation of 26 U.S.C. § 7201. The Government's theory was that Miller's Offer in Compromise constituted an attempt to evade his income taxes in that he lied by stating that because of unavailability of assets he could only pay $7,500 to *509 satisfy his tax liabilities. This was a lie because Miller believed that he had over $1 million overseas, which he did not reveal to the IRS. The case went to trial, and Matich testified as a Government witness. The jury found Miller guilty, and the district court sentenced him to 46 months' imprisonment and three years supervised release, and ordered him to pay $968,836.27 in restitution. Miller appealed.
After Miller filed his opening brief, the Assistant U.S. Attorney notified him that she had become aware of a criminal referral involving Matich by the U.S. Trustee in Montana. The referral referenced the Government's possession of Matich's business records. We abated Miller's appeal so he could file a motion for a new trial in the district court. Miller did so, arguing that the Government violated Brady by failing to disclose the criminal referral and turn over all of Matich's business records. The district court denied Miller's motion, and he filed a supplemental brief in this court raising the Brady issue.

II
Miller challenges the sufficiency of the evidence. We review the evidence in the light most favorable to the Government, drawing all reasonable inferences and credibility determinations in favor of the jury's verdict.[1] "If any rational trier of fact could have found proof of the essential elements of the crime beyond a reasonable doubt, the verdict will stand."[2]
26 U.S.C. § 7201 provides that "[a]ny person who willfully attempts in any manner to evade or defeat any tax imposed by this title or the payment thereof shall . . . be guilty of a felony." "The crime of tax evasion as defined in 26 U.S.C. § 7201 has three essential elements: (1) the existence of a tax deficiency; (2) willfulness; and (3) an affirmative act constituting evasion or attempted evasion of the tax."[3] "[W]illfulness is `a voluntary, intentional violation of a known legal duty.' Evidence is usually circumstantial as direct proof is rarely available."[4] Many kinds of conduct can constitute a willful attempt to evade taxation:
keeping a double set of books, making false entries or alterations, creating false invoices or documents, destroying books or records, concealing assets or covering up sources of income, handling one's affairs to avoid making the records normally accompanying transactions of a particular kind, any conduct likely to mislead or conceal, holding assets in others' names, providing false explanations, giving inconsistent statements to government agents, failing to report a substantial amount of income, a consistent pattern of underreporting large amounts of income, or spending large amounts of cash that cannot be reconciled with the amount of reported income.[5]
There is no question that Miller had a tax deficiency. Miller's argument is a hybrid of the second and third elements: he claims that the Government failed to prove that he had access to, or control of, the money he transferred out of his IRA and, therefore, his Offer in Compromise, which was based on his claim of unavailability of assets, was not fraudulent. Put differently, the Government failed to prove that the *510 funds he transferred were "available" to him. This proof, his argument goes, is necessary for conviction. We are not persuaded.
Where Miller's money was located, and who had access to and control of it, matters, on the facts here, only to the extent that it bears on Miller's knowledge and belief as to the state of his financial affairs when he submitted his Offer; that is, what Miller's intent was in submitting his Offer.
The evidence was sufficient for the jury to conclude that when Miller submitted his Offer, he believed that he had $1 million squirreled away overseas. The recorded phone call with Matich, which occurred after submission of the Offer, makes clear that Miller continued to believe that the money he transferred was his. The call further reveals that, while Miller had an inkling that there was a problem with his money, he did not know his money was in fact gone. Moreover, Miller's responses to the IRS's requests for further information after he submitted his Offer are compelling evidence that he was trying to hide his assets from the IRS. Miller did not say that the money transferred from his IRA had disappeared or that he could not retrieve it; rather he twice told the IRS that he used the money to satisfy the fictitious Euromex loan obligation, which Miller knew did not exist and, in fact, had helped to concoct.
The irony in Miller's argument is that he transferred his money to Matich precisely because he believed this would shield it from the IRS. Despite his understanding that he had $1 million overseas, Miller stated in his Offer that he could only afford to pay $7,500 in satisfaction of his tax liabilities. One can understand his submission of the Offer as, inter alia, "concealing assets," "conduct likely to mislead or conceal," "providing false explanations," or some combination thereof. The Government proved the required affirmative act.
The Government also introduced sufficient evidence to support a finding of willfulness, including admissions made by Miller during the recorded phone call; Miller's statements to the IRS, both written and oral, including his telling the IRS that he used the IRA funds to pay off the fictitious Euromex debt; and, other documentary evidence, such as Miller's and Matich's various letters, emails, and faxes.
There is sufficient evidence to support the jury's verdict.

Ill
Miller challenges some of the district court's evidentiary rulings. We review the district court's evidentiary ruling for abuse of discretion.[6] "If this court finds an abuse of discretion in admitting or excluding evidence, this court will `review the error under the harmless error doctrine, affirming the judgment, unless the ruling affected substantial rights of the complaining party.'"[7]

A
Miller argues that the district court erred by limiting the testimony of his witness, Donald Williams, a former IRS employee. The district court ruled that it would exclude three areas of Williams's testimony: (1) because Miller's Offer was "incomplete," the IRS ran afoul *511 of its internal policies by assigning it to an offer specialist; (2) the offer specialist assigned to Miller's Offer was unusually knowledgeable; and, (3) Williams's opinion regarding whether Miller had access to the funds that were transferred to Euromex when Miller submitted his Offer.
The first and second areas of testimony are plainly irrelevant. Rule 402 provides that "[e]vidence which is not relevant is not admissible." Rule 401 defines "relevant evidence" as "evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence." Neither the IRS's adherence to its internal procedures nor the offer specialist's knowledge bears upon what Miller did, knew, or intended. The testimony is not probative of any fact of consequence and was properly excluded.
Assuming Williams's opinion about Miller's access to the money is relevant, the exclusion was harmless. The excluded evidence does not bear on the contested issue at trial: Miller's intent in submitting his Offer. Williams would have testified only that he believed Miller did not have access to the money when he submitted his Offer because the documents Williams reviewed did not show where the money was or even if it still existed. Williams would not have testified about what Miller knew.
Moreover, Matich testified that the money "disappeared" shortly after Miller transferred it, which of course means that Miller could not access it. The evidence further demonstrated that Matich had control of the overseas bank accounts into which the money was transferred. Finally, the evidence of Miller's guilt was substantial. The "exclusion was harmless because it could not have affected the jury's determination [on] any of the charged counts."[8]

B
Miller next urges that the district court erred by admitting evidence of a past act of his under Rule 404(b). Our review of the admission of Rule 404(b) evidence is "heightened."[9] The Rule provides that
[e]vidence of other crimes, wrongs, or acts is not admissible to prove the character of a person in order to show action in conformity therewith. It may, however, be admissible for other purposes, such as proof of motive, opportunity, intent, preparation, plan, knowledge, identity, or absence of mistake or accident. . . .
Our decision in United States v. Beechum creates a two-step inquiry for analyzing the admissibility of Rule 404(b) evidence. "`First, it must be determined that the extrinsic offense evidence is relevant to an issue other than the defendant's character. Second, the evidence must possess probative value that is not substantially outweighed by its undue prejudice and must meet the other requirements of [R]ule 403.'"[10]
The district court admitted evidence that in 1997 Miller opened a bank account under a false name and with fraudulent identification for the purpose of, as Miller euphemistically told investigators, "financial *512 privacy." Miller had attempted to deposit $5,000 in cash in the account. The evidence was admitted as intent evidence.
A large part of Miller's defense turned on his mental state, that he lacked an unlawful intent in submitting his Offer. Miller also based his defense on a claim that he was innocently following Matich's orders. Yet, in 1997, Miller was caught attempting to hide money under false pretenses, and he did so, according to Matich's testimony, even though Matich told him not to. Miller's acts in 1997, therefore, are probative of his intent.
Miller argues that the past act is too remote in time to be admissible. While the length of time is relevant to our analysis, the past acts occurred shortly before Miller began transferring money from his IRA and his involvement in developing the sham Euromex loan, the course of conduct that culminated in Miller's submission of his Offer. And, there were common actors, Miller and Matich, involved in both schemes. The time lapse on these facts does not render the past acts inadmissible.[11] Nor was the other evidence of Miller's intent so substantial that it was error to admit the past acts. Thus, the evidence was relevant to an issue other than Miller's character, and its probative value was not substantially outweighed by undue prejudice.
Finally, the district court instructed the jury  orally after the jury heard the evidence and in its written charge  that the evidence could be used only for the limited purpose of evaluating Miller's intent, which minimizes any prejudicial effect.[12] Accordingly, the district court did not abuse its discretion.

IV
Miller contends that the indictment is duplicitous because it describes both the transfer of money from his IRA and the submission of his Offer, which created the danger of a nonunanimous verdict. Miller's argument runs thus. The Government, under its theory of the case, had to prove that Miller's submission of his Offer was the affirmative act of evasion. But, because of the wording of the indictment, some jurors might have viewed Miller's transfer of money as the affirmative act while others viewed his submission of his Offer as the affirmative act. Thus, there is a danger of a nonunanimous verdict.
We review de novo a claim that an indictment is duplicitous.[13] Duplicity occurs when a single count in an indictment contains two or more distinct offenses.[14] Even if an indictment is duplicitous, a defendant must be prejudiced to receive relief;[15] the risk of a nonunanimous *513 verdict is one recognized source of prejudice,[16] and it is the only prejudice Miller alleges. Assuming that the indictment is duplicitous, an assumption that is not without problems, there was no danger of a nonunanimous verdict.
"The danger of a nonunanimous jury verdict may be avoided by proper jury instructions."[17] The district court instructed the jury that
[t]he phrase "attempts in any manner to evade or defeat any tax" involves two things: first, the formation of an intent to evade or defeat a tax; and, second, willfully performing some act to accomplish the intent to evade or defeat that tax.
The phrase "attempts in any manner to evade or defeat any tax" contemplates and charges that the Defendant knew and understood that during the calendar years 1993, 1995, 1996, and 1997, he owed a substantial additional federal income tax and then tried in some way to avoid that additional tax.
In order to show "attempts in any manner to evade or defeat any tax," therefore, the government must prove beyond a reasonable doubt that the Defendant Miller intended to evade or defeat the tax due, and that the Defendant Miller also willfully submitted the Offer in Compromise in order to accomplish this intent to evade or defeat that tax. (emphasis added)
The court did not simply charge the jury that it had to find that Miller committed "an act" to accomplish his unlawful intent; rather, the instruction specifically required that the jury find that Miller's submission of his Offer was the affirmative act of evasion. The jury also received a general unanimity instruction. The instructions thus required the jury to agree unanimously that the Government proved beyond a reasonable doubt that Miller willfully submitted the Offer to accomplish his intent of evading his taxes. In other words, the jury was required to find exactly what Miller says the Government had to prove.
Miller contends that the instructions are insufficient because "one without a legal mind" could have voted to convict based on Miller's transfer of money from his IRA. This argument is without merit. The "legal mind" does not describe a closed universe of intelligence, and certainly not common sense. The instructions were plainly worded and clear. The instructions dovetailed with the Government's theory of the case and squarely framed the contested issue at trial: whether Miller willfully *514 submitted his Offer to accomplish his intent to evade his tax obligations. Indeed, during closing the Government succinctly explained to the jury that "in order to convict, you must find beyond a reasonable doubt . . . that there was an affirmative attempt to evade  in this case, it's the submission of the Offer in Compromise  and, third, that the Defendant made the affirmative attempt in a willful manner." Because Miller was not prejudiced, his duplicity claim fails.

V
Finally, we turn to Miller's allegation of Brady error. "While the standard of review for a motion for a new trial is typically abuse of discretion, if the reason for the motion is an alleged Brady violation then we review the district court's determination de novo."[18] We have cautioned that, as we review Brady claims "at an inherent disadvantage" because of the cold record, we must accord due deference to the trial court's ruling on the alleged Brady error.[19]
To make out a Brady violation, "a defendant must show that (1) evidence was suppressed; (2) the suppressed evidence was favorable to the defense; and (3) the suppressed evidence was material to either guilt or punishment."[20] "Evidence is material under Brady when there is a `reasonable probability' that the outcome of the trial would have been different if the suppressed evidence had been disclosed to the defendant."[21] The Supreme Court has explained that
the materiality inquiry is not just a matter of determining whether, after discounting the inculpatory evidence in light of the undisclosed evidence, the remaining evidence is sufficient to support the jury's conclusions. Rather, the question is whether "the favorable evidence could reasonably be taken to put the whole case in such a different light as to undermine confidence in the verdict."[22]
"When there are a number of Brady violations, a court must analyze whether the cumulative effect of all such evidence suppressed by the government raises a reasonable probability that its disclosure would have produced a different result."[23] Impeachment evidence falls within Brady's reach.[24]
Miller bases his claim on the criminal referral letter sent by the Office of the U.S. Trustee to the U.S. Attorney in Montana regarding Matich's petition for bankruptcy. The letter references the Government's possession of Matich's business records, not all of which were given to Miller. We agree with the district court that, assuming the evidence was suppressed, Miller has failed to establish a "reasonable probability" that the outcome of trial would have been different had the evidence been disclosed.
Miller claims that the evidence would have established beyond peradventure that Matich had control of his money. However, this would have been cumulative of *515 other evidence introduced at trial. "`[W]hen the undisclosed evidence is merely cumulative of other evidence [in the record], no Brady violation occurs.'"[25] The trial evidence established that Miller's money "disappeared" soon after Miller transferred it overseas, which of course means Miller had no access to it; that Matich controlled the overseas bank and trust accounts; and that Miller wanted his money overseas and out of his control so the IRS could not seize it. More fundamentally, that Matich may have stolen Miller's money, as opposed to someone else stealing it or the banks losing it, and how Matich stole the money is relevant only to the extent that it sheds light on what Miller knew and intended when he submitted his Offer. Miller has not shown that the suppressed evidence speaks to these critical issues.
Miller also contends that his ability to cross-examine Matich was impeded by his lack of access to the suppressed evidence. It is true that Matich's testimony was less than a paradigm of specificity. But Miller's allegations regarding the value of the suppressed documents are, as the district court noted, "conclusory," and some of those allegations are flatly contradicted by the record. Even assuming the-documents could fill factual gaps in Matich's testimony, those details would not bear on what Miller did, knew, and intended  the documents would have revealed what Matich did and knew. And, while Miller states, without any elaboration, that the documents would reveal his good-faith reliance on Matich's advice, the trial evidence reveals that Miller was a full partner in the scheme, developing it alongside of Matich and fully aware of what he was doing.
Nor does the impeachment value of the evidence establish materiality. Although the suppressed evidence may well have impeached Matich's testimony about what happened to Miller's money after Miller transferred it overseas and Matich's financial holdings, that does not touch upon the critical issues at trial: what Miller did and intended. Moreover, Miller probed Matich's credibility at trial, examining him based on his guilty plea, his plea agreement and cooperation with the Government, his financial holdings, and his control of his clients', including Miller's, money.
Wholly apart from Matich's testimony, there was a substantial body of evidence establishing Miller's guilt that is left unscathed by the suppressed evidence, including, Miller's admissions in the recorded phone call; Miller's statements, both written and oral, to the IRS regarding why he transferred the money; Miller's acts in 1997; and the documentary evidence presented by the Government.[26] While the criminal-referral letter would have presented Miller a new angle from which to impeach Match, the impeachment value of the evidence does not cast sufficient, if any, doubt on the verdict.
The cumulative effect of the suppressed evidence does not undermine confidence in the verdict, and therefore, Miller's Brady claim fails.

VI
Accordingly, we AFFIRM.
NOTES
[1]  United States v. Bishop, 264 F.3d 535, 549 (5th Cir.2001).
[2]  Id.
[3]  Id. at 545.
[4]  Id. at 550 (quoting United States v. Kim, 884 F.2d 189, 192 (5th Cir.1989)) (citations omitted).
[5]  Id.
[6]  United States v. Sharpe, 193 F.3d 852, 867 (5th Cir.1999).
[7]  United States v. Ragsdale, 426 F.3d 765, 774-75 (5th Cir.2005) (quoting Bocanegra v. Vicmar Servs., Inc., 320 F.3d 581, 584 (5th Cir.2003)).
[8]  United States v. Harms, 442 F.3d 367, 377 (5th Cir.2006), cert. denied, ___ U.S. ___, 127 S.Ct. 2875, 167 L.Ed.2d 1152 (2007).
[9]  United States v. Mitchell, 484 F.3d 762, 774 (5th Cir.2007), cert. denied, ___ U.S.___, 128 S.Ct. 297, 169 L.Ed.2d 212 (2007), and cert. denied, ___ U.S. ___, 128 S.Ct. 869, 169 L.Ed.2d 736 (2008).
[10]  Id. (quoting United States v. Beechum, 582 F.2d 898, 911 (5th Cir.1978) (en banc)).
[11]  See United States v. Arnold, 467 F.3d 880, 885 (5th Cir.2006) ("We have upheld the admission of Rule 404(b) evidence where the time period in between was as long as 15 and 18 years."), cert. denied, ___ U.S. ___, 127 S.Ct. 2445, 167 L.Ed.2d 1144 (2007); United States v. Adair, 436 F.3d 520, 527 (5th Cir. 2006) ("Third, Adair's prior money-laundering scheme was temporally significant [under Rule 404(b)], as it occurred less than three years before the conduct at issue in the instant appeal."), cert. denied, 547 U.S. 1155, 126 S.Ct. 2306, 164 L.Ed.2d 826 (2006).
[12]  See, e.g., Adair, 436 F.3d at 527 (explaining that one reason the admitted Rule 404(b) evidence "had little opportunity of creating unfair prejudice" was that "the district court mitigated any prejudicial effect by giving the jury a limiting instruction").
[13]  United States v. Caldwell, 302 F.3d 399, 407 (5th Cir.2002).
[14]  Id.
[15]  See, e.g., United States v. Lampazianie, 251 F.3d 519, 526 (5th Cir.2001) ("We have held that even when an indictment is duplicitous, reversal is not required if no prejudice results."); United States v. Baytank (Houston), Inc., 934 F.2d 599, 608 (5th Cir.1991) ("If an indictment is duplicitous and prejudice results, the conviction may be subject to reversal.").
[16]  See United States v. Cooper, 966 F.2d 936, 939 n. 3 (5th Cir.1992) ("The ban against duplicitous indictments derives from four concerns: prejudicial evidentiary rulings at trial; the lack of adequate notice of the nature of the charges against the defendant; prejudice in obtaining appellate review and prevention of double jeopardy; and risk of a jury's nonunanimous verdict." (emphasis added)).
[17]  United States v. Fisher, 106 F.3d 622, 633 (5th Cir.1997), abrogated in part on other grounds by Ohler v. United States, 529 U.S. 753, 120 S.Ct. 1851, 146 L.Ed.2d 826 (2000); see also Baytank (Houston), Inc., 934 F.2d at 609 ("Thus, the complaint comes down to whether the jury instructions were sufficient, as it is clear that this aspect of a duplicity problem [danger of a nonunanimous verdict] can be cured by appropriate special instructions which, for example, inform the jury that it must unanimously agree on the specific basis (e.g., a given date or the like) on which it finds the defendant guilty under the count in question.").
[18]  United States v. Martin, 431 F.3d 846, 850 (5th Cir.2005).
[19]  United States v. Sipe, 388 F.3d 471, 479 (5th Cir.2004).
[20]  United States v. Runyan, 290 F.3d 223, 245 (5th Cir.2002).
[21]  Id.
[22]  Strickler v. Greene, 527 U.S. 263, 290, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999) (quoting Kyles v. Whitley, 514 U.S. 419, 435, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995)) (citations omitted).
[23]  Sipe, 388 F.3d at 478.
[24]  Id. at 477, 478.
[25]  Id. at 478 (quoting Spence v. Johnson, 80 F.3d 989, 995 (5th Cir.1996)).
[26]  See United States v. Weintraub, 871 F.2d 1257, 1262 (5th Cir.1989) ("Courts have found, for example, that impeachment evidence improperly withheld was not material where the testimony of the witness who might have been impeached was strongly corroborated by additional evidence supporting a guilty verdict.").
