Thomas Carruth and Jackson Reed appeal their conviction for conspiracy to defraud the United States in violation of 18 U.S.C. § 371 . Both appellants contend that they were impermissibly prejudiced by the government’s delay in seeking an indictment. Carruth also claims that there was a variance between the indictment and his conviction, that the evidence was insufficient to sustain a conviction, and that the district court erred in two evidentiary rulings. We reject these arguments and affirm.

FACTS

Appellants were indicted in February, 1981, by a federal grand jury for tax fraud in connection with the operation of limited partnership tax shelter schemes. According to the indictment, Carruth, through his wholly-owned corporation, Thomas A. Carruth, Sr. and Associates, Inc. (TAC), syndicated over 100 limited partnerships to engage in cattle breeding. TAC contracted with Reed, or with corporations owned or controlled by Reed, to acquire cattle, and to feed and manage the herds for the limited partnerships. The indictment charged that Carruth and Reed used Reed’s corporations to create the appearance of and documentation for nonexistent cattle, feed purchases, and loans to the partnerships. Carruth, as general partner, signed and filed federal income tax returns for the partnerships, and caused a Schedule K-l to be prepared for each limited partner for the taxable years 1971-1974. These tax forms reflected the nonexistent transactions.

Reed, joined later by Carruth, made a timely motion to dismiss the indictment, alleging that pre-indictment delay had prejudiced the defense. The district court refused to grant the motion. Carruth and Reed were convicted after a jury trial in January, 1982, and each was sentenced to three years’ imprisonment. They appeal.

II.

PRE-INDICTMENT DELAY

A pre-indictment delay may lead to the denial of a defendant’s right to due process of law. United States v. Lovasco, 431 U.S. 783 , 97 S.Ct. 2044 , 52 L.Ed.2d 752 (1977). In considering whether a pre-indictment delay requires the dismissal of an indictment, a court must first determine whether the defendant suffered actual prejudice because of the delay. United States v. Swacker, 628 F.2d 1250, 1254 (9th Cir. 1980). The defendant bears the burden of establishing actual prejudice, and the proof must be definite, not speculative. United States v. Mills, 641 F.2d 785, 788 (9th Cir.), cert. denied, 454 U.S. 902 , 102 S.Ct. 409 , 70 L.Ed.2d 221 (1981). If prejudice is shown, the court must then consider the reasons for and length of the delay. Id.

A. Carruth’s Claims

Carruth contends that he suffered actual prejudice as a result of the pre-indictment delay because he destroyed many of his personal and business records following his bankruptcy in 1978, and because Harold Cardwell, TAC’s accountant, died shortly before the indictment, and therefore could not testify on Carruth’s behalf. The district court found that these contentions did not amount to a showing of actual prejudice. We agree.

First, Carruth failed to demonstrate that the lost records or Cardwell’s testimony would have exonerated him. The government’s case rests on the assumption that Carruth and Reed created documentation for nonexistent transactions involving the syndicates’ cattle breeding operations. Carruth has made no showing that the missing records would have proved that the transactions really did take place. Cf. United States v. Kendrick, 692 F.2d 1262, 1267 (9th Cir.1982).

Moreover, the evidence does not indicate that Carruth destroyed his records because of the pre-indictment delay. Carruth testified that the records were destroyed sometime between June 29, 1978, and August 8, 1978. The destruction took place after Carruth had met with an IRS special agent, and had been served with one, and possibly two, summonses for those records. To allow Carruth’s prejudice claim here would be to hold that those under criminal investigation have a right to destroy documents and then to argue that they are prejudiced because the documents are unavailable to support their defense. This we refuse to do.

Finally, according to government agents who interviewed him, Cardwell’s testimony would have been limited to his examination of the TAC files, and would not have encompassed the underlying transactions on which the convictions were based. It is difficult to see how Cardwell could have exonerated Carruth, and we cannot overturn an indictment on mere speculation that missing evidence would have contained exculpating material. United States v. West, 607 F.2d 300, 304-05 (9th Cir.1979).

B. Reed’s Claim

On May 5, 1980, the Criminal Section of the Department of Justice Tax Division sent Reed a letter informing him that his case was being transferred to the IRS. According to Reed’s testimony, he then wrote to the Tax Division for an explanation of the letter. The Tax Division, however, viewed Reed’s letter as a request for an interpretation of the Tax Division’s reference number code system, and answered accordingly. Reed then destroyed his business records. Reed contends that his destruction of the business records was done in reasonable reliance on the Tax Division’s letters, and that he suffered actual prejudice as a result of the destruction of the records.

As was the case with Carruth, the district court found no actual prejudice as a result of the destruction of the records. We affirm.

First, it is obvious that the loss of the records was due to Reed’s mistaken interpretation of the Tax Division’s letters, and not to the delay in bringing the indictment. A reasonable person would, at least, have sought legal advice or further clarification from the Tax Division of its letters before destroying any records, especially since the May 5 letter informed Reed that he was still under investigation by the IRS.

Second, in 1977, IRS agents had microfilmed Reed’s records. These were made available to Reed in preparation for trial. Reed claims, however, that the microfilmed records were not properly organized. This claim is frivolous. The records were Reed’s own business records, and he should have been in a better position than the IRS to organize them. In addition, there is no indication that the records were organized before they were microfilmed.

Reed also argues that some documents were missing from the IRS microfilms. This statement is contradicted by the testimony of the IRS agents that they had microfilmed all of the records. Moreover, Reed admitted that some of the records were lost due to his own carelessness before the IRS agents had copied them. Finally, Reed testified at trial as to the contents of the records, and failed to show that the presence of the missing records would have done more to exonerate him. See United States v. West, 607 F.2d 300, 304-05 (9th Cir.1979).

Because we find that there was no actual prejudice to Carruth or to Reed, we need not balance the prejudice suffered by the defendants against the reasons for and length of the pre-indictment delay. United States v. Mills, 641 F.2d 785, 789 (9th Cir. 1981). We note, however, that the delay was caused by the unusual complexity of the tax shelter transactions involved in Carruth and Reed’s operations and not by the government’s intentionally or recklessly delaying the indictment to gain a tactical advantage, as is normally necessary for a defendant to prevail in a pre-indictment claim. Id. at n. 2. Also, the three year delay in this case from the beginning of the criminal investigation to the return of the indictment was not inordinate, given the difficulty of unraveling the defendants’ schemes. Cf. United States v. Mays, 549 F.2d 670 (9th Cir.1977) (no due process violation from four and one-half year delay).

III.

CARRUTH’S OTHER CLAIMS

A. Variance

The indictment alleged that Reed and Carruth conspired to defraud the United States in violation of 18 U.S.C. § 371 , “by impeding, impairing, disrupting and defeating the lawful Governmental functions of the Internal Revenue Service in the ascertainment, computation, assessment and collection of the revenue.”

Carruth claims that there was a variance between the indictment and the evidence presented at trial. He urges that the evidence did not amount to a conspiracy to defraud the United States, but encompassed at most a civil action for fraud on the investors. Moreover, Carruth contends that the government’s fraud claim is based on the notion that Carruth and Reed conspired to force the IRS to audit the tax returns of the limited partners, and that the evidence did not show that Carruth and Reed had the requisite intent to commit such a fraud. Finally, Carruth argues that to be guilty of a conspiracy to defraud the United States, he must have conspired to receive benefits directly from the United States, whereas Carruth and Reed sought benefits not for themselves, but for the tax shelter investors. These arguments are without merit.

First, the defendants were in the business of “selling” tax shelters, which had as their purpose the reduction or elimination of the investors’ tax burden. The evidence showed that Carruth and Reed knew that the deductions that the limited partners would take on their tax returns were based in large part on nonexistent transactions, and that the Treasury would be deprived of substantial sums m tax revenues as a result.

Second, the conspiracy described in the indictment was not limited to causing the IRS to devote resources to auditing the limited partners — although this did occur, and was the logical result of a tax shelter fraud on the scale of the present one — but included “defeating” the lawful collection of tax revenues. As noted above, the evidence shows that this was the defendants’ intent in putting together their tax shelter schemes.

Finally, a conspiracy against the United States can encompass transactions such as the present ones, in which the conspirators do not realize benefits directly from the United States, but conspire to defraud the United States for the direct benefit of others and the indirect benefit of themselves. See, e.g., United States v. Winograd, 656 F.2d 279 (7th Cir.1981), cert. denied, 455 U.S. 989 , 102 S.Ct. 1612 , 71 L.Ed.2d 848 (1982) (upholding conviction under 18 U.S.C. § 371 of commodities broker who operated illegal tax straddle to reduce the tax burden of an investor).

B. Sufficiency of the Evidence

Carruth claims that there was insufficient evidence presented at trial to support his conviction under 18 U.S.C. § 371 for conspiracy to defraud the United States. He contends that in preparing Schedule K-l forms for the limited partnerships, he merely relied on information supplied to him by Reed, and that he had no reason to doubt Reed’s word. Therefore, Carruth argues, he lacked knowledge of any fraudulent activities of Reed, and did not agree with Reed to participate in a conspiracy. The jury verdict against Carruth must be sustained, however, if, viewing the evidence in the light most favorable to the government,- a reasonable jury could find the defendant guilty beyond a reasonable doubt. United States v. Universal Trade and Industries, Inc., 695 F.2d 1151, 1153 (9th Cir.1983). After examining the record, we conclude that there was sufficient evidence to support the jury’s verdict.

The evidence shows that Carruth had a long-term exclusive business arrangement with Reed and with corporations owned or controlled by Reed. The evidence also establishes that there was a circular flow of money through the Reed entities and back to Carruth’s partnerships, and that Carruth was aware of this money flow. Finally, the evidence indicates that Carruth was responsible for creating documentation for illusory cattle and feed purchases and loans, as well as the partnership income tax returns, and that Carruth actively concealed the nature of the partnership transactions from the investors. While this evidence is merely circumstantial, circumstantial evidence can be sufficient to support a conviction for conspiracy to defraud, as is the case here. Cf. United States v. Sears, 663 F.2d 896, 905 (9th Cir.1981), cert. denied, 455 U.S. 1027 , 102 S.Ct. 1731 , 72 L.Ed.2d 148 (1982).

C. Evidentiary Claims

Carruth contends that the district court committed reversible error by admitting into evidence Carruth’s personal income tax returns for 1973 and 1974, testimony concerning statements made under oath to the IRS agent by Harold Cardwell, Carruth’s accountant, shortly before Cardwell’s death, as well as testimony about Cardwell’s statements to the TAC employees. We review these claims under an abuse of discretion standard, see United States v. Patterson, 678 F.2d 774, 778 (9th Cir.), cert. denied, - U.S. -, 103 S.Ct. 219 , 74 L.Ed.2d 174 (1982), and hold that the district court did not abuse its discretion in making these rulings.

The income tax returns are admissible under Fed.R.Evid. 404(b) to show Carruth’s intent to defraud, and to impeach his testimony. Under cross-examination, Carruth admitted that he had bank accounts in Mexico and Bermuda during 1973 and 1974, but claimed that the accounts were inactive. The prosecutor used Carruth’s 1973 and 1974 income tax returns, which stated that he had no foreign bank accounts, to refresh Carruth’s memory. The government later offered bank records to show that the accounts were very active during those years, as well as the tax forms to indicate that Carruth intended to defraud the United States.

Carruth argues, however, that even if the tax returns were admissible under Rule 404(b), the district court should have excluded the tax returns as being prejudicial under Fed.R.Evid. 403, and erred by failing to enunciate its reasons for rejecting Carruth’s prejudice objection. We disagree. Our reading of the record shows that the district court did not abuse its discretion in rejecting Carruth’s Rule 403 claim. Moreover, while the district court normally must present more than a “mechanical recital” of the factors of probative value and prejudice in striking a Rule 403 balance, see United States v. Mehrmanesh, 689 F.2d 822, 830 (9th Cir.1982), where, as is the case here, the record indicates that the district court engaged in a Rule 403 balance, the demands of that rule have been met. United States v. Sangrey, 586 F.2d 1312, 1315 (9th Cir. 1978).

Carruth also argues that the testimony of an IRS agent and TAC employees relating statements made by Harold Card-well was inadmissible hearsay. This contention fares no better than the Rule 403 claim. Cardwell’s statements indicate that he had prepared the partnerships’ tax re turns without examining the underlying documentation, and that he prepared tax returns knowing that the cattle and feed figures listed on them were highly inflated. These are statements against interest, the declarant being unavailable, and are therefore admissible under Fed.R.Evid. 804(b)(3).

The judgment of the district court is affirmed.

AFFIRMED.

. The district court found that the government was not negligent in delaying the defendants’ indictment. That finding was not clearly erroneous, and we therefore decline to disregard it. . 18 U.S.C. § 371 provides in part: If two or more persons conspire to commit any offense against the United States, or to defraud the United States, or any agency thereof in any manner or for any purpose, and one or more of such persons do any act to effect the object of the conspiracy, each shall be fined not more than $10,000 or imprisoned not more than five years, or both. . Carruth did not raise the variance argument at trial. We address the variance issue here, however, on the assumption that it was subsumed in Carruth’s sufficiency of the evidence claim. . Carruth contended at oral argument that his tax shelter syndicates did not deprive the United States of revenues, since, had his tax shelters been unavailable, the investors would have put their money into another tax avoidance scheme. We emphatically reject this argument. It assumes — as we cannot do — that every investor would have found a legitimate tax shelter for each of the years in question. Moreover, taking Carruth’s argument to its logical conclusion, anyone guilty of fraud could seek a reversal of his conviction by contending that if he had not defrauded the victim, someone else would have done so. . Reed apparently also argues in his Reply Brief that the evidence presented was insufficient to sustain his conviction. However, Reed waived this claim by failing to present it in his opening brief. Fed.R.App.P. 28. We note that even were we inclined to invoke Fed.R.App.P. 2 to waive Reed’s default, see United States v. Anderson, 584 F.2d 849, 853 (6th Cir.1978), we would find that the evidence against Reed was sufficient to support the jury verdict against him.