Bernard J. Ebbers appeals from his conviction by a jury on nine counts of conspiracy, securities fraud, and related crimes and from the 25-year jail sentence imposed by Judge Jones.

Ebbers was the Chief Executive Officer ("CEO") of WorldCom, Inc., a publicly traded global telecommunications company. During the pertinent times—from the close of the fourth quarter of the 2000 fiscal year through the first quarter of the 2002 fiscal year—he engineered a scheme to disguise WorldCom's declining operating performance by falsifying its financial reports. Although the scheme was multifaceted, the fraud primarily involved the treating of hundreds of millions of dollars of what had always been recorded operating costs as capital expenditures for several fiscal quarters. After a seven week trial, the jury convicted Ebbers on all counts. He was sentenced to 25 years' imprisonment, to be followed by 3 years' supervised release.

On appeal, Ebbers principally contends that the district court erred in permitting the government to introduce testimony by immunized witnesses while denying immunity to potential defense witnesses who were rendered unavailable to Ebbers by their invocation of the privilege against self-incrimination. He also claims that the court should not have given a conscious avoidance instruction and that the government should have been required to allege and prove violations of Generally Accepted Accounting Principles ("GAAP"). Finally, he challenges his sentence as based on an inaccurate calculation of losses to investors, as significantly greater than those imposed on his co-conspirators, and as unreasonable in length. We affirm.

We must of course view the evidence in the light most favorable to the government and draw all permissible inferences from that evidence in its favor. Glasser v. United States, 315 U.S. 60, 80, 62 S. Ct. 457, 86 L. Ed. 680 (1942).

a) Beginnings

There is an element of tragedy here in that it was not a lack of legitimate entrepreneurial skills that caused Ebbers to resort to fraud. Before WorldCom, he was, among other things, a teacher, coach, and warehouse manager. He was a motel operator when, in 1983, he first invested in Long Distance Discount Services ("LDDS"), a small long distance company in Mississippi. When LDDS was in danger of failing in 1985, Ebbers agreed to become its CEO and led it to profitability by merging with other long distance providers. In 1989, LDDS went public by merging with Advantage Companies, another telecommunications company that was listed on NASDAQ. In 1995, LDDS changed its name to WorldCom, Inc. After WorldCom acquired MCI, Inc., in 1998, it was a global company with subsidiaries in Brazil, Mexico, and Canada. WorldCom then tried to acquire Sprint, but the Justice Department and the European Union stopped the merger on antitrust grounds. Having exhausted the market for acquisition targets in the long distance business, WorldCom began to acquire web hosting services. By 2000, WorldCom had about 90,000 employees in 65 countries, and reported revenues of $39 billion.

As part of its business, WorldCom built a global network of fiber-optic cables and telephone wires to transmit data and telephone calls. It also leased capacity on other companies' network facilities to transmit data and calls. The cost of the leasing was WorldCom's single largest expense—styled "line costs." When the "dot-com bubble" burst in early 2000, WorldCom's business slowed dramatically as some of its dot-com customers were unable to pay their bills and demand for WorldCom's internet services declined. Anticipating growth rather than declining demand, WorldCom had added 10,000 new employees, continued to invest heavily in new equipment, and had taken on long-term line leases with fixed monthly payments. By the end of the third quarter of 2000, as its revenue growth decreased and its expenses increased, the company could no longer meet investors' expectations of revenue and profit growth.

b) Ebbers' Personal Finances

By this time, Ebbers had powerful personal as well as occupational motives to see that investors' expectations were met and that WorldCom's stock price did not fall. Although Ebbers had become very wealthy since his earlier days, his consumption and investment habits outpaced his income. Ebbers had accumulated millions of shares of WorldCom stock but had borrowed over $400 million from banks, using his stock in WorldCom as collateral. As WorldCom's stock price began to drop in 2000, Ebbers received margin calls from the banks, requiring him either to put up more stock as collateral or to pay back a portion of the money he owed. Because he had used much of the borrowed money to buy relatively illiquid assets, such as a ranch, timber lands, and a yacht-building company, Ebbers could not use those assets to meet the margin calls. As WorldCom's stock price continued to fall, Ebbers pledged more of his WorldCom stock until every share he owned was collateral for the loans. By October 2000, Ebbers entered into a forward sale transaction, allowing Bank of America to sell some of his WorldCom stock at a future date in exchange for $70.5 million in cash to pay off his margin debts. WorldCom assumed the liability for the debts to the banks in October 2000, requiring Ebbers to make payments directly to WorldCom in the amount the company owed the banks; the debts to WorldCom and to the banks were still secured by Ebbers' WorldCom stock.

c) Third Quarter 2000

As a public company, WorldCom was required to file quarterly financial statements and annual reports with the SEC. When it became clear that the company would be unable to meet analysts' expectations in the third quarter of 2000, Ebbers and WorldCom's Chief Financial Officer ("CFO") Scott Sullivan reviewed the monthly revenue reports and discussed the company's options. Sullivan told Ebbers that WorldCom's financial performance had deteriorated and that they should issue an earnings warning to investors. Ebbers refused. Sullivan then told Ebbers that to meet expectations the company would have to make an improper adjustment to the revenue figure. Ebbers replied that "[W]e have to hit our numbers." Sullivan instructed others to increase the publicly reported revenues by adding $133 million in anticipated under-usage penalties to the revenue calculation, even though he believed that those penalties were not likely to be collected.

Soon after, Sullivan learned that line cost expenses would be almost $1 billion greater than expected. He reported that to Ebbers, who reiterated that the company had to hit its quarterly earnings estimates. Sullivan instructed Controller David Myers and his subordinates Buford Yates, Betty Vinson, and Troy Normand to reduce line cost expense accounts in the general ledger while also reducing reserves in the same amounts, which lowered the reported line costs by about $828 million. As a result, WorldCom's reported earnings were increased by the same amount.

Vinson and Normand believed the entries were wrong and considered resigning. When Sullivan told Ebbers that the accounting staff might quit, Ebbers told Sullivan that "we shouldn't be making adjustments; we've got to get the operations of this company going; we shouldn't be putting people in this position." Ebbers then spoke to Controller Myers, apologizing for the position that Myers and his staff were put in. In November 2000, WorldCom lowered its future earnings estimates and offered new guidance to analysts.

d) Fourth Quarter 2000

WorldCom's revenues and line costs did not improve in the fourth quarter of 2000. In January 2001, Ebbers and Sullivan agreed that WorldCom would not be able to meet even the analysts' revised expectations if it reported its actual results. Sullivan asked Ebbers if he would again reduce the earnings estimate given to analysts, but Ebbers refused to do so. Sullivan asked Myers to alter the reported revenue and expense numbers to meet expectations. The commissions paid to airlines as part of a marketing partnership were no longer removed from the reported revenues, increasing the revenue reported by about $42 million.

WorldCom's line cost expenses were $800 million above analysts' expectations. Sullivan directed Myers to bring the reported line costs in line with expectations. Myers and his staff then reduced the income tax reserve by $407 million, and altered other accounts until they were able to reduce the reported line costs by $797 million for the fourth quarter. Monthly reports sent to Ebbers, referred to at trial as the Monthly Budget Variation Reports ("MBVRs"), detailed the company's financial results and included the reduced line costs, giving the company an apparent gross margin of 78% in September 2000 and 74% in December 2000—margins that had never been achieved by WorldCom before. The 2000 annual report and Form 10-K also contained the false information.

e) First Quarter 2001

In early 2001, WorldCom's line costs were still hundreds of millions of dollars higher than the company had predicted, again making it impossible to meet analysts' expectations without further manipulation of the company's financial reports. The staff had been asked to find ways to reduce line costs, but the proposed cost savings were far smaller than needed to meet expectations. When the first quarter ended, reserves had been largely exhausted and could no longer be used to reduce line costs. Sullivan suggested capitalization of the line costs, that is, shifting a portion of the costs out of reported current expenses into capital expenses. Because line costs had always been treated as operating expenses, their unannounced treatment as capital expenses would disguise the decline in earnings. Myers and his staff agreed to capitalize about $771 million in line costs, although they believed it to be improper. At a dinner in Washington in March 2001, Sullivan and Ebbers discussed the line cost problem. Sullivan told Ebbers that the planned allocation of current expenses to capital expenses—in an amount over $500 million—"wasn't right." Ebbers did not deter him from the allocation.

Ebbers approved the capitalization of line costs in a later conversation with Sullivan. He told Sullivan that "[w]e have to grow our revenue and we have to cut our expenses, but we have to hit the numbers this quarter." Sullivan told Myers to change the general ledger to capitalize a portion of the line cost expenses in an amount totaling hundreds of millions of dollars. Ebbers later told Sullivan to change the format of the reports to remove the line cost figures. When Ebbers spoke to analysts and the public about WorldCom's first quarter performance in the earnings conference call, he did not mention the change in how the company was booking line costs. Instead, he said "there were no storms on the horizon," urging them to "go out and buy stock."

f) Second Quarter 2001

Capitalizing WorldCom's line cost expenses left another problem unaddressed: revenues were not growing at the 12% annual rate that Ebbers had predicted. Missing the revenue growth target was likely to lower WorldCom's stock price. Sullivan, Ebbers, and a handful of other executives created a new program called "Close the Gap" to "get [the] operating performance . . . up to the market guidance expectations" by finding new items to include in revenue. Each month, and sometimes more often, the business operations group presented revenue data to Ebbers in detail as part of the "Close the Gap" program. Sullivan told Ebbers that there was no basis for including many of the opportunities presented in the "Close the Gap" program in reported revenues. In a voicemail to Ebbers, Sullivan described some of the items eventually included in reported revenues as "accounting fluff," "one-time stuff," and "junk." In July 2001, Ebbers sent a memorandum to Chief Operating Officer ("COO") Ron Beaumont, who was involved in the "Close the Gap" program, asking him "[w]here we stand on those one time events that had to happen in order for us to have a chance to make our numbers." Ebbers and Sullivan were aware that the company's true results fell far short of analysts' expectations, but ordered the improper revenue accounting so that those expectations would be met.

Once again, Sullivan told Ebbers that the company could reach the analysts' estimates only by capitalizing a portion of its line costs. Ebbers attended one of the line cost meetings around this time, and explained to the employees there that his "lifeblood was in the stock of the company" and that if the price fell below about $12 per share, he would be wiped out financially by margin calls. Although the line costs had improved slightly since the previous quarter, the accounting staff still had to capitalize over $610 million in line costs in order to meet earnings estimates.

g) Third Quarter 2001

In the third quarter of 2001, WorldCom's actual revenue growth rate, as reported internally to Ebbers, had fallen to about 5.5%. However, Ebbers announced that WorldCom had sustained its 12% revenue growth rate when the third quarter results were reported. The "Close the Gap" program added several new revenue items, largely one-time items not previously counted in revenue. Sullivan told Ebbers that the purpose of the adjustments to revenue was to reach the 12% growth target. WorldCom's press release announcing the quarterly results quoted Ebbers as saying the company had "delivered excellent growth this quarter." During the earnings conference call with analysts, Ebbers said "[w]e were able to achieve very solid growth." However, over $700 million in line costs had to be capitalized to create the appearance of meeting the earnings target for the quarter.

At the time, WorldCom was in merger negotiations with Verizon. Concerned that Verizon might discover the capitalization of line costs and the revenue adjustments in the course of a due diligence inquiry, Ebbers abruptly ended the merger negotiations.

At the board meeting in June 2001, board members began to ask about the "Close the Gap" program when COO Ron Beaumont presented several slides on it to them. One board member approached Sullivan privately to question the program. When Sullivan broached the subject with Ebbers, Ebbers told Beaumont and Sullivan that the next board presentation should be at a higher level and not include "Close the Gap" information. Beaumont's next board presentation, in September 2001, did not include any information about the "Close the Gap" program.

h) Fourth Quarter 2001

By the fourth quarter of 2001, even the "Close the Gap" program could not generate enough one-time revenue opportunities to create double-digit revenue growth. Nor could the staff find ways to adjust the line cost expenses sufficient to hit the earnings target. After Myers capitalized over $941 million in line costs, the accounting staff still had to adjust the SG & A (sales, general, and administrative) expenses in order to reach the target. On the fourth quarter earnings conference call, Ebbers assured investors that "[w]e stand by our accounting," and later said in a CNBC interview that "[w]e've been very conservative on our accounting."

i) First Quarter 2002

WorldCom's revenue declined in the first quarter of 2002. The accounting staff added new sources of revenue to improve the results but were unable to bring the revenue up to analysts' expectations. Sullivan informed Ebbers that even with the improper revenue adjustments and the capitalization of line costs, the company would be unable to meet investors' expectations that quarter. The accounting staff capitalized about $818 million in line costs, but WorldCom still had to announce that its results had fallen below investors' expectations.

j) Investigation, Trial, and Sentence

In March 2002, the Securities and Exchange Commission ("SEC") began to investigate WorldCom. At the end of April 2002, WorldCom's board asked Ebbers to resign, which he did on April 29th. Ebbers began to liquidate some of his assets in order to pay back his debts, but during May 2002 he also bought three million more shares of WorldCom stock. A month after Ebbers' departure, WorldCom's Internal Audit Department learned of the line cost capitalization, and alerted the new CEO. Sullivan was soon fired, and WorldCom disclosed the fraud to the public on June 25, 2002. WorldCom's stock collapsed, losing 90% of its value, and the company filed for bankruptcy.

On September 15, 2004, Ebbers was charged in a superseding indictment with one count of conspiracy to commit securities fraud and related crimes, one count of securities fraud, and seven counts of making false filings with the SEC. See 18 U.S.C. § 371 (conspiracy); 15 U.S.C. §§ 78j (b) & 78ff (securities fraud); 15 U.S.C. §§ 78m(a) & 78ff (false filings).

A jury convicted Ebbers on all counts on March 15, 2005. The pre-sentence report ("PSR") recommended a base offense level of six, plus sentencing enhancements of 26 levels for a loss over $100 million, of four levels for involving more than 50 victims, of two levels for receiving more than $1 million from financial institutions as a result of the offense, of four levels for leading a criminal activity involving five or more participants, and of two levels for abusing a position of public trust, bringing the total offense level to 44 levels. The government also sought a two-level enhancement for obstruction of justice on the basis of Ebbers' having testified contrary to the jury's verdict. With Ebbers' criminal history category of I, the Guidelines range calculated in the PSR was life imprisonment. The Probation Department recommended a 30-year sentence. Judge Jones declined to apply the enhancements for deriving more than $1 million from financial institutions or for obstruction of justice. She also denied Ebbers' motions for downward departures based on the claims that, inter alia, the loss overstated the seriousness of the offense, his medical condition was poor, and he had performed many beneficial community services and good works. She determined that his total offense level was 42 and that the advisory Guidelines range would be 30 years to life. She then sentenced Ebbers to 25 years' imprisonment and three years' supervised release, and imposed a $900 special assessment but no fines.

This appeal followed.

Ebbers argues that: (i) he was deprived of a fair trial when the government refused to immunize certain potential witnesses and the district court erred in its rulings on related issues; (ii) the court should not have charged the jury on conscious avoidance; (iii) the government should have been required to allege and prove violations of GAAP; and (iv) the sentence imposed is unreasonable.

a) Selective Immunization of Witnesses

Ebbers contends that he was denied a fair trial because the government granted immunity only to witnesses whose testimony incriminated him and not to witnesses whose testimony would exculpate him but who would have invoked the privilege against self-incrimination if called to testify. This alleged selective immunization was aggravated in his view by the government's eliciting hearsay testimony from immunized witnesses as to statements of the non-immunized witnesses on a co-conspirator theory. Fed.R.Evid. 801(d)(2)(E). He finally asserts that the district court erred in substantially denying his motion to impeach the alleged co-conspirator statements with prior admissions and in declining to give a "missing witness" instruction to the jury with regard to the non-immunized witnesses.

We have not previously adopted a standard of review for district court decisions not to compel the government to choose between giving use immunity to defense witnesses or forgoing its own use of immunized testimony. At least three other circuits have applied the abuse of discretion standard to such determinations. United States v. Burke, 425 F.3d 400, 411 (7th Cir.2005); United States v. Perez, 280 F.3d 318, 348 (3d Cir.2002); United States v. LaHue, 261 F.3d 993, 1015 (10th Cir.2001). But see United States v. Alvarez, 358 F.3d 1194, 1216 (9th Cir.2004) (applying de novo review to issue except to findings of fact, which are reviewed for clear error). Following those circuits, we also adopt an abuse of discretion standard.

Such a decision requires consideration whether "(1) the government has engaged in discriminatory use of immunity to gain a tactical advantage or, through its own overreaching, has forced the witness to invoke the Fifth Amendment; and (2) the witness' testimony will be material, exculpatory and not cumulative and is not obtainable from any other source." United States v. Burns, 684 F.2d 1066, 1077 (2d Cir.1982) (citations omitted). Therefore, a district court must find facts as to the government's acts and motives and then balance factors relating to the defendant's need for the evidence and its centrality, or lack thereof, to the litigation. Factual findings would of course be reviewed under the clear error rule. United States v. Lucien, 347 F.3d 45, 53 (2d Cir.2003). De novo review of the balancing analysis would not be appropriate because trial courts have a comparative advantage over appellate courts when it comes to weighing the needs of the parties and the centrality of particular pieces of evidence to a trial. Cf. Percy v. San Francisco General Hospital, 841 F.2d 975, 978 (9th Cir.1988). Therefore, we adopt the abuse of discretion standard to the balancing analysis.

The government is under no general obligation to grant use immunity to witnesses the defense designates as potentially helpful to its cause but who will invoke the Fifth Amendment if not immunized. United States v. Turkish, 623 F.2d 769, 774 (2d Cir.1980) (discussing difference between prosecutorial powers and obligations and those of a defendant). See also United States v. Praetorius, 622 F.2d 1054, 1064 (2d Cir.1979) (refusing to require the government to confer use immunity absent "extraordinary circumstances").

A grant of use immunity may well hamper the government in a future prosecution of a witness. United States v. Todaro, 744 F.2d 5, 9 (2d Cir.1984). In such a prosecution, the government would have to show that the immunized testimony was not the source of any evidence it presents, Kastigar v. United States, 406 U.S. 441, 460, 92 S. Ct. 1653, 32 L. Ed. 2d 212 (1972), and that the testimony of government witnesses was not tainted by their knowledge of the immunized testimony, see United States v. North, 920 F.2d 940 (D.C.Cir.1990). Although the government may gain protection in completed investigations by establishing a record of the evidence collected before the immunized testimony is given, it may have difficulty shielding all its potential witnesses from that testimony.

However, the ability to give immunity to one witness but not another is a potentially powerful tool for a prosecutor, particularly in light of the prosecutor's ability to create incentives for witnesses to invoke the privilege against self-incrimination. United States v. Dolah, 245 F.3d 98, 106 (2d Cir. 2001), abrogated on other grounds by Crawford v. Washington, 541 U.S. 36, 124 S. Ct. 1354, 158 L. Ed. 2d 177 (2004). There are, therefore, limits on the government's use of immunity.

In an extreme case, a court might hold that the absence of the non-immunized witness caused the government's evidence to fall short of proof beyond a reasonable doubt. In addition, a court may order the prosecution to choose between forgoing the testimony of an immunized government witness or granting use immunity to potential defense witnesses. See United States v. Horwitz, 622 F.2d 1101, 1105-06 (2d Cir.1980); Dolah, 245 F.3d at 105. To obtain such an order, a defendant must make a two-pronged showing. United States v. Diaz, 176 F.3d 52, 115 (2d Cir.1999).

First, the defendant must show that the government has used immunity in a discriminatory way, id. at 115, has forced a potential witness to invoke the Fifth Amendment through "overreaching," id., or has deliberately denied "immunity for the purpose of withholding exculpatory evidence and gaining a tactical advantage through such manipulation." Id.

We have said that a discriminatory grant of immunity arguably may be no more than "a decision . . . to confer immunity on some witnesses and not on others." Dolah, 245 F.3d at 105-06. However, it may also be the case that the immunity decisions in question are so obviously based on legitimate law enforcement concerns —e.g., granting immunity to a witness who has pleaded guilty and has been sentenced to substantial jail time while denying it to a principal target of the ongoing criminal investigation—that it is clear that a court cannot intervene without substantially hampering the administration of justice.

Prosecutorial "overreaching" can be shown through the use of "threats, harassment, or other forms of intimidation [which have] effectively forced the witness to invoke the Fifth Amendment." Blissett v. Lefevre, 924 F.2d 434, 442 (2d Cir.1991). The "manipulation" standard overlaps to a degree with the discrimination test but involves an express finding of a tactical purpose on the government's part. Id.

Second, the defendant must show that the evidence to be given by an immunized witness "will be material, exculpatory and not cumulative and is not obtainable from any other source." Burns, 684 F.2d at 1077. In that regard, exculpatory evidence is material when it "tends to show that the accused is not guilty." United States v. Gil, 297 F.3d 93, 101 (2d Cir.2002) (citing In re United States (Coppa), 267 F.3d 132, 139 (2d Cir.2001)). The bottom line at all times is whether the non-immunized witness's testimony would materially alter the total mix of evidence before the jury.

In particular, Ebbers argues that the testimony of WorldCom COO Ronald Beaumont, Vice President for Financial Reporting Stephanie Scott, and Vice President Ronald Lomenzo would have exculpated him by showing that there were no "`red flags' that would have made WorldCom personnel outside the Accounting Department aware of any fraud," by denying that they had made the statements attributed to them by the government's witnesses, and by providing testimony "about actions by Ebbers inconsistent with awareness of impropriety."

Whether Ebbers meets the first prong of the test is in doubt. Arguably, the immunity decisions were consistent with legitimate law enforcement concerns. Of the six immunized government witnesses, three pled guilty and received jail sentences, and a fourth pled guilty but was not incarcerated. The remaining two were useful but not critical to the government's case and were not central players in the criminal scheme. As the ensuing discussion makes clear, Beaumont, Scott, and Lomenzo, whose "I knew nothing" defenses were in tension with the executive positions they held at WorldCom, were necessarily legitimate targets of the investigation. There is no evidence of "overreaching" or the manipulation of immunity expressly for tactical reasons. Ebbers' claim in this regard therefore relies heavily on Dolah's remark that "discriminatory use" of immunity is arguably no more than "simply a decision . . . to confer immunity on some witnesses and not on others." Dolah, 245 F.3d at 105-06.

We do not resolve that issue, however, because Ebbers has not shown that the absence of testimony by Beaumont, Scott, or Lomenzo affected the total mix of evidence before the jury. There was therefore no abuse of discretion in denying Ebbers' requests. We discuss the potential testimony of each of those witnesses in turn.

(i) Beaumont

Ebbers suggests1 that, if immunized, WorldCom Group COO Ronald Beaumont would have testified that: (i) WorldCom's 3Q 2000 reported results were accurate; (ii) Beaumont had no knowledge of the reserve release in 2000; (iii) therefore Sullivan falsely stated that Beaumont had told Sullivan and Ebbers in March 2001 "we don't have reserves to take like we did last year"; (iv) in another conversation, a reference by Beaumont to "Scott's stuff" did not refer to line cost capitalization; and (v) again contrary to Sullivan's testimony, Ebbers instructed Beaumont to include the breakdown of "Close the Gap" items in the second quarter 2001 Board presentation.

However, there is no basis to conclude that Beaumont would have been a witness helpful to appellant. As for (i), Beaumont's purported opinion that the 3Q 2000 report was accurate, the issue concerned the reserve release, but nothing in the record before us, see Note 1 supra, indicates what Beaumont's opinion was regarding whether the release of the reserves was proper or improper.

Moreover, even if Beaumont believed that the reserve release was proper and would have so testified, that testimony would not have been helpful to appellant. As argued by the government, the underlying issue was whether Ebbers knew of the prior reserve release and the lack of other reserves and, because of that lack, authorized the capitalization of line costs. Beaumont's opinion as to the propriety of the release therefore did not undercut the government's case.

It is true that, if Beaumont claimed ignorance of the reserve release, he could not have said to Ebbers in March 2001, "We don't have reserves to take like we did last year." However, the jury was highly unlikely to credit any such claim of ignorance of the reserve release and denial of Sullivan's testimony that Beaumont told Ebbers of the lack of further reserves. An April 2001 email message from Beaumont to Myers was in evidence that stated "last year we released a good deal of reserves which we don't have this year to release." This message surely would have devastatingly refuted any testimony by Beaumont that he could not have said anything about the reserves to Ebbers.

Sullivan had also testified that, in a conversation with Beaumont at which Ebbers was present, Beaumont had discussed the line cost capitalization, stating that part of the capital budget was reserved for "Scott's stuff." Ebbers contends that, had Beaumont testified, he would have denied that the reference to "Scott's stuff" referred to line cost capitalization.

Ebbers claims that this testimony would have been helpful to him in two ways. First, it would show that the specific conversation did not involve line costs. Second, Beaumont's ignorance of the frauds is evidence that Sullivan kept others, including Ebbers himself, in the dark. We are unpersuaded.

First, the record basis for expecting Beaumont to give such testimony is that, in his interview with the FBI, Beaumont claimed ignorance of the capitalizing of line costs until May 2002. Ebbers infers from this that Beaumont would have denied that "Scott's stuff" referred to line cost capitalization although Beaumont never discussed the use of that phrase in his interview. In any event, such testimony would have been highly self-serving and of dubious credibility. One of Beaumont's major responsibilities as COO was to prepare the capital expenditure budget and find ways to reduce it. To credit such testimony, the jury would have had to believe that he had no idea what was in that budget.

Second, Beaumont's testimony, even if credited, would not have shown what Sullivan and Ebbers understood "Scott's stuff" to be.

Third, Ebbers' argument that Sullivan kept all top management in the dark, including Ebbers, as to the various financial reporting frauds, and that Beaumont's assertions of ignorance show this, simply doesn't wash. Beaumont did not become COO until January 2001, and his ignorance of prior frauds would not show that the CEO was similarly ignorant. In any event, even if Sullivan kept Beaumont in the dark, that fact would not show Ebbers' ignorance. Keeping the COO in the dark is different from keeping the CEO in the dark. Moreover, if Sullivan acting alone would have had a motive to conceal the scheme from Beaumont, Sullivan and Ebbers acting in concert may well have had a similar motive.

Appellant also suggests that Beaumont would have testified that Ebbers told him to include a slide in the 2Q 2001 Board presentation about the "Close the Gap" program and that Beaumont would have defended the "Close the Gap" process as proper. Ebbers argues that if "the jury [had] known that WorldCom's COO denied knowledge of the fraud and directly refuted Sullivan's claims that he, Ebbers and Sullivan had conspiratorial conversations, the outcome of this trial would likely have been different."

We disagree. The jury knew that a "Close the Gap" slide was included in the 2Q 2001 presentation, and Beaumont's testimony that Ebbers told him to put it in would hardly have been exculpatory. The jury also knew that Ebbers claimed to believe the "Close the Gap" program was proper, and Beaumont's self-serving agreement would have added nothing. Moreover, Beaumont gave no explanation in his interview for why the "Close the Gap" information was not included in subsequent board presentations. In sum, we cannot conclude that Beaumont would have been a witness helpful to Ebbers.

(ii) Scott

Stephanie Scott was WorldCom's Vice President for Financial Reporting from 2000 through late 2002. Ebbers argues that, if immunized, she would have countered Lisa Taranto's testimony that Scott ordered changes to the monthly revenue reports presented to Arthur Andersen, WorldCom's outside accounting firm. Also, Scott could have denied participating in the line cost fraud. Taranto testified that around Q3 of 2001, Scott asked her to "create a new version of the Mon Rev [a monthly report] and to remove some items that were in the corporate unallocated line item, and to reclass them into the appropriate sales channels that they related to." Our review of Scott's interview with the government indicates that her testimony would have differed only as to which quarter she might have asked Taranto to correct the corporate unallocated items. That is not an inconsistency of significance.

As for Scott's potential testimony that she was unaware of the line cost adjustments, Sullivan testified that he had spoken to Scott about capitalizing the line costs and that she told him it would not be legitimate accounting. Because there was no testimony that Ebbers was present for any such conversation between Sullivan and Scott or was aware of it, this contradiction of Sullivan is hardly exculpatory of Ebbers. And, while Scott's testimony would have contradicted Sullivan's, Scott's version was entirely self-serving and of little, if any, value as an impeachment of Sullivan.

Ebbers also argues that, if Scott was unaware of the line cost capitalization, Ebbers' claim that he was also unaware of it would be strengthened. For the same reasons discussed with regard to Beaumont's testimony, Scott's testimony in this regard would not have been helpful.

(iii) Lomenzo

Appellant claims that Ronald Lomenzo, a WorldCom Vice President who reported directly to Sullivan, "would have testified that (1) the `Close the Gap' program was employed to `ensure that all revenue was captured,' [and] (2) neither the pressure to record revenue nor the number of revenue adjustments increased in 2001." Lomenzo described the "Close the Gap" program to the government as one used by others in WorldCom's management to monitor his efforts at capturing all revenue opportunities. He said that he was not personally involved in it. Sullivan had testified about the "Close the Gap" program, described it as a "more formalized" and larger version of Lomenzo's revenue opportunities list, but never designated Lomenzo as involved in the program. Because Lomenzo was not directly involved in the program, his (self-serving) testimony about his understanding of its purpose would have had little, if any, probative value regarding its actual purpose.

As for whether the pressure to record revenue and revenue adjustment increased during 2001, Lomenzo's claim that he felt no greater pressure to meet revenue targets in 2001 than in 2000 is not probative of Ebbers' or Sullivan's state of mind. Furthermore, Lomenzo's account of Sullivan and Myers attempting to convince him to release $370 million in line cost reserves in 2000 indicates that the pressure over revenues was already high in 2000.

We therefore conclude that Lomenzo's testimony would not have been materially helpful to Ebbers.

b) Impeaching Co-Conspirator Statements under FRE 806

We review a district court's evidentiary rulings for abuse of discretion, and will reverse only if we find that there was a violation of a substantial right. Marcic v. Reinauer Transp. Cos., 397 F.3d 120, 124 (2d Cir.2005).

Rule 806 states in relevant part that "[w]hen a hearsay statement . . . has been admitted in evidence, the credibility of the declarant may be attacked, and if attacked may be supported, by any evidence which would be admissible for those purposes if declarant had testified as a witness." Fed.R.Evid. 806. Ebbers argues that he should have been allowed to impeach Beaumont's hearsay statement that "`we don't have reserves to take like we did last year . . . so we've got some real cutting to do in [the line cost] area,'" with evidence that Beaumont was not involved in that reserve release. The district court concluded that there was no contradiction because Beaumont might have learned of the releases later. We agree.

Beaumont did state that he would have had to approve a reserve release that large and did not, but it is unclear from the interview notes whether Beaumont was referring to a release in 2000, before he was COO, or 2001, after he was COO. Because Beaumont presumably had no role in approving reserve releases in 2000 while President of WorldCom's Network Services division, and Sullivan was testifying about Beaumont's statement about the 2000 releases, Sullivan's testimony would not have been impeached by the quoted language from Beaumont's interview. See United States v. Trzaska, 111 F.3d 1019, 1024-25 (2d Cir.1997) (citing two tests to determine inconsistency: "any variance between the statement and testimony that has a reasonable bearing on credibility" (citations and emphasis omitted), and "could the jury reasonably find that a witness who believed the truth of the facts testified to would have been unlikely to make a statement of this tenor" (citation omitted)).

Ebbers also contends that he should have been allowed to impeach "testimony that Beaumont complied with a direct order from Ebbers to remove a `Close the Gap' slide from a Board of Directors presentation" with "Beaumont's prior statements that no one had instructed him to remove the slide from the presentation at issue and, in fact, Ebbers had instructed him to include a `Close the Gap' slide in a prior Board Presentation." Sullivan testified that "[t]here was a conversation between Bernie, Ron Beaumont and myself, where Bernie told us to keep the presentations at a higher level, that our jobs were on the line, and he told Ron Beaumont not to get into close the gap items for the third quarter of 2001." Sullivan then testified that Beaumont did not present a "Close the Gap" slide at the 3Q 2001 board meeting. However, he did not testify to any statements by Beaumont on the matter, and therefore no hearsay statement by Beaumont was introduced that might have been impeached under Rule 806.

Ebbers next argues that he should have been allowed to impeach "Beaumont's alleged co-conspirator statement that a large portion of WorldCom's capital expenditures budget was dedicated to `Scott's stuff,' an alleged reference to the line cost capitalization" with "evidence that Beaumont had previously told the government that his statement `was never tied to capitalized line costs' . . . ." In denying the attempted impeachment, the district court ruled that Ebbers was attempting to impeach Sullivan's understanding of Beaumont's statement, rather than the content of the statement itself. Because Sullivan testified that Beaumont did not clarify what was meant by "Scott's stuff" at the meeting, Beaumont's purported statement would not have been expressly contradicted by his profession of ignorance of line cost capitalization. Sullivan was subject to cross-examination as to his own understanding of "Scott's stuff," and we therefore find no violation of substantial rights.

Finally, Ebbers claims that he should have been allowed to impeach "Scott's alleged co-conspirator statement that she instructed Taranto to create a special MonRev in order `to minimize the amount of revenue items that were corporate unallocated for her presentation to Arthur Anderson'" with her statements to the government. As discussed above, her statement to the government was not materially inconsistent with Taranto's testimony, and there was no violation of substantial rights.

c) Missing Witness Instruction

Ebbers requested that a missing witness instruction be given to the jury regarding Beaumont, Lomenzo and Scott, but the district court denied it. We review a district court's refusal to provide a requested missing witness instruction for abuse of discretion and actual prejudice. United States v. Gaskin, 364 F.3d 438, 463 (2d Cir.2004).

In Myerson, we stated that "in the absence of circumstances that indicate the government has failed to immunize an exculpatory witness, a district court does not abuse its discretion by refusing to give a missing witness charge." United States v. Myerson, 18 F.3d 153, 160 (2d Cir.1994). For reasons discussed, none of the three proposed witnesses would have exculpated Ebbers, and the district court did not err in refusing to give a missing witness charge.

d) Conscious Avoidance Charge

"A conscious-avoidance charge is appropriate when (a) the element of knowledge is in dispute, and (b) the evidence would permit a rational juror to conclude beyond a reasonable doubt that the defendant was aware of a high probability of the fact in dispute and consciously avoided confirming that fact." United States v. Hopkins, 53 F.3d 533, 542 (2d Cir.1995) (citations and internal quotation marks omitted). "We review a claim of error in jury instructions de novo, reversing only where, viewing the charge as a whole, there was a prejudicial error." United States v. Aina-Marshall, 336 F.3d 167, 170 (2d Cir.2003).

Q: Did you ever believe that any of the statements contained in those public filings were not true?

A: No, sir.

Q: Did you ever believe that WorldCom had reported revenue that it was not entitled to report?

A: No, sir.

Q: Did you ever believe that WorldCom had an obligation to announce changes in accounting practices that it had failed to announce?

A: No, sir.

Q: Did you ever believe that WorldCom was putting out bad numbers in its financial statements in any way at all?

A: No.

He also denied that he knew about discrepancies in the actual and reported line costs; that Sullivan had told him he would make a transfer of line costs to lower the reported number; that he looked at the SG & A reports he was sent; that he knew of improper entries made in the books; that he knew of the special MonRev report given to the accountants; and that he thought any of the "Close the Gap" process was illegitimate. The first prong of the test, that knowledge be disputed, is therefore easily met.

The evidence that Ebbers either actually knew or was aware of the high probability that the financial statements were false was not limited to Sullivan's testimony, as Ebbers claims. Ebbers testified that he attended some of the line cost meetings, that he read the preliminary and final MonRev reports, and that he went to "Close the Gap" meetings with Sullivan and Beaumont. He also testified to practices that would allow a jury to find that he was consciously avoiding information: using a procedure for signing documents he didn't bother to read in full, including the 10-Ks, and tossing the management budget variance report in the trash without reading it.

The district court found that Ebbers' own testimony rendered the instruction proper, because, based on that testimony, a rational juror could find he was consciously trying to avoid knowledge that the financial reports were inaccurate. We agree.

e) The Need to Prove GAAP Violations

Ebbers argues that the indictment was flawed because it did not allege that the underlying accounting was improper under GAAP,2 and that the district court should have required the government to prove violations of GAAP at trial. He claims that where a fraud charge is based on improper accounting, the impropriety must involve a violation of GAAP, because financial that comply with GAAP necessarily meet SEC disclosure requirements. See Ganino v. Citizens Utilities Co., 228 F.3d 154, 160 n. 4 (2d Cir.2000) ("The SEC treats the FASB's standards as authoritative."); 17 C.F.R. § 210.4-01(a)(1) ("Financial statements filed with the [SEC] which are not prepared in accordance with generally accepted accounting principles will be presumed to be misleading or inaccurate. . . ."). Before trial he moved to dismiss the indictment on those grounds, and after trial moved for judgment of acquittal pursuant to Federal Rule of Criminal Procedure 29 based on the Government's failure to prove violations of GAAP at trial. The district court denied both motions. We review both the denial of a motion to dismiss an indictment and the denial of a Rule 29 motion for judgment of acquittal de novo. United States v. Florez, 447 F.3d 145, 154 (2d Cir.2006); United States v. Yousef, 327 F.3d 56, 137 (2d Cir.2003).

We addressed a similar argument in United States v. Simon, 425 F.2d 796, 805-06 (2d Cir.1969) (Friendly, J.), when three accountants asked for a jury instruction that they could not be found guilty of securities fraud if the financial statements in question were in compliance with GAAP. We ruled that the district court properly refused to give the instruction.

We see no reason to depart from Simon. To be sure, GAAP may have relevance in that a defendant's good faith attempt to comply with GAAP or reliance upon an accountant's advice regarding GAAP may negate the government's claim of an intent to deceive. Id. at 805. Good faith compliance with GAAP will permit professionals who study the firm and understand GAAP to accurately assess the financial condition of the company. This can be the case even when the question of whether a particular accounting practice complies with GAAP may be subject to reasonable differences of opinion.

However, even where improper accounting is alleged, the statute requires proof only of intentionally misleading statements that are material, i.e., designed to affect the price of a security. 15 U.S.C. § 78ff. If the government proves that a defendant was responsible for financial reports that intentionally and materially misled investors, the statute is satisfied. The government is not required in addition to prevail in a battle of expert witnesses over the application of individual GAAP rules.

For example, an addition to revenue used in the "Close the Gap" program may or may not have been improper under particularized GAAP rules. However, where an addition intentionally involved funds that had not previously been used to calculate revenue and were a one-time addition to revenue, investors would not have been alerted to the fact that revenue as previously calculated was actually down. Such an intentionally misleading financial statement violates the statute. For similar reasons, the addition of underusage penalties to revenue may or may not have been proper under some GAAP rule, but was intentionally misleading because the penalties were not expected to be realized. Finally, appellant claims that capitalization of some leases may have been proper under GAAP, but the capitalization of line costs—again an unannounced change in bookkeeping—was based not on an examination of particular leases but on the financial targets needed to keep share price high.

In a real sense, by alleging and proving that the financial statements were misleading, the government did, in fact, allege and prove violations of GAAP. According to the AICPA's Codification of Statements on Accounting Standards, AU § 312.04, "[f]inancial statements are materially misstated when they contain misstatements whose effect, individually or in the aggregate, is important enough to cause them not to be presented fairly, in all material respects, in compliance with GAAP." Thus, GAAP itself recognizes that technical compliance with particular GAAP rules may lead to misleading financial statements, and imposes an overall requirement that the statements as a whole accurately reflect the financial status of the company.

To be sure—and to repeat—differences of opinion as to GAAP's requirements may be relevant to a defendant's intent where financial statements are prepared in a good faith attempt to comply with GAAP. The rules are no shield, however, in a case such as the present one, where the evidence showed that accounting methods known to be misleading—although perhaps at times fortuitously in compliance with particular GAAP rules—were used for the express purpose of intentionally misstating WorldCom's financial condition and artificially inflating its stock price.

f) Reasonableness of Sentence

With regard to his sentence, Ebbers urges that the district court's loss calculation was incorrect and that his sentence was unreasonably long. After Booker, we review a district court's conclusions of law de novo, its application of the Guidelines on issues of fact for clear error, and its exercise of discretion with respect to departures for abuse of that discretion. United States v. Fuller, 426 F.3d 556, 562 (2d Cir.2005).

The district court applied the loss calculation from then-applicable the fraud Guidelines at U.S.S.G. § 2B1.1 (2001). No detailed definition of loss relevant to the issues before us is set out in the Guidelines. The Commentary does state, "The court need only make a reasonable estimate of the loss." U.S. Sentencing Guidelines Manual § 2B1.1 cmt. 2(c) (2001). Moreover, where fraud in investments is concerned, the loss to a buyer or seller who relied upon the fraud is not to be reduced by the gain to an innocent seller or buyer on the other side of the transaction. Id. at cmt. 2(F)(iv). In this case, therefore, the loss is that suffered by those investors who bought or held WorldCom stock during the fraud period either in express reliance on the accuracy of the financial statements or in reliance on what Basic, Inc. v. Levinson described as the "integrity" of the existing market price. 485 U.S. 224, 247, 108 S. Ct. 978, 99 L. Ed. 2d 194 (1988).

Determining this amount is no easy task. One version of the so-called market capitalization test would, in its simplest form, take the share price on the date of a fraudulent statement—X-day, we shall call it—subtract from it the share price on the day after the fraud is revealed—Y-day— and multiply that amount by the number of outstanding shares.

There is a problem, however, with this simplistic analysis. If the truth had been told on X-day, shareholder A would have suffered an immediate loss commensurate with the fraud loss because potential buyers at the earlier price would have immediately disappeared upon the bad news. When perpetrated, therefore, the fraud would not damage A any more than the truth, at least immediately. However, were investor B to buy the stock after the fraudulent statement and in reliance upon the integrity of the market price, B would suffer a loss in the amount of the price paid less the intrinsic value, which, under the market capitalization test, would usually be deemed to be the price after the disclosure of the fraud on Y-day.

While shareholder A is as damaged by the truth as by the fraud on X-day, many frauds are ongoing, and, contrary to the testimony of Ebbers' expert, shareholder A may suffer a loss over time in being misled in assessing whether to hold or sell the stock. While A can be said not to have lost anything as a result of the fraud on X-day —assuming no prior disclosure obligation on the defendant's part—if new fraudulent statements are issued on X +1, X +2, etc., and the company's true value has further diminished on each occasion, the succeeding X-day frauds would have the effect of preventing A from making an informed judgment about holding the stock.

The securities laws are intended to allow investors to buy, sell, or hold based on accurate information. An investor who buys securities before an extended fraud begins, and holds them during the period of the fraud, may therefore be little different from one why buys in mid-fraud.

For example, the ongoing fraud here involved a series of periodic, fraudulent financial reports that systematically inflated WorldCom's operating profits. If the first report had been accurate, some decrease in fundamental value would have been revealed, but the decrease would have been far less than that revealed in June 2002 after several more fraudulent reports. Investors who held their stock throughout the fraud period were therefore denied the opportunity to reassess and perhaps sell according to their own informed estimates of the declining performance.

The loss to investors who hold during the period of an ongoing fraud is not easily quantifiable because we cannot accurately assess what their conduct would have been had they known the truth. However, some estimate must be made for Guidelines' purposes, or perpetrators of fraud would get a windfall. Moreover, revelation of an extended period of fraudulent financial statements may cause losses beyond that resulting from the restatement of financial circumstances because confidence in management and in even the truthful portions of a financial statement will be lost. AUSA Life Ins. Co. v. Ernst & Young, 206 F.3d 202, 230 (2d Cir.2000) (Winter, C.J., dissenting) ("Reasonable investors surely view firms with an untrustworthy management and auditor far more negatively than they view financially identical firms with honest management and a watch-dog auditor."). Credit may become totally unavailable even where an otherwise viable firm remains.

Worse, there is another variable. The loss must be the result of the fraud. United States v. Olis, 429 F.3d 540, 547 (5th Cir.2005). Many factors causing a decline in a company's performance may become publicly known around the time of the fraud and be one cause in the difference in price between X-day and Y-day. Id. at 548 (explaining that numerous factors, not just defendant's fraud, contributed to stock price decline). For example, the dot-com bubble burst and its likely negative future effect on WorldCom's business was public knowledge. The effect of that knowledge would be a downward pressure on share price not attributable to the defendant. Losses from causes other than the fraud must be excluded from the loss calculation. Id. at 547.

Other complications would undoubtedly appear in a case where more than the grossest calculation is needed. This is not such a case. All of Ebbers' arguments with regard to the loss calculation encounter a hard fact. A 26-level loss calculation has a $100 million threshold, which is easily surpassed under any calculation. For example, the Probation Office calculated the loss at $2.23 billion, based on a price of $0.83/share on June 25, 2002, when the company announced the improper accounting and restated its results, and the price on July 1, 2002, $0.06. There were about 2.9 billion shares of WorldCom stock outstanding on June 25, 2002. Id. Even excluding the 20,436,193 shares owned by Ebbers, the 5,000 shares owned by Sullivan, and shares owned by other guilty executives, there was still a $2.2 billion loss to investors not involved in the conspiracy, using the Probation Office's estimate of 77 cents loss per share.

To be sure, this calculation is flawed. Ebbers' expert testified that at least some of the decline in WorldCom's stock price immediately after June 25, 2002, was attributable to factors other than accounting fraud, citing "(1) planned sharp reductions in capital expenditures, (2) lay-offs affecting 17,000 employees, (3) the abandonment of non-core businesses, and (4) the deferral or elimination of dividends." His expert estimated that these other factors might have been responsible for 35% or more of the stock decline.

Even so, the loss amount is still well above $1 billion, or ten times greater than the $100 million dollar threshold for the 26-level enhancement. U.S. Sentencing Guidelines Manual § 2B1.1 (2001). Moreover, it is probably the case that large numbers of investors holding shares on June 25, 2002, had either held the shares during the period when the repeated fraudulent financial statements were used or had bought them during the scheme at prices much higher than 83¢ per share. And neither their loss nor those of bondholders —estimated by the Probation Office at $10 billion—is included in the Probation Office's calculations. Even a loss calculation of $1 billion is therefore almost certainly too low, and there is no reasonable calculation of loss to investors that would call for a remand.3

Ebbers argues that his sentence should have been closer to those imposed on his co-defendants: CFO Scott Sullivan, who received five years; Controller David Myers, who received one year and one day; Accounting Director Buford Yates, who received one year and one day; Director of Management Reporting Betty Vinson, who received five months; and Director of Legal Entity Accounting Troy Normand, who received three years on probation.

District courts must consider "the need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct," 18 U.S.C. § 3553(a)(6), and we may remand cases where a defendant credibly argues that the disparity in sentences has no stated or apparent explanation. See United States v. McGee, 408 F.3d 966, 988 (7th Cir.2005) (remanding for reconsideration of sentencing disparities between equally culpable codefendants). However, a reasonable explanation of the different sentences here is readily apparent, namely, the varying degrees of culpability and cooperation between the various defendants. All of those named above cooperated and pled guilty. Ebbers did not. Moreover, each was a subordinate of Ebbers. Ebbers, as CEO, had primary responsibility for the fraud.

At oral argument, the overall reasonableness of the sentence was raised by the court. Twenty-five years is a long sentence for a white collar crime, longer than the sentences routinely imposed by many states for violent crimes, including murder, or other serious crimes such as serial child molestation. However, Congress has directed that the Guidelines be a key component of sentence determination. Under the Guidelines, it may well be that all but the most trivial frauds in publicly traded companies may trigger sentences amounting to life imprisonment—Ebbers' 25-year sentence is actually below the Guidelines level. Even the threat of indictment on wafer-thin evidence of fraud may therefore compel a plea. For example, a 15¢ decline in share price in a firm with only half the number of outstanding shares that WorldCom had would constitute a loss of $200 million. No matter how many reasons other than the fraud may arguably account for the decline, a potential defendant would face an enormous jeopardy, given the present loss table, and enhancements for more than 250 victims, for being a leader of a criminal activity involving 5 or more participants, and for being an officer of the company.4

However, the Guidelines reflect Congress' judgment as to the appropriate national policy for such crimes, United States v. Rattoballi, 452 F.3d 127, 2006 WL 1699460, at *5 (2d Cir. June 21, 2006) (stating that the court will "continue to seek guidance from the Sentencing Commission as expressed in the Sentencing Guidelines and authorized by Congress.") (citation omitted), and Ebbers does not argue otherwise.

Moreover, the securities fraud here was not puffery or cheerleading or even a misguided effort to protect the company, its employees, and its shareholders from the capital-impairing effects of what was believed to be a temporary downturn in business. The methods used were specifically intended to create a false picture of profitability even for professional analysts that, in Ebbers' case, was motivated by his personal financial circumstances. Given Congress' policy decisions on sentences for fraud, the sentence is harsh but not unreasonable.

For the reasons stated, we affirm.