JON O. NEWMAN, Circuit Judge:

This appeal principally concerns the proper computation, for sentencing purposes, of the tax loss for which each of the participants in a sophisticated criminal tax evasion conspiracy may be held accountable. This appeal also presents the often encountered but seldom discussed issue of how a reviewing court should proceed when it determines that a provision in a plea agreement waiving a defendant's right of appeal is unenforceable. Angel L. Martinez-Rios, Sr. ("Martinez"), Abraham Garcia, and Richard Danziger appeal from judgments entered on January 8 and February 11, 1997, by the District Court for the Eastern District of New York (Charles P. Sifton, Chief Judge), convicting them, upon their guilty pleas, of conspiracy to evade income taxes and sentencing them to various terms of imprisonment. Appellants dispute numerous aspects of the District Court's approach in computing the tax losses caused by the scheme. The Government maintains that the District Court calculated the tax losses correctly, and that Garcia and Danziger waived their right to appeal when they pleaded guilty.

We conclude that the waiver provisions in the plea agreements of Danziger and Garcia are unenforceable, and that we should regard those provisions as severable and therefore consider the merits of their appeals. On the merits, because we disagree with certain aspects of the District Court's methodology for calculating tax losses, we vacate the sentences of all three defendants and remand for resentencing.

Background

I. Defendants' Tax Evasion Scheme

At all relevant times, appellant Martinez was the president and sole shareholder of Brooklyn-based AL Pen Manufacturing Company ("AL Pen"). In 1985, Martinez incorporated 20th Century Promotion ("20th Century"), which was to serve as AL Pen's alter ego. Appellant Danziger was the president, and appellant Garcia was the vice-president, of Roburn International ("Roburn"), a pen manufacturing company based in New Jersey. Danziger and Garcia were equal shareholders in Roburn. Between 1987 and 1992, all three appellants implemented a sophisticated tax evasion scheme.

To conceal income from pen sales, Martinez regularly instructed his customers to pay sums due to AL Pen by checks made out to a fictitious individual named "Juan Rosario," to his girlfriend, to his sister, or to "Marc Write," a company that had performed contract labor for AL Pen prior to Marc Write's dissolution in 1989. With the help of an individual named Carlos Cruz-Brandenberger ("Cruz"), an officer at First Federal Savings Bank in Santurce, Puerto Rico, Martinez set up two accounts at the bank in the name of the fictitious Juan Rosario, and deposited the Juan Rosario and Marc Write checks in those accounts. In most cases, Cruz would either return the funds to Martinez, or would use the funds to purchase certificates of deposit for Martinez.

Martinez permitted Danziger and Garcia to use the Puerto Rican accounts to facilitate the concealment of income from sales of Roburn pens. Danziger and Garcia periodically instructed their customers to pay sums due to Roburn by checks made out to Juan Rosario, 20th Century, or Marc Write, and many of those checks were deposited in the Juan Rosario accounts. In most cases, these funds were either returned by cashier's check to Martinez, Danziger, or Garcia, or used to purchase certificates of deposit. On some occasions, Danziger and Garcia also deposited checks payable to Roburn in the Juan Rosario accounts, without reporting the amounts of the checks as income.

To generate bogus deductions, Martinez periodically wrote checks drawn on AL Pen and 20th Century accounts to Juan Rosario, to Marc Write, and to cash, for fictitious business and labor expenses. These checks were sometimes cashed by Martinez's sister and sometimes deposited in the Juan Rosario accounts. Danziger and Garcia generated similarly improper deductions for Roburn by issuing checks for fictitious business expenses to Juan Rosario and 20th Century. Martinez would deposit the checks in Puerto Rico or negotiate them in New York, and would then return the funds to Danziger and Garcia. 20th Century generally reported the sums received as income, but ultimately never paid income taxes because it claimed various improper deductions that entirely offset its income.

Martinez also organized an off-the-books pen assembly business utilizing home labor, and used some of the cash diverted to the Juan Rosario accounts to pay the home workers. After consulting with Martinez, Garcia set up a similar operation for the assembly of Roburn pens. Periodically, Garcia would furnish Danziger with a list of amounts owed to the Roburn home workers, together with a Juan Rosario or 20th Century invoice obtained from Martinez. Danziger would pay the invoice with a Roburn check and would claim the payment as a deduction for Roburn. As noted above, checks issued by Roburn to 20th Century were reported as income by 20th Century. In addition, Martinez gave Garcia $2,000 to $3,000 per week in cash (which Martinez withdrew from the Juan Rosario accounts) for payments to the Roburn home workers.

Prior to the dissolution of Marc Write, Martinez entered into a kickback arrangement with the company's owner, Moses Geffen, to generate additional phony deductions for Martinez's corporations. Martinez would instruct Marc Write to bill AL Pen and 20th Century for twice the sum actually owed on each invoice. Geffen would return the overcharges to Martinez, but Martinez would claim the full amount of the overcharge as a business expense deduction on his corporations' returns. Martinez entered into a similar arrangement with an individual named Tomas Rivera, another independent contractor for AL Pen. Danziger and Garcia organized a substantially similar overcharge and kickback scheme with a Roburn supplier known as Davro. Davro would refund the overcharges to Danziger and Garcia by sending checks payable to 20th Century.

On numerous occasions between 1987 and 1991, Danziger and Garcia also concealed income earned from sales to AL Pen of inventory of Roburn pen parts. Martinez would pay for the inventory with funds from the Juan Rosario accounts or from the certificates of deposit, and Danziger and Garcia did not report these sums as income. In addition, Danziger and Garcia occasionally instructed their customers to issue checks to false payees for sums owed to Roburn. Danziger and Garcia cashed these checks without reporting them as income.

II. District Court Proceedings

Martinez, Garcia, and Danziger each pled guilty to one count of conspiracy to commit income tax fraud. See 18 U.S.C. § 371 (1994); 26 U.S.C. § 7201 (1994). Because the Sentencing Guidelines correlate a tax evader's sentence to the amount of the tax loss, see U.S.S.G. §§ 2T1.1(a), 2T4.1 (1991), the District Court was obliged to determine the tax loss for which each defendant was responsible. Though the precise amounts of tax loss are appropriately determined in civil proceedings, the Guidelines require a sentencing court to determine which of 19 ranges of tax loss apply to a defendant (21 ranges in the current version).

In determining the appropriate range, the District Court used a five-step process. First, the Court calculated gross unreported income for each corporation, and derived net unreported income by subtracting legitimate amounts, supported by evidence at the sentencing hearing, for which deductions could have been claimed against the unreported income. Second, the Court calculated the unpaid corporate tax for each corporation as 34 percent of the net unreported income, and then held each corporation's owner or owners responsible for a portion of the unpaid corporate tax, allocating the tax loss according to each shareholder's percent of stock ownership. Third, the Court added personal income tax losses, which it calculated as (i) 28 percent of any unreported interest income from certificates of deposit, plus (ii) 28 percent of any corporate income which could be attributed to each defendant as a constructive dividend. Fourth, if the defendant's corporation was permitted to deduct payments to home workers as labor expenses, the Court increased the tax loss to reflect unpaid social security taxes. Finally, the Court increased the tax loss figure for each defendant by the amount of his co-conspirators' tax losses, to the extent that those losses could be deemed "relevant conduct" of the defendant under the Sentencing Guidelines.

The District Court attributed to Martinez a total tax loss of $1,525,513.87, resulting in a base offense level of 18. The Court held Martinez accountable for most of his co-conspirators' tax losses, finding that Martinez was a direct participant in the tax evasion committed by Garcia and Danziger. Martinez received a three-level enhancement based on his role in the offense, for a total offense level of 21. Martinez received a 37-month term of imprisonment, which was, as the Court noted, "the minimum sentence permitted under the guidelines."

The Court held Garcia accountable for most of Martinez's tax losses, and computed a total tax loss of $907,568.30, resulting in a base offense level of 17. Garcia received offsetting adjustments for the use of sophisticated means to impede discovery of the offense (a two-level enhancement) and acceptance of responsibility (a two-level reduction). The Court sentenced Garcia to 24 months' imprisonment, which was at the bottom of the Guideline range for his total offense level of 17.

The Court held Danziger accountable for most of Martinez's tax losses, and computed a total tax loss of $695,818.97, resulting in a base offense level of 16. With adjustments, including an enhancement for obstruction of justice based on Danziger's initial denials of knowledge about Martinez's tax evasion, Danziger's total offense level was 20, which corresponded to a sentencing range of 33 to 41 months. However, the Court imposed a term of imprisonment of only 24 months, concluding that Danziger's extraordinary family circumstances warranted a downward departure.

Discussion

I. Waiver of Appeal by Garcia and Danziger

Initially, we consider the Government's contention that Garcia and Danziger, in their plea agreements, have waived their right to appeal their sentences. The form of waiver used in this case is significantly different from other appeal waivers that we have encountered. Usually, the form of waiver states that the defendant will not appeal a sentence within (or below) a specified guideline sentencing range. See, e.g., United States v. Chen, 127 F.3d 286, 288 (2d Cir. 1997); United States v. Maher, 108 F.3d 1513, 1531 (2d Cir. 1997); United States v. Ready, 82 F.3d 551, 554 (2d Cir. 1996); United States v. Yemitan, 70 F.3d 746, 747 (2d Cir. 1995); United States v. Stevens, 66 F.3d 431, 436 (2d Cir. 1995); United States v. Jacobson, 15 F.3d 19, 23 n. 1 (2d Cir. 1994); United States v. Salcido-Contreras, 990 F.2d 51, 51 (2d Cir. 1993); United States v. Rivera, 971 F.2d 876, 896 (2d Cir. 1992).

By contrast, our case involves a form of waiver in which the defendant waives a sentencing appeal if the sentence is within or below whatever guideline range is determined by the District Court to be applicable. We first encountered this form of sentence appeal waiver in United States v. Rosa, 123 F.3d 94, 99 (2d Cir. 1997). Noting that this agreement assured the defendant only that he could appeal an upward departure but denied him the opportunity to appeal the correctness of any applicable guideline range determination made by the sentencing judge, we characterized the waiver as an "unorthodox agreement" that "presents grave dangers and implicates both constitutional questions and ordinary principles of fairness and justice." Id.

Rosa noted that one consequence of this unusual form of waiver was that it "implicates the `knowing and voluntary' inquiry to an even greater extent than does the standard plea [agreement]." Id. at 100. We had previously made clear that a waiver of appellate rights must be "knowing and voluntary." Ready, 82 F.3d at 557; Stevens, 66 F.3d at 437; Salcido-Contreras, 990 F.2d at 51. Indeed, we have stated that "a waiver of the right to appeal should only be enforced by an appellate court if the record `clearly demonstrates' that the waiver was both knowing (in the sense that the defendant fully understood the potential consequences of his waiver) and voluntary." Ready, 82 F.3d at 557 (citing United States v. Schmidt, 47 F.3d 188, 190 (7th Cir. 1995)).

Our approach to ascertaining whether a waiver of appeal is knowing and voluntary has varied. Sometimes we have enforced the waiver without any explicit inquiry as to whether the appellate waiver was knowing and voluntary. See Maher, 108 F.3d at 1531; Rivera, 971 F.2d at 896. Sometimes we have simply noted the absence of any dispute as to whether the waiver was knowing and voluntary. See Rosa, 123 F.3d at 102 n. 11 (waiver issue deemed "waived"); Yemitan, 70 F.3d at 747. Sometimes we have examined the Rule 11 plea allocution and determined that the appellate waiver was not adequately or accurately explained. See Chen, 127 F.3d at 290; Ready, 82 F.3d at 557. Sometimes we have examined the record and noted that it contained an inadequate basis to determine whether the waiver was knowing and voluntary, and we therefore remanded for fact-finding. See Stevens, 66 F.3d at 437.

In the pending case, the Government contends that the waiver issue has been waived because it was not raised until the filing of the appellants' reply brief. To this, the defendants reply in kind by pointing out that the Government, rather than filing a motion to dismiss the appeal, sought to invoke the appellate waiver for the first time in its main brief on the appeal, after which the defendants timely challenged the effectiveness of the waiver in their reply brief. We think the issue of the effectiveness of the waiver has not been waived.

In this case, the record fails to demonstrate the effectiveness of the waiver. At the plea allocution there was no colloquy concerning appellate waiver. The waiver was mentioned at the sentencing hearing, but at that time, the Judge told the defendants that they did have a right to appeal (A264), and then, when the Government mentioned the waiver, Chief Judge Sifton said, "There [are] still substantial issues, I assume, as to whether I got the right guidelines which I assume is not covered by an agreement assuming the validity of an agreement . . . ." (A266)

In the absence of any adequate indication that the defendants understood and knowingly agreed to this unusual form of appellate waiver, we conclude that it is ineffective. That conclusion requires us to consider an appropriate remedy, an issue on which we sought and have received briefs from the parties. There are three choices:

1. The Government urges us to proceed to decide the merits of the appeals of Danziger and Garcia, and, if we were to deem them entitled to any relief, only then face the issue of the consequence of the appellate waiver. In the Government's view, at that point we would afford the Government the option of (a) letting the District Court amend the sentences to conform to our reversal or (b) vacating the plea agreement.

That remedy is clearly unacceptable. We will not issue what might become an advisory opinion on the merits in order to help the Government make up its mind.

2. A second, and more plausible, possibility is to structure a series of choices whereby the Government would first be given the choice of forgoing the appellate waiver provision of the plea agreement or electing to have the plea agreement vacated in its entirety, and then, if the Government chose to have the plea agreement vacated, the defendants would have the choice of permitting the waiver provision to be enforced (i.e., withdrawing their appeal) or having the plea agreement vacated. The idea of a structured sequence of choices is not new in this Court. See United States v. Showerman, 68 F.3d 1524, 1529 (2d Cir. 1995). And we have previously ruled that, where a defendant's "success" on appeal might expose him to unsatisfactory consequences, the defendant should have the option of withdrawing his appeal, rather than have exposure to such consequences forced on him. See United States v. Bohn, 959 F.2d 389, 392 (2d Cir. 1992). Many defendants would much prefer to accept part of the benefits of a plea bargain, even if they lose some anticipated benefit. They should not necessarily be forced into an all or nothing choice.

3. The defendants urge us simply to "sever" the waiver provisions and proceed to adjudicate the merits of their sentencing issues. That is what we did in Chen, 127 F.3d at 290-92, and Ready, 82 F.3d at 560. Others courts have done the same thing. See, e.g., United States v. Buchanan, 59 F.3d 914, 918 (9th Cir. 1995); United States v. Bushert, 997 F.2d 1343, 1353 (11th Cir. 1993); United States v. Baty, 980 F.2d 977, 979 (5th Cir. 1992); United States v. Wessells, 936 F.2d 165, 168 (4th Cir. 1991).

Appellants contend that severance is warranted because the appellate waiver is an unconscionable provision that should be severed as a matter of contract law. See, e.g., N.Y.U.C.C. § 2-302(1) (McKinney 1993). Though the waiver provision is unusual and fraught with dangers, as we pointed out in Rosa, we ultimately ruled that this form of waiver was not unfair in the circumstances of that case. In this case, however, there is an aggravating circumstance that weighs in favor of severance. Our decision on the merits of Martinez's appeal accords him the benefit of a deduction in calculating his personal tax liability to reflect the amount of the corporate tax that his corporation should have paid (in essence, a reduction of imputed income). Since Garcia and Danziger are deemed liable for participating in Martinez's scheme, and their tax losses are calculated on the basis of his tax loss, it would be unduly harsh to enforce the waiver and deny them the corporate tax offset we are giving him. Under these circumstances, we will sever the ineffective waiver provision and proceed to the merits. We select the severance option only because the waiver is of the unusual form used in Rosa and the merits of the claims of Garcia and Danziger are so closely related to that of Martinez.

II. Merits

Consideration of the merits of the defendants' challenges to their sentences brings into sharp focus one of the more objectionable aspects of the Sentencing Guidelines. Unlike guideline systems adopted in any of the states, the federal guideline system insists on a precise determination of each aspect of a defendant's wrongful conduct, including a dollar quantification of all monetary offenses. These refined calculations are required to implement a key component of the Guidelines' sentencing philosophy — the idea that there must be some precise incremental punishment for every identifiable increment of wrongdoing. This principle of "incremental immorality," as it has been called, see Conference on the Federal Sentencing Guidelines: Summary of Proceedings, 101 Yale L. J. 2053, 2072-73 (1992) (remarks of Jon O. Newman), carries to an extreme extent the rather general directive of Congress that the Sentencing Commission should frame guidelines that take into account "the nature and degree of the harm caused by the offense." 28 U.S.C. § 994(c)(3) (1994). Moreover, in some cases, including the pending one, the principle requires a sentencing judge to engage in laborious fact-finding and analysis far beyond the normal requirements of criminal sentencing. Rather than simply determine whether a tax evader has cheated the Government of small, medium, or large sums, the sentencing judge is obliged to make a precise determination of tax liabilities, resolving issues normally determined in administrative proceedings of the Internal Revenue Service, sometimes subject to subsequent civil litigation.

Though the Sentencing Commission may have made an ill-advised decision in imposing such a detailed obligation on sentencing judges, those judges must perform the task, and we must determine whether they have done so in conformity with applicable law.

A. Which Version of the Guidelines Applies?

Turning to the merits, we face an initial issue as to which version of the Guidelines is applicable. The District Court's sentencing memorandum and the submissions of the parties on this appeal suggest some confusion on this point. Sentencing courts generally must apply the version of the Sentencing Guidelines in effect at the time of sentencing, except where this would result in a more severe sentence than would be appropriate under the version in effect at the time of the commission of the offense. See 18 U.S.C. § 3553(a)(4)(A); Berrios v. United States, 126 F.3d 430, 433 (2d Cir. 1997); United States v. Rodriguez, 989 F.2d 583, 587 (2d Cir. 1993). The District Court purported to apply the version of the Sentencing Guidelines incorporating amendments effective November 1, 1991 (the "1991 Guidelines"). This version was in effect at the time of the commission of the last overt act in furtherance of defendants' tax evasion conspiracy. Use of the 1991 Guidelines was based on the parties' agreement that the 1991 version was "generally more favorable to defendants" than the version of the Guidelines incorporating amendments effective November 1, 1995 (the "1995 Guidelines"), which was in effect when the defendants were sentenced in early 1997. See Brief for the Appellee at 7 n. 3.

However, the first step of the District Court's analysis — allowing credit for legitimate but unclaimed deductions for which proof was offered — was, in fact, inconsistent with the 1991 Guidelines. Under the 1991 Guidelines, the base offense level for the crime of conspiracy to evade taxes depends on the defendant's "tax loss," subject to an overriding minimum offense level of 10. See U.S.S.G. §§ 2T1.1(a), 2T1.9(a) (1991). "Tax loss" is defined as "the greater of: (A) the total amount of tax that the taxpayer evaded or attempted to evade; and (B) the `tax loss' defined in § 2T1.3." Id. § 2T1.1(a) (1991) (emphasis added). Section 2T1.3(a) of the 1991 Guidelines defines "tax loss" as

28 percent of the amount by which the greater of gross income and taxable income was understated, plus 100 percent of the total amount of any false credits claimed against tax. If the taxpayer is a corporation, use 34 percent in lieu of 28 percent.

Id. § 2T1.3(a) (1991). The 1991 version of section 2T1.3 calls for a calculation based on gross income and does not entitle the taxpayer to credit for legitimate but unclaimed deductions. The Guideline thus establishes an "alternative minimum standard for the tax loss" which "should make irrelevant the issue of whether the taxpayer was entitled to offsetting adjustments that he failed to claim." Id. § 2T1.1 comment. (n. 4) (1991). As the Seventh Circuit explained in United States v. Harvey, 996 F.2d 919 (7th Cir. 1993), "This rough-and-ready calculation applies the highest marginal rate to the amount of concealed income, disregarding deductions that would have been available had the taxpayer filed an honest return." Id. at 920; accord United States v. Valentino, 19 F.3d 463, 465 (9th Cir. 1994) (quoting and following Harvey).

In contrast, the 1995 Guidelines, which were in effect at the time of sentencing, do not foreclose consideration of legitimate but unclaimed deductions. The 1995 version of section 2T1.1 defines "tax loss" as "the total amount of loss that was the object of the offense (i.e., the loss that would have resulted had the offense been successfully completed)." U.S.S.G. § 2T1.1(c)(1) (1995). The Guideline provides, in pertinent part:

If the offense involved filing a tax return in which gross income was underreported, the tax loss shall be treated as equal to 28% of the unreported gross income (34% if the taxpayer is a corporation) plus 100% of any false credits claimed against tax, unless a more accurate determination can be made.

Id. § 2T1.1(c)(1)(A) (emphasis added) (1995). Under this Guideline, the sentencing court need not base its tax loss calculation on gross unreported income if it can make "a more accurate determination" of the intended loss and that determination of the tax loss involves giving the defendant the benefit of legitimate but unclaimed deductions.

Because the 1995 Guideline permits consideration of legitimate but unclaimed deductions, it tends to produce smaller tax loss figures than the 1991 Guideline. However, the 1995 "Tax Table," which specifies 21 different base offense levels corresponding to 21 different ranges of tax loss, see id. § 2T4.1 (1995), is generally harsher on defendants than the 1991 Tax Table, see id. § 2T4.1 (1991). At each level of tax loss in the range relevant to this appeal, the 1995 Tax Table prescribes a greater offense level (and thus a heavier sentence) than the 1991 Tax Table. It is apparently for this latter reason that the parties agreed that the 1991 Guidelines are "generally more favorable" to appellants. We will apply the 1991 Guidelines in considering all of appellants' challenges, giving each appellant the benefit of the more lenient 1991 Tax Table, but not taking into account legitimate but unclaimed deductions for which the defendants may have offered proof.

B. Martinez

1. Deduction for Executive Compensation Expenses. Martinez first challenges the District Court's inclusion of 34 percent of AL Pen's corporate income as part of his tax loss. Martinez argues that if AL Pen had reported its income truthfully, the company would have paid out all of its net income as a compensation bonus to Martinez, and therefore would have incurred no corporate tax liability. Martinez's accountant testified that it is typical for small, closely held corporations such as AL Pen to pay out all net income as additional executive compensation to prevent taxation at the higher corporate rates, and that additional payments by AL Pen to Martinez would have qualified as "reasonable" compensation under the Internal Revenue Code.

As explained above, the 1991 Guidelines call for a tax loss calculation based on gross unreported income and do not permit the sentencing court to give the tax evader the benefit of unclaimed deductions. Thus, even if we were to assume that the deduction Martinez seeks for AL Pen would be legitimate under the Tax Code, a proposition which is doubtful, see United States v. Cseplo, 42 F.3d 360, 365 n. 6 (6th Cir. 1994), Martinez would not be entitled to any offsetting adjustment of the corporate taxable income for purposes of sentencing. There was no error in the District Court's refusal to make such an adjustment.

2. Double Counting of AL Pen Income. Federal tax law provides for sequential taxation of corporate income. Income received by corporations is taxed at corporate rates, and distributions received by shareholders out of after-tax corporate earnings are then taxed at the generally lower individual rates. For sentencing purposes, unreported income is taxable to corporations at 34 percent; income received from corporations by shareholders in the form of actual or imputed dividends is taxed at 28 percent. See U.S.S.G. § 2T1.3(a) (1991) (repealed and consolidated with § 2T1.1, see id. App. C, amendment 491); Cseplo, 42 F.3d at 363; Harvey, 996 F.2d at 920. The parties disagree as to how much corporate income should be deemed distributed to Martinez for purposes of his personal income tax loss computation. In dispute is whether the individual should receive credit for the amount of corporate tax that the corporation should have paid.

Martinez concedes that unreported corporate income should first be taxed at the 34 percent rate, but argues that the imputed dividend (to be taxed at 28 percent) should consist of unreported corporate income minus amounts calculated as corporate tax liabilities. Martinez's approach yields an effective tax rate of approximately 52 percent (34% plus 28% of 66%). The Government contends that the entire sum of unreported corporate income should be taxed at both the 34 percent and 28 percent rates, yielding an effective tax rate of 62 percent (34% plus 28%). The District Court sided with the Government.

The Guidelines are silent on this precise issue, and the two courts of appeals that have considered it have reached opposite conclusions. In Harvey, supra, the Seventh Circuit adopted the approach urged by Martinez, reasoning that the other method "overstates the revenues lost to the Treasury." Harvey, 996 F.2d at 921. In contrast, the Sixth Circuit in Cseplo, supra, employed the method used by the District Court here, based on its view that the Harvey method did not adequately account for the fact that two separate crimes — personal tax evasion and corporate tax evasion — were committed. See Cseplo, 42 F.3d at 364.

We agree with the Seventh Circuit's approach, primarily because it bases the calculation on a better approximation of the tax revenue lost to the federal treasury. Although, as we have acknowledged, the 1991 Guidelines do not call for a tax loss calculation based exclusively on the amount of tax liability that the defendant would have incurred had he reported his income truthfully, we think that the 1991 Guidelines' punitive purposes are adequately served by denying defendants the benefit of legitimate but unclaimed deductions. Though the tax law imposes a tax on income received by a corporation and a second tax on income distributed by the corporation to shareholders, we do not think the framers of the 1991 Guidelines intended to exacerbate the double taxation phenomenon by computing shareholders' tax losses without regard to the corporate taxes that their corporations were obliged to pay, at least in circumstances where the shareholders are being punished for their share of the unpaid corporate taxes. Thus, on remand, the District Court should recalculate Martinez's personal tax loss after allowing a deduction for the corporate tax.

3. Unearned 20th Century Income. Approximately $732,700 of the 20th Century income for which Martinez was held accountable was, in fact, Roburn income that was diverted to 20th Century by Danziger and Garcia. 20th Century generally reported these sums as income, but did not pay any taxes because it claimed roughly equivalent amounts in improper deductions. The District Court charged the improper deductions back to Martinez, but did not credit him with $732,000 to reflect income 20th Century reported but had not really earned. The District Court did, however, allow an offset of approximately $461,000, to reflect 20th Century cash that was used to pay legitimate Roburn labor expenses. Martinez argues that because 20th Century did not earn the $732,000, it should not have been attributed to him.

We disagree. A "claim of right" exists for purposes of tax law "when funds are received and treated by a taxpayer as belonging to him." Healy v. Commissioner, 345 U.S. 278, 282 (1953). Generally, "[i]f a taxpayer receives earnings under a claim of right and without restriction as to its disposition, he has received income which he is required to return, even though it may still be claimed that he is not entitled to retain the money, and even though he may still be adjudged liable to restore its equivalent." North American Oil Consolidated v. Burnet, 286 U.S. 417, 424 (1932). This doctrine applies even to funds obtained illegally. See, e.g., James v. United States, 366 U.S. 213, 218-20 (1961). We think the evidence supports the District Court's determination that Martinez treated the funds paid to 20th Century, his wholly owned corporation, as belonging to him, and that this income was therefore properly counted in determining his tax loss. See U.S.S.G. § 2T1.3 comment. (n. 3) (1991) ("[A]ll conduct violating the tax laws should be considered as part of the same course of conduct or common scheme or plan unless the evidence demonstrates that the conduct is clearly unrelated."). And even if 20th Century truly did over-report its income, the applicable 1991 Guidelines make no provision for an offsetting adjustment to reduce the tax loss. Indeed, if there was any error in the District Court's treatment of 20th Century income, it was in the Court's reduction of the tax loss by $461,000 based on legitimate but unclaimed labor expenses.

4. Unreported Interest Income. Martinez also contends that the District Court erred in including in the tax loss calculation unreported interest earned on the Puerto Rican certificates of deposit. Martinez maintains that he should not be held responsible for failing to report this income because he honestly believed that he was not legally obliged to pay taxes on it. This belief was reasonable, according to Martinez, because he was misled by Cruz and because he never received a Form 1099 income report from the bank. Martinez also claims that he was confused by the supposedly complex tax laws applicable to interest earned in Puerto Rico, and that it was his understanding that such income was not taxable until withdrawn from Puerto Rico.

These contentions lack merit. We agree with the District Court that Martinez's "honest ignorance" defense is simply not credible since Martinez knew enough about the Internal Revenue Code to design a sophisticated tax evasion scheme, and since Martinez purchased the certificates with funds withdrawn from an account expressly created for the purpose of hiding income from the tax collector. Moreover, it appears that Martinez failed to receive Forms 1099 only because he originally purchased the certificates in bearer form or under fictitious names and social security numbers; an available inference is that he did this intentionally in an effort to make his evasion of taxes on interest income more difficult to detect. And Martinez's own conduct seems inconsistent with his professed ignorance, since Martinez did, in fact, take some of the income he earned in Puerto Rico back to the mainland, yet did not at that time report it. For all of these reasons, we agree with the District Court that this income was properly counted in calculating the tax loss.

5. Social Security Taxes. The District Court held Martinez responsible for $162,944.40 in unpaid social security taxes based on $2,172,592 he paid, apparently in cash, as compensation to home workers who assembled pens for AL Pen. Martinez contends that no liability for social security taxes was incurred in connection with the home assembly operation because the home workers were independent contractors rather than employees.

Under the Internal Revenue Code, a home worker is an employee for purposes of social security taxes if the worker

perform[s] work, according to specifications furnished by the person for whom the services are performed, on materials or goods furnished by such person which are required to be returned to such person or a person designated by him . . . if the contract of service contemplates that substantially all of such services are to be performed personally by such individual . . . .

26 U.S.C. § 3121(d)(3). Martinez contends that "pen parts were distributed to various individuals who, in turn, distributed those parts to family members and others who performed the actual work." Brief for Appellant Martinez at 41. This claim, if accepted, arguably might tend to establish that the work was not performed personally by the individuals to whom Martinez furnished the pen parts, and that the home workers were therefore not "employees" under the statute. However, the District Court simply found the facts to be otherwise, and that finding is not clearly erroneous. As the District Court noted, "Records produced by [Martinez] to substantiate the deductions for labor expenses reveal a detailed listing of the workers whom the defendant claims to have paid in cash." This evidence belies Martinez's claim that he had no control over, or knowledge of the identities of, the home workers. We therefore conclude that Martinez was properly held accountable for unpaid social security taxes.

6. Responsibility for Co-conspirators' Tax Losses. The District Court held Martinez accountable for a substantial portion of his co-conspirators' tax losses. Martinez challenges the attribution of three elements of those losses to him: (i) unreported profits earned by Garcia from his home pen assembly operation, (ii) unreported interest earned by Garcia on Puerto Rican certificates of deposit purchased with unreported Roburn income, and (iii) unreported income received by Roburn when it sold inventory to AL Pen. Martinez contends that these losses were not reasonably foreseeable by him.

Under the 1991 Guidelines, the "relevant conduct" for which a defendant may be held accountable includes "all acts and omissions committed or aided and abetted by the defendant, or for which the defendant would be otherwise accountable . . . ." U.S.S.G. § 1B1.3(a)(1) (1991). One of the 1991 application notes (portions of which appear in the Guideline itself in later versions of the Guidelines) explained as follows:

Conduct "for which the defendant would be otherwise accountable" . . . includes conduct that the defendant counseled, commanded, induced, procured, or willfully caused. (Cf. 18 U.S.C. § 2.) In the case of criminal activity undertaken in concert with others, whether or not charged as a conspiracy, the conduct for which the defendant "would be otherwise accountable" also includes conduct of others in furtherance of the execution of the jointly-undertaken criminal activity that was reasonably foreseeable by the defendant. Because a count may be broadly worded and include the conduct of many participants over a substantial period of time, the scope of the jointly-undertaken criminal activity, and hence relevant conduct, is not necessarily the same for every participant.

Id. § 1B1.3 comment. (n. 1) (1991). Under this Guideline, a defendant may be held accountable for (i) any tax evasion "in which he had a direct, personal involvement," and (ii) as to jointly undertaken criminal activity, any reasonably foreseeable tax losses. See United States v. Chalarca, 95 F.3d 239, 243 (2d Cir. 1996) (considering relevant conduct in context of drug conspiracies). The "reasonable foreseeability" requirement "applies only to the conduct of others." Id.

We think that Martinez, who was unquestionably the mastermind of this scheme, may fairly be held responsible for each of the three disputed types of income on the basis of his "direct, personal involvement" in the evasion of taxes by Danziger and Garcia. Martinez directly participated in Garcia's home assembly business by providing advice as to how to set up the operation, by providing large sums of cash for payments to Garcia's home workers, and by providing 20th Century invoices to facilitate improper deductions. Martinez also became directly involved in Garcia's failure to report interest earned on the certificates of deposit by allowing Garcia's money to be commingled with his own in the Juan Rosario accounts (which funded the purchases of the certificates), and by traveling to Puerto Rico on several occasions to purchase certificates for Garcia. Finally, Martinez was directly involved in the pen part inventory transactions as the purchaser of the pen parts.

7. Double Counting of Roburn Income. Martinez complains that he was held accountable for certain Roburn income twice. As explained above, 20th Century reported the income it received from Roburn, but did not pay taxes on it because it claimed improper offsetting deductions. This income was attributable to Martinez because he owned 100 percent of the shares of 20th Century. The District Court held Martinez responsible for the same income a second time by counting this income as Roburn income that was part of Martinez's relevant conduct.

We think that this form of double counting is consistent with the 1991 Guidelines. Under those Guidelines, Martinez is responsible for two different wrongs: improper deductions taken by his corporation, 20th Century, and underreporting of income by his coconspirators, Danziger and Garcia, and their corporation, Roburn. That the payments upon which the improper deductions were based originated with the same cash that Danziger, Garcia, and Roburn failed to report is merely a product of the unusual way in which appellants structured their scheme. Because Martinez's relevant conduct must reflect "all conduct violating the tax laws," see U.S.S.G. § 2T1.3 comment. (n. 3) (1991) (emphasis added), and because "[t]he purpose of the guideline rules is to measure the size of the lie, not the size of the government's loss after all corrections in both directions," Valentino, 19 F.3d at 465, there was no error in the District Court's attribution of Roburn and 20th Century income to Martinez.

8. Arithmetic Error. The District Court attributed a total of $804,104.94 of Garcia's unreported personal income to Martinez, and calculated the tax loss as 28 percent of this figure. However, due apparently to an arithmetic error, the Court determined 28 percent of $804,104.94 to be $255,149.38 rather than the correct figure, $225,149.38. This $30,000 error was significant because the total tax loss determined by the District Court — $1,525,513.87 — put Martinez just barely above the $1.5 million threshold for base offense level 18. See U.S.S.G. § 2T4.1(M) (1991). Had the District Court not made the error, it would have arrived at a tax loss figure of $1,495,513.87, corresponding to a base offense level of 17 under the 1991 Guidelines. See id.

The Government concedes that there was an arithmetic error, but contends that Martinez waived his right to object by failing to bring the error to the attention of the District Court. Alternatively, the Government relies on the rule articulated in United States v. Bermingham, 855 F.2d 925 (2d Cir. 1988), and contends that the sentence can be sustained because the sentence actually imposed — 37 months — was within the Guidelines ranges for both of the relevant adjusted offense levels (21 and 20).

Rule 35(c) of the Federal Rules of Criminal Procedure, which permits the District Court to correct any sentence imposed as a result of an arithmetical or technical error, has no application here because Martinez failed to file a motion pursuant to the Rule within seven days of sentencing. See Fed. R. Crim. P. 35(c). However, this Court may notice "[p]lain errors or defects affecting substantial rights" even if not brought to the attention of the District Court. See Fed. R. Crim. P. 52. We think that the District Court's arithmetical error amounts to "plain error" even under the rigorous standards recently announced by the Supreme Court in Johnson v. United States, 117 S.Ct. 1544 (1997). As the Government concedes, the District Court made a mistake, and that mistake is clear and obvious at the time of appellate consideration. See id. at 1549. The error undoubtedly "affected substantial rights" within the meaning of Rule 52, because it resulted in Martinez's receiving a longer sentence than the District Court intended to give him. Finally, we think that this sort of error "seriously affects the fairness, integrity or public reputation of judicial proceedings," id. at 1550 (quoting United States v. Olano, 507 U.S. 725, 736 (1993) (citations and alteration omitted)), since one would be hard-pressed to think of a more senseless injustice than the deprivation of a citizen's liberty for several months as a result of a clerical error. Indeed, the Government's reluctance to concede error on this point presses the limits of reasonable advocacy.

It is not clear whether a $30,000 error will have any effect on Martinez's base offense level when his tax loss is recalculated in accordance with this opinion. But it is clear that if it will, Bermingham is not properly invoked here. Bermingham permits this Court to affirm a sentence derived from an incorrect offense level only where the sentence also falls within the sentencing range for the correct offense level, and the District Court has indicated that it would have imposed the same sentence under either offense level. See Bermingham, 855 F.2d at 935. In the pending case, the District Court stated at the time of sentencing that "all of these defendants have been collaterally punished by the proceedings here" and that it "could not in good conscience impose any sentence above the minimum." The Court thus sentenced Martinez and Garcia at the bottoms of the applicable Guideline ranges, and departed downward in sentencing Danziger. This suggests that if the Court had calculated an adjusted offense level of 20, it would have sentenced Martinez to no more than 33 months (the bottom of the Guideline range) rather than 37 months (which falls in the middle of the Guideline range).

C. Garcia

1. Roburn Income Retained by Martinez. As explained above, Roburn wrote checks to 20th Century and Juan Rosario to create improper deductions, and Martinez periodically paid at least some of those funds in cash back to Garcia, who generally used the funds to pay his home workers. According to Martinez's records, he owed Garcia $227,436 at the time the scheme was uncovered. Garcia argues that because these funds were never returned to him, this amount should be subtracted from income attributable to him in calculating his tax loss.

We disagree. Garcia personally participated in the diversion of Roburn income to 20th Century as a means to create bogus deductions. Because Garcia owned a 50 percent interest in Roburn, he is chargeable with 50 percent of Roburn's unreported income, and the 1991 Guidelines make no allowance for a downward adjustment of tax loss based on unreported imputed income that did not reach the tax evader's pocket.

2. Unreported Interest Income. Like Martinez, Garcia claims that he did not realize that interest earned on the Puerto Rican certificates of deposit was taxable, and that he believed he was under no obligation to report the income unless he withdrew it from Puerto Rico. Garcia argues that his mistaken belief might have been reasonable even if Martinez's was not, because Garcia speaks little English and did not set up the Juan Rosario accounts or purchase the certificates.

There is no basis for disturbing the District Court's determination that Garcia's story is no more credible than Martinez's. As noted above, some of the interest earned on the certificates was, in fact, withdrawn from Puerto Rico, yet Garcia did not at that time report the income, as one would expect if Garcia's misunderstanding of the tax laws was as he said it was. The interest on Garcia's certificates of deposit thus was properly considered in the tax loss calculation.

3. Responsibility for Martinez's Tax Losses. Garcia concedes that he is responsible for tax losses caused by his business partner, Danziger, see Brief for Appellant Garcia at 32, but contends that he should not be held accountable for losses caused by Martinez and his corporations because those losses were not foreseeable by Garcia. Three elements of Martinez's tax loss are at issue: unreported AL Pen income, unreported interest income from certificates of deposit purchased by Martinez, and charge-backs of improper deductions generated by Martinez through checks for fictitious business expenses.

A threshold matter is who bears the burden of proof with respect to the issue of reasonable foreseeability. Generally, the Government bears the burden of proving by a preponderance of the evidence facts relating to sentencing, such as drug quantities or tax loss amounts. See, e.g., United States v. Desimone, 119 F.3d 217, 228 (2d Cir. 1997). However, "when a defendant asserts that he is not responsible for the entire range of misconduct attributable to the conspiracy of which he was a member, the Guidelines place on him the burden of establishing the lack of knowledge and lack of foreseeability." United States v. Negron, 967 F.2d 68, 72 (2d Cir. 1992). Thus in United States v. Hendrickson, 26 F.3d 321 (2d Cir. 1994), for example, where the Government had already met its burden of proving a conspiratorial agreement to produce a specified quantity of drugs, we noted that the defendant had the burden of proving his lack of knowledge and lack of foreseeability of the quantities agreed upon by his coconspirators. See id. at 334.

Negron and Hendrickson are controlling here. Garcia pled guilty to conspiring with Martinez and Danziger to evade taxes, and the Government met its burden of proving the tax losses caused by the scheme. We agree with the District Court that Garcia bears the burden of proving that any particular elements of Martinez's conspiracy-related tax loss were not foreseeable by him. See Hendrickson, 26 F.3d at 334; see also Negron, 967 F.2d at 72.

In attempting to discharge this burden, Garcia relies on United States v. Studley, 47 F.3d 569 (2d Cir. 1995). That case involved a fraudulent telemarketing loan scheme. Studley was one of between 10 and 20 sales representatives hired by the scheme's organizer to process telephone calls from would-be borrowers. The sales representatives would direct callers to send $250 to cover an "application fee" for a loan that the organizer's firm had no intention of making. Over a period of several weeks, Studley collected between $5,000 and $10,000 in phony fees. In sentencing Studley for mail fraud, the District Court determined that all of the fees collected by the other sales representatives were reasonably foreseeable to Studley for purposes of relevant conduct analysis. We reversed, holding that the District Court must make particularized findings as to both (i) the scope of the criminal activity agreed upon by the defendant, and (ii) whether the activity in question was foreseeable by the defendant. See id. at 574.

We observed in Studley that "a defendant's knowledge of another participant's criminal acts is not enough to hold the defendant responsible for those acts," and that "[t]he relevant inquiry is what role the defendant agreed to play in the operation, either by an explicit agreement or implicitly by his conduct." Id. at 575 (citations omitted). In addition, we noted that one relevant factor in this analysis is "whether the defendant assisted in designing and executing the illegal scheme." Id. (citation omitted; emphasis in original). We determined that a remand was necessary because the District Court had relied exclusively on the defendant's knowledge of the activities of the other sales representatives and on the sales representatives' use of the same office space and phone bank to carry out the scheme. See id. at 576.

We think the District Court's findings as to Garcia's involvement in Martinez's tax loss were sufficient under Studley. With respect to the unreported income of AL Pen, the Court relied on the extensive commingling of Roburn and AL Pen funds and the "interdependent nature of [Martinez's] and Garcia's use of" the Juan Rosario accounts, 20th Century, and Marc Write. With respect to the unreported interest income, the District Court noted that Martinez and Garcia pooled funds in the Juan Rosario accounts, used those funds to purchase certificates of deposit, and withdrew interest at the same times each year. With respect to the improper deductions, the Court found that Garcia knew that the checks for phantom expenses were being used by Martinez in part to generate large sums of cash to fund Garcia's home assembly operation.

Garcia has maintained that he was not aware of the scope of Martinez's tax evasion, but the District Court was entitled to disbelieve him. The Court properly determined that a joint undertaking existed, and that Garcia did not meet his burden of proving that the elements of Martinez's tax loss for which Garcia was held accountable were either not within the scope of his conspiratorial agreement or not foreseeable by him.

D. Danziger

1. Responsibility for Martinez's Tax Losses. For similar reasons, we conclude that Danziger was properly held accountable for most of Martinez's tax loss. As the District Court found, Danziger pooled funds with Martinez and Garcia in the Juan Rosario accounts, and all three defendants "shared the evading mechanism of Juan Rosario, 20th Century, and Marc Write through their joint use of the names, accounts, and corporate structures of the entities." In addition, Danziger received cashier's checks drawn on accounts that were funded primarily by customers of AL Pen. The District Court was entitled not to credit Danziger's unsubstantiated claim that he believed that all of the entities and transactions were legitimate. We thus agree that Danziger did not meet his burden of proving that the elements of Martinez's tax loss for which he was held accountable were either not within the scope of his conspiratorial agreement or not foreseeable by him.

2. Obstruction of Justice Enhancement. Prior to sentencing, Danziger submitted an "Affidavit in Connection with Sentencing" in which he "emphatically den[ied] that [he] had knowledge of or was knowingly involved in any joint activity to help evade the taxes of Mr. Martinez-Rios or AL Pen." The District Court imposed a two-level enhancement for obstruction of justice based on the statements in the affidavit. Because the District Court was entitled to find that the claims in Danziger's affidavit were false, we conclude that there was a sufficient basis for an obstruction of justice enhancement. See U.S.S.G. § 3C1.1, comment. (n. 3(h)) (false information concerning sentencing). For substantially the same reasons, the District Court did not err in failing to accord a reduction for acceptance of responsibility.

Conclusion

We have considered appellants' remaining contentions, and conclude that they are without merit. As set forth above, the sentences of all three defendants are vacated, and the case is remanded for recalculation of defendants' tax losses and resentencing in accordance with this opinion.