Appellants Hall and Uranga were convicted on jury verdicts of two counts each of tax evasion under 26 U.S.C. § 7201 . They claim the District Court’s failure to instruct the jury on the “bank deposits” and “net worth” methods of proof constituted “plain error”; that the Government relied on inaccurate figures in its calculations utilizing these methods; that the Government did not negate the appellants’ explanations of the source of their increased wealth; and that they were prejudiced by unconstitutionally inadequate assistance of counsel. We note jurisdiction under 28 U.S.C. § 1291 and reverse and remand.

We agree that the omission of instructions on the inferences and assumptions underlying the “net worth” and “bank deposits” methods of proof was plain error which prejudiced the appellants.

I. Background

Appellants Hall and Uranga were equal business partners operating several retail stores selling antiques, men’s and women’s clothing, jewelry, cosmetics, and novelty items. In 1975, the Internal Revenue Service discovered that they had failed to file individual or partnership tax returns for 1970-1974. A criminal investigation commenced and the appellants filed tax returns for this period. For the years 1972 and 1974, Hall and Uranga reported net losses and no income tax due.

The Government’s investigation, however, concluded that the appellants had understated their income for 1972 and 1974. According to the Government’s analysis, Hall and Uranga each owed an income tax of about $7,200 for 1972 and $4,200 for 1974. Appellants were tried before a jury in September, 1979, and found guilty on all counts.

II. Absence of Jury Instructions on Methods of Proof

The Government found the appellants’ records inadequate to accurately determine income and tax liability. At trial, the prosecution elicited testimony from its experts establishing appellants’ income by both the “net worth” and the “bank deposits” methods of proof. At the close of trial, no instructions concerning these methods of proof were requested, and none were given.

A. Net Worth Method

The use of the net worth method of proving unreported income has been approved by the Supreme Court and often encountered in this circuit. Holland v. United States, 348 U.S. 121 , 75 S.Ct. 127 , 99 L.Ed. 150 (1954); e. g., United States v. Hamilton, 620 F.2d 712 (9th Cir. 1980); and United States v. Gardner, 611 F.2d 770 (9th Cir. 1980). When this method is invoked, however, it triggers special protections for the accused and particularly careful scrutiny by the courts. The Supreme Court has enumerated a number of the hazards to the innocent imposed by this circumstantial method of proof. Holland, 348 U.S. at 127-29 , 75 S.Ct. at 131-32 . After reviewing the potential shortcomings, the Court concluded:

The dangers are evaluated from the perspective of the trier of fact, usually a jury. Of particular concern is the possibility that the trier of fact will not give the defendant the full benefit of doubt he deserves. The Supreme Court has noted that “[t]here is great danger that the jury may assume that once the Government has established the figures in its net worth computations, the crime of tax evasion automatically follows.” Id. at 127-28 , 75 S.Ct. at 131 . The crime, of course, does not automatically follow, and the danger that such a conclusion will be drawn lies in the complexity of the net worth method itself.

The net worth method is not simple to understand. Even when its operation is described by experts as part of the Government’s case, the jury, without careful instruction, cannot be expected to perceive the basic underlying assumptions, nor to understand the nature of the inferences they are implicitly being asked to make.

The net worth method rests on the primary assumption that most increases in net worth are from taxable sources, and that when this is not true, the taxpayer is able to explain their origin. While this may often be true, it may not be transformed from permissible inference into presumption. The jury must pointedly be made aware of the nature of this underlying assumption and their freedom to draw or not draw the inference, as the facts may in their eyes command. The Government may not be relieved of its burden to prove all elements of the crime beyond a reasonable doubt. Id. at 126 , 75 S.Ct. at 130 . To obtain a proper verdict of conviction, the prosecution must establish evidence suffi cient to convince the jury beyond a reasonable doubt that the inference of a taxable source should be made.

Recognizing the inherent danger to the defendant’s fair trial due to the complex underpinnings of the net worth method, the Supreme Court in Holland established the requirement of detailed, comprehensive jury instructions on the net worth method of proof:

We interpret and adopt this as a clear requirement for explanatory jury instructions in net worth cases. Accord, United States v. Tolbert, 367 F.2d 778 (7th Cir. 1966); United States v. O'Connor, 237 F.2d 466, 472-73 (2d Cir. 1956).

The Government argues that through its experts, it presented to the jury a clear and concise explanation of the net worth method, and that this satisfies the requirement of Holland. It contends the issue was one of credibility, and the jury understood that if it believed Hall and Uranga’s explanations it would acquit, but if not, it should convict. We do not believe' this is sufficient to insure the integrity of the trial process. Where such assumptions and inferences are involved, it is difficult to conceive of adversary testimony adequately substituting for impartial judicial instructions given at the time in the trial when the jury is attentive to its mandate. Further, there is no indication that the prosecution’s evidence had any comment on the underlying assumptions and existing inferences of the method. This does not comport with the Supreme Court’s mandate in Holland', and we reject the Government’s contention.

B. Plain Error

No objections to the instructions given were made by appellants at trial, nor did they themselves request any explanatory instructions. We, therefore, must review appellants’ challenge to the instructions under the “plain error” standard. United States v. Krasn, 614 F.2d 1229 (9th Cir. 1980). Fed.R.Crim.P. 30, 52(b). Under this standard, a criminal conviction will be reversed when there has been “highly prejudicial error affecting substantial rights.” United States v. Giese, 597 F.2d 1170, 1199 (9th Cir.), cert. denied, 444 U.S. 979 , 100 S.Ct. 480 , 62 L.Ed.2d 405 (1979). This occurs only in exceptional circumstances. Id. “It must be a situation where reversal is necessary to preserve the integrity and reputation of the judicial process, or to prevent a miscarriage of justice.” Krasn, 614 F.2d at 1236 . Because the omission of these explanatory instructions goes to the very basis of the jury’s ability to evaluate the evidence, we conclude that a finding of plain error is warranted. Accord, Tolbert, 367 F.2d at 781 . See O'Connor, 237 F.2d at 471-72 .

Finding that plain error was present does not end the inquiry. We must look to the effect of the error. United States v. Lopez, 575 F.2d 681, 685 (9th Cir. 1978). Did it affect the outcome of the trial? The courts have developed different standards of review depending upon whether the error was perceived to be of constitutional or non-constitutional dimension. We need not here delve into the niceties of the distinctions between constitutional and non-constitutional error as we find that the failure to instruct on the assumptions and inferences of the net worth method so tainted the jury’s deliberative tools that we simply cannot say that the verdict would probably have been the same had the error not been made. As explained above, an understanding of this method of proof is essential to the jury’s proper evaluation of the evidence, and goes to the heart of the deliberative process. Such a structural infirmity cannot be passed over lightly, and a conviction may not be allowed to stand when tarnished by these doubts about such a fundamental aspect of trial. See Tolbert, 367 F.2d at 781 .

Accordingly, we conclude that the omission of explanatory instructions, as required by Holland, was plain error. We cannot say that it was more-probably-than-not harmless. We must, therefore, reverse the convictions of both defendants.

C. Bank Deposits Method

The Government argues that it relied on the bank deposits method of proof to show appellants’ unreported income, using the net worth method only for corroboration. Noting that Holland concerned only the net worth method, the Government contends that reversal is thus not called for nor necessary in this case. We do not agree.

Although the net worth method may have been used for corroboration, the results of the net worth analysis were thoroughly presented to the jury by the Government’s expert. We cannot speculate on the role which the Government’s net worth analysis played in the minds of the jury, Beck v. United States, 298 F.2d 622, 631 (9th Cir. 1962), but it may have been substantial. If the jury had disbelieved the Government’s net worth result, it may very well have cast doubt on the bank deposits result as well, inasmuch as both analyses yielded the same figures. But we need not rest our decision on our estimation of the role played by the net worth method, for we believe that explanatory instructions are similarly required when the bank deposits method of proof is used.

Like the net worth method of proof, the bank deposits method seeks to show by circumstantial- means that the defendant had income which was not reported. And like the net worth method, it asks the jury to infer that this excess income was from a taxable source. Although the mechanics of arriving at an income figure are different, both methods involve similar underlying assumptions and afford much the same inferences for and against the accused. Moreover, these assumptions and inferences are not self-evident, and the technicalities of the bank deposits method of proof are just as subtle as those of the net worth method. For the reasons detailed in Section II-A above, we conclude that comprehensive explanatory instructions must be given when the bank deposits method of proof is used, just as is required by Holland for the net worth method. Accord, Greenberg v. United States, 295 F.2d 903, 907 (1st Cir. 1961).

III. Inventory Cost

Hall and Uranga argue that the Governnient’s figures did not accurately reflect their inventory cost, and consequently yielded inaccurate figures for “cost of goods sold.” Appellants point out that the cost of goods sold is part of the Government’s calculation of the business’s gross profit and directly related to the income of the business. Thus, inventory valuation becomes an essential part of the Government’s case.

When choosing to proceed against a defendant using the net worth or bank deposits methods of proof, the Government assumes a special responsibility of thoroughness and particularity in its investigation and presentation. Holland, 348 U.S. at 135-36 , 75 S.Ct. at 135 ; Gardner, 611 F.2d at 775 . This responsibility imposes the duty to, inter alia, accurately establish the figures upon which the methods are based, and to reasonably investigate leads which may reveal that the defendants properly report ed their income. Gardner, 611 F.2d at 775 . See United States v. Keller, 523 F.2d 1009, 1011 (9th Cir. 1975). Here, both this duty to investigate and the duty to establish figures with reasonable certainty are implicated by the Government’s treatment of Hall and Uranga’s inventory valuation. In particular, the Government must show that it. had followed through on appellant Hall’s prior notation suggesting that the inventory figures used by the Government were too high. This is a possible explanation for the apparent unreported income and may not be overlooked by the Government.

Because we remand this case, we leave to the District Court the task of applying these guidelines to the Government’s proof on retrial. Should the Government continue to use the 100% markup factor for valuing inventory, the Court should require a showing by the Government that it has investigated the appellants’ claimed figures and has justifiably rejected them. If there is no investigation of this lead, the trial court may consider the appellants’ version as true, and so instruct the jury. See Holland, 348 U.S. at 136 , 79 S.Ct. at 135. This may especially imperil the 1974 conviction. Of course, if it is shown arithmetically that even under the appellants’ version there would be a substantial amount of unreported income, the error would be inconsequential and the Government relieved of the need to pursue the matter.

IV. Other Issues

Appellants raise several other assignments of error which we deal with briefly.

A. Failure to Instruct on Forms of NonTaxable Income

The District Court gave no instructions that gifts, loans, and inheritances do not constitute taxable income. Appellants argue that it was error to fail to instruct on this portion of the tax law. They contend that because it was a theory of their defense that excessive increases in net worth and deposits were due to these sources, they were entitled to such an instruction. A defendant is certainly entitled to instructions on his theory of the case. Here, however, appellants requested no such instructions. Our standard of review is thus the “plain error” standard. See Section II-B, supra. Given the focus of the trial on the sources of income, and the testimony concerning the effect of loans, gifts, and inheritances on the appellants’ taxable income, the District Court could reasonably have concluded that the jury would not be misled by the omission of non-taxable income instructions.

Although we do not find this omission to constitute the “highly prejudicial error affecting substantial rights” necessary to constitute plain error, Giese, 597 F.2d at 1199 , we do believe it would be the better practice in this situation to instruct on non-taxable income. Accordingly, we suggest that the District Court include such an instruction on retrial.

B. Negating Claimed Non-Taxable Sources of Income

Appellants asserted at trial that the apparent increases in wealth actually resulted from gifts, loans, inheritances, and sales of personal property on which no gain was realized, all of which are non-taxable. They claim on appeal that the Government failed to negate these reasonable explanations of their excess income, as required by Holland. See Holland, 348 U.S. at 135 , 75 S.Ct. at 135 .

The record indicates, however, that the Government’s investigation did extend to the explanations offered by the appellants. Testimony and evidence at trial, including appellants’ prior inconsistent statements, discredited their claimed sources of income. The Government has met its threshold burden of investigating and negating explanations, and from the evidence, the jury could properly disbelieve the appellants’ version. There was no violation of Holland’s investigation mandate here, nor was there insufficient evidence to support the jury’s apparent conclusions as to these claimed transactions. Glasser v. United States, 315 U.S. 60, 80 , 62 S.Ct. 457, 469 , 86 L.Ed. 680 (1942); United States v. Winn, 577 F.2d 86, 91 (9th Cir. 1978).

C. Inadequacy of Counsel

Appellants claim, for numerous reasons, that they were afforded unconstitutionally ineffective assistance of counsel. Because we remand this case for a new trial, we do not reach this assignment of error.

CONCLUSION

The several judgments of conviction and sentence entered on October 22, 1979 are reversed and the case is remanded for a new trial.

REVERSED AND REMANDED.

. I.R.C. § 7201 ( 26 U.S.C. § 7201 ) provides as follows: “Any person who willfully attempts in any manner to evade or defeat any tax imposed by this title or the payment thereof shall, in addition to other penalties provided by law, be guilty of a felony and, upon conviction thereof, shall be fined not more than $10,000, or imprisoned not more than 5 years, or both, together with the costs of prosecution.” . The Government’s computations showed tax due for Hall of $7,152.47 in 1972 and $4,259.92 in 1974, and for Uranga of $7,339.39 in 1972 and $4,259.92 in 1974. . The net worth method of proof is a circumstantial way of attempting to show unreported taxable income. It purports to demonstrate that excess income must exist because of otherwise unaccountable increases in the defendant’s net worth and expenditures. The net worth (assets less liabilities) at the beginning of the tax year (opening net worth) and at the end of the tax year (closing net worth) are established. Assuming the closing net worth is greater, the difference is the increase in the defendant’s net worth over the course of the tax year. To this is added the defendant’s non-deductible expenditures (e. g., subsistence, major purchases, other personal expenses), and all known non-taxable income is subtracted (e. g., gifts, inheritances, etc.). The resulting figure is compared to the reported taxable income on the defendant’s return, and the Government will contend that any excess is unreported taxable income. . The bank deposits method of proof is also a circumstantial way of establishing unreported income. It purports to demonstrate that ex cess income must exist by showing excessive unaccounted for bank deposits. The bank deposits for the tax year are totaled, with adjustments made for funds in transit at the beginning and the end of the year. Non-income deposits are then excluded, and non-deposited income is included. This constitutes a reconstructed gross income. Calculation of taxable income then proceeds in the usual way, taking into account the legitimate deductions, exceptions, exclusions, and credits. In the case of a business, these would include the business’s cost of goods sold and other expenses. If the resulting figure differs from what the taxpayer has reported, the Government will contend that the difference is unreported taxable income. . For an additional discussion of the dangers attached to the net worth and bank deposits methods of proof, see Duke, Prosecutions for Attempts to Evade Income Tax: A Discordant View of a Procedural Hybrid, 76 Yale L.J. 1 , 16-34 (1966). . The test to be applied where the error is of non-constitutional dimension is whether it is more probable than not that the error was harmless. Where the error is found to be constitutional, the test is whether it was harmless beyond a reasonable doubt. Chapman v. California, 386 U.S. 18, 24 , 87 S.Ct. 824, 828 , 17 L.Ed.2d 705 (1967); United States v. Valle-Valdez, 554 F.2d 911, 915 (9th Cir. 1977). . We need not be deterred by this Court’s decision in Percifield v. United States, 241 F.2d 225 (9th Cir. 1957). In Percifield , appellant claimed the trial court did not clearly instruct that all increases in net worth do not result from taxable income. However, this Court found that the matter was sufficiently covered by the instructions which were given. Here, in contrast, no instructions whatsoever were given on the methods of proof. . See note 4, supra.