SILBERMAN, Circuit Judge:

This is an appeal from a conviction of income tax evasion. Appellant, Fred Black, complains of insufficiency of the Government's evidence, of error in the trial court's charge to the jury, and of improper anti-deadlock instructions.

Black was indicted and prosecuted on numerous counts, including a RICO Act violation, one count of conspiracy, seven counts of concealment of material facts, seven counts of causing a failure to file currency transaction reports, five counts of Travel Act violations, mail and wire fraud counts, and four counts of tax evasion. After a forty day trial, Black was convicted on three counts of tax evasion. The Government charged that although Black received $65,827 of taxable income in 1978, $109,251 of taxable income in 1979, and $174,755 of taxable income in 1981, he failed to file a return for any of those years.

I.

The resolution of Black's claims concerning sufficiency of evidence and adequacy of the jury charge turns entirely upon the proper characterization of the actual method used by the Government to prove Black's tax evasion. The Government contends it employed the "specific items" method of proof, a direct method of demonstrating tax evasion in which the Government "produce[s] evidence of the receipt of specific items of reportable income by the defendant that do not appear on his income tax return." United States v. Marabelles, 724 F.2d 1374, 1377 n. 1 (9th Cir. 1984). Black claims, however, that the Government used the "bank deposits/cash expenditures" method. When using that indirect method of proof, the Government shows, either through increases in net worth, increases in bank deposits, or the presence of cash expenditures, that the taxpayer's wealth grew during a tax year beyond what could be attributed to the taxpayer's reported income, thereby raising the inference of unreported income.

In any indirect method case, the Government must prove that the increased wealth did not come from nontaxable sources. Otherwise the evidence will be insufficient, for

[t]here is always the possibility that the taxpayer deposited cash that he received from a non-taxable source or from income taxed in a prior year but kept on hand as cash or even from unreported income from a prior year kept on hand in cash. Such events are common human occurrences, and this possibility may of itself create reasonable doubt. Therefore, the government must establish in some fashion the amount of cash the taxpayer had on hand at the start of the period. This is part of the government's duty to negate the possibility that bank deposits or cash expenditures in the year under investigation originated from nontaxable sources.

United States v. Boulet, 577 F.2d 1165, 1168 (5th Cir. 1978), cert. denied, 439 U.S. 1114, 99 S.Ct. 1017, 59 L.Ed.2d 72 (1979).

On the other hand, where the Government's case is based on evidence showing specific items of unreported income, the safeguards required for indirect methods of proof are not necessary, as the possibility that the defendant may be convicted because non-taxable income is mistakenly presumed to be taxable income, or because cash expenditures are mistakenly assumed to be made from taxable income, is not present. See United States v. Lewis, 759 F.2d 1316, 1328 (8th Cir.) (proof of opening net worth not required in case involving both net worth and specific-item methods), cert. denied, 474 U.S. 994, 106 S.Ct. 406, 88 L.Ed.2d 357 (1985); Conford v. United States, 336 F.2d 285, 287 (10th Cir. 1964) (rule of Holland v. United States, 348 U.S. 121, 75 S.Ct. 127, 99 L.Ed. 150 (1954), requiring proof of net worth, not applicable where expenditures evidence used only to corroborate specific items proof).

Black claims that the Government relied on a bank deposits/cash expenditures method of proof, but utterly failed to rebut the possibility that his expenditures originated from non-taxable sources, and therefore the evidence was insufficient to sustain a conviction. In particular, Black maintains that the Government was obliged to negate the possibility that his bank deposits and cash expenditures were from non-income sources, and to establish his opening net worth for the years in question. Black, moreover, argues that the jury instructions omitted necessary explanations of the assumptions inherent in indirect methods of proof, and of the inferences that may properly be made by the jury, all in violation of the Supreme Court's clear guidance in Holland v. United States, 348 U.S. 121, 75 S.Ct. 127, 99 L.Ed. 150 (1954). In short, Black claims the Government tried to convict him of tax evasion "by simply showing that he spent money and did not file a tax return during the tax years in question."

The Government's response is that since it introduced evidence of specific items of income received by Black, it was not required to disprove the likelihood of a cash hoard or a non-taxable source of income. From approximately 1975 to the time of the trial, Black was subject to an IRS lien of approximately three million dollars. During this time, Black created two corporations, Dunbar and Machine-A-Rama, portrayed by the Government as dummy corporations which had neither paid employees nor offices. At trial, Black disputed the bogus nature of these entities, claiming the corporations were involved in developing a casino in Atlantic City — a project which never materialized — and he also insisted that any money he took from these corporations was in the form of loans which he felt obligated to repay. Nevertheless, it was uncontroverted that during the period covered by the indictment Black had no personal bank accounts and that many of Black's personal expenses were paid by checks drawn on accounts of these two corporations. Black further conceded that he created Dunbar because he did not want to put property in his own name and because he wished to conceal from the IRS money he was spending.

In the Government's view, Black received taxable income each time he wrote a check on the accounts of Dunbar and Machine-A-Rama to cover his personal expenses. Evidence that Black paid for personal expenses with checks drawn on corporate accounts and that Black never truly considered the checks to be loans would be sufficient for conviction, for "[a]ll the law requires is that there be proof sufficient to establish that there has been a receipt of taxable income by the accused and a willful evasion of the tax thereon." United States v. Nunan, 236 F.2d 576, 586 (2d Cir. 1956), cert. denied, 353 U.S. 912, 77 S.Ct. 661, 1 L.Ed.2d 665 (1957).

Black, by focusing on isolated remarks at trial, argues that the Government presented only a cash expenditures case against him. We disagree. If the statements by the prosecutor, the testimony of the Government's tax witness, and the trial judge's instructions to the jury, are each considered in light of the evidence actually submitted, it is clear that the Government presented direct proof that Black received specific items of taxable income and did not pay tax on that income.

In the brief part of his opening statement devoted to the tax charge, the prosecutor told the jury the Government would show that, during the years in question, Black had personal expenditures of $538,000, that the Government would prove this by evidence of checks made out for personal expenses, and that the expenditures were taxable income, as distinguished from non-taxable business expenses. The prosecutor then proceeded to list some of the expenditures, which included rent for an apartment at the Watergate complex in Washington, D.C., purchases of jewelry, payments to restaurants, and then reiterated that these expenditures were personal — not business related. And at the close of the trial, the prosecutor summed up the tax case by describing it as based on Black's expenditures for "personal purposes, as against any so-called business purpose." While the prosecutor did in fact refer to personal expenditures, he did so to distinguish checks Black wrote that could arguably have been to cover business expenses related to Machine-A-Rama and Dunbar (and so did not result in specific items of income to Black), from checks Black wrote to cover personal expenses, which on the prosecutor's theory did result in income.

The Government's tax case against Black was presented largely through the testimony of James May, an IRS agent. Explaining how he arrived at a figure for Black's taxable income for 1979, the witness said

[b]asically, I did an analysis of all expenditures from the [checking] account of Dunbar and Machine-A-Rama for the year 1979. I broke those into categories of personal expenditures for the benefit of Mr. Black or his family members, and then those which could be classified as business in nature, and all of those checks to cash. And I used those personal expenditures to arrive at a gross income figure.

Later, the witness again explained his method of calculating Black's income as "a[n] expenditures method based on expenditures or disbursements from the accounts of Dunbar and Machine-A-Rama." Just as did the prosecutor, May referred to personal expenditures and the expenditures method, but he was using that term merely to distinguish business from personal expenditures. The personal expenditures Black paid for by corporate checks were not circumstantial evidence of income from some hidden source; on the Government's theory the checks were themselves the specific items of income.

Similarly, in his charge to the jury, the trial judge also referred to the purposes for which these checks were written.

[i]n order to prove the defendant received substantial additional income which was not disclosed to the Internal Revenue Service, the prosecution relies upon proof by the "Bank Deposit/Expenditures Method" — that is, the Government has examined the sources of the funds deposited into the bank accounts of Dunbar and Machine-A-Rama for the tax years in question.

The Government has also examined all of the checks written by Mr. Black on the Dunbar Management and Machine-A-Rama accounts, as well as the purposes for these expenditures.

As you will recall from the evidence presented during the case, there were numerous stipulations agreed to by the Government and Mr. Black describing checks written by him or at his direction to various payees for Mr. Black's own personal use and benefit.

While there were several explicit references to the "personal expenditures method" by the prosecutor, the Government's expert witness, and the trial judge in his instructions, at no point in the trial was it suggested to the jury that evidence of personal expenditures, without more, would be sufficient to convict Black of tax evasion. Evidence of personal expenditures was relevant only because the Government contended that the very writing of the checks created income to Black. Thus, the danger encountered in a classic "cash expenditure" case — that the defendant could be convicted for spending non-taxable income — is not at all present here. See United States v. Meriwether, 486 F.2d 498, 505 (5th Cir. 1973) (failure to include figures for net worth or cash on hand at beginning of taxable years cannot prejudice defendant in a specific items case), cert. denied, 417 U.S. 948, 94 S.Ct. 3074, 41 L.Ed.2d 668 (1974); see also United States v. Cramer, 447 F.2d 210, 218 (2d Cir. 1971), cert. denied, 404 U.S. 1024, 92 S.Ct. 680, 30 L.Ed. 2d 674 (1972). In this case, the use of the phrase "personal expenditures method" was not associated at all with the "cash expenditures method" of proving tax evasion; the phrase was used solely to distinguish Black's business expenditures from his personal expenditures.

During the trial, moreover, Black's counsel undoubtedly understood the Government was not presenting a cash expenditures case, for no objection was made to the jury instructions given by the trial judge, and yet those instructions would have been inadequate had the Government relied on a cash expenditures method of proof.

Black's defense to the tax charge was not that the expenditures were made from a source of non-taxable income unknown to the Government, for example an inheritance or a sum of cash squirreled away in previous years, yet that would be a typical defense in a cash expenditures case. See, e.g., United States v. Rifkin, 451 F.2d 1149, 1151-53 (2d Cir. 1971). Rather, Black argued that the specific items of income the Government alleged he received — the checks drawn on the Dunbar and Machine-A-Rama accounts and used for personal expenses — were loans that he was obligated to repay to Dunbar and Machine-A-Rama, and therefore were not income.

That claim, however, the jury was entitled to reject, as their verdict indicates they did. See United States v. Meyer, 808 F.2d 1304, 1306 (8th Cir. 1987) (jury may reject controverted claim that transactions were informal loans rather than unreported income); United States v. Pisani, 773 F.2d 397, 405-07 (2d Cir. 1985) (whether gifts to campaign fund yield taxable income when spent on personal items is jury question); see also United States v. Marabelles, 724 F.2d 1374, 1378-79 (9th Cir. 1984) (jury could reject claim that unreported income went to unclaimed business expenses). Viewing the evidence most favorably to the Government, Glasser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942), the Government established that Black received substantial taxable income that he did not report to the IRS. We thus decline to reverse Black's conviction on the grounds of insufficient evidence.

Black also challenges the adequacy of the trial judge's instructions. But because no objection was made to the instructions at trial, we may reverse only if we find plain error. FED.R.CRIM.P. 30, 52(b). It is true that the trial judge's reference to the "bank deposits/expenditures method" was misconceived, but nevertheless the instructions did direct the jury to that part of the Government's case concerning the checks written by Black on the accounts of Dunbar and Machine-A-Rama, and the stipulations that the checks were written for Black's personal use and benefit. In addition, Black's counsel, in his closing argument, reiterated Black's claim that these checks were actually loans. We think, therefore, the jury was properly apprised of the issue to be resolved. See United States v. Horton, 526 F.2d 884, 887-88 (5th Cir.) (colloquy among Government, defense attorney, and the bench served as "functional equivalent of a limiting instruction"), cert. denied, 429 U.S. 820, 97 S.Ct. 67, 50 L.Ed.2d 81 (1976). Considering the strength of the Government's evidence against Black, the uncontested personal nature of the expenditures, and the incredibility of Black's claim that he considered the transactions to be loans, we do not believe any shortcomings in the instructions rose to the level of plain error affecting substantial rights. See United States v. Cramer, 447 F.2d 210, 219 (2d Cir. 1971).

We thus reject Black's argument that under the reasoning of United States v. Meriwether, 440 F.2d 753 (5th Cir. 1971), we should reverse because the jury might have convicted Black merely because he spent money. In Meriwether the jury was instructed on both a specific items and net worth method of proof, with the emphasis placed on the net worth method. The court of appeals reversed because the instructions on the net worth method were flawed and there was "no way to be certain upon which method of proof the jury based its verdict of guilty." Id. at 757. In this case, however, the jury was never instructed on the cash expenditures method, nor was it ever argued to the jury that Black could be convicted on the theory that cash expenditures were circumstantial evidence of taxable income. Ironically, a tax lawyer sitting in the courtroom could perhaps have been confused by the use of the phrase "personal expenditures method," for it might well have suggested the cash expenditures method, but the slight possibility that a jury never instructed on the cash expenditures method would have been confused is so insignificant that it cannot justify a reversal on grounds of plain error.

II.

Black contends the trial judge erroneously delivered multiple Thomas-type anti-deadlock charges to the jury. "The Thomas charge instructs deadlocked juries that each member is to consult with other jurors and to be open to reexamination of his or her views, but that jurors should not surrender their honest beliefs solely to return a verdict." United States v. Glover, 731 F.2d 41, 43 n. 5 (D.C. Cir. 1984); see generally United States v. Thomas, 449 F.2d 1177 (D.C. Cir. 1971) (en banc); cf. Allen v. United States, 164 U.S. 492, 17 S.Ct. 154, 41 L.Ed. 528 (1896). As we do not think the Thomas charge was actually given more than once, we reject Black's argument. To be sure, the judge quoted a portion of the Thomas charge to the jury in response to a note from the jury foreman asking whether "a juror who gives a verdict to the other jurors [must] give his or her reasons for reaching that verdict to the other jurors[.]" It would be incorrect, however, to characterize the judge's answer to the jury as a Thomas charge, for the judge merely asked the jurors to exchange views with each other, and did not say, as he would have had he given a Thomas charge, that a juror should not hesitate to reexamine his views and change his opinion if convinced of error. We do not believe this instruction by itself constituted a Thomas charge. See United States v. Solomon, 565 F.2d 364, 366 (5th Cir. 1978) (charge not coercive where it did not refer to the need for minority to reconsider its vote). Indeed, as the trial judge indicated in an exchange with counsel prior to responding to the jury's question, a Thomas charge would not have been responsive, for the note did not say the jurors were deadlocked.

After the jury had been deliberating for three days and part of the morning of the fourth day, the jury sent a note to the judge saying "[w]e are unable to reach a unanimous verdict. We are hopelessly deadlocked." Concerned that it was rather early in-deliberations for a complete deadlock, especially considering that the trial had lasted for eight weeks and the jury had numerous counts to consider against two defendants, the judge inquired of the jury by note whether they were deadlocked with respect to both defendants and on every count of the indictment. A trial judge may take reasonable steps to ensure that a jury is in fact deadlocked when informed that this is a possibility. See United States v. Ross, 626 F.2d 77, 81 (9th Cir. 1980); United States v. Smoot, 463 F.2d 1221, 1223 (D.C. Cir. 1972). When the jury responded in the negative, the judge gave a partial verdict instruction, informing the jury it could return a verdict concerning only one of the defendants or covering less than all the charges. After giving this instruction, the judge asked the jury to continue its deliberations — an entirely proper and noncoercive request. See, e.g., United States v. D'Antonio, 801 F.2d 979, 983-84 (7th Cir. 1986). Again, we see nothing similar to a Thomas charge.

Immediately following the partial verdict instruction, the jury asked whether they could turn in the partial verdict or whether they were obligated to continue deliberating on the other charges. The court interpreted this to mean that the jury wanted to know if, upon turning in their partial verdict, their jury duty would be complete. In response, the court simply informed the jury that if they returned a partial verdict, they would "continue to deliberate on the remaining charges." The court's interpretation of the jury's question was reasonable, and its instruction that the jury would continue to deliberate after returning a partial verdict was proper — it included none of the coercive elements of a Thomas charge that may possibly bring into doubt whether the jury's verdict was freely given. See United States v. Burke, 700 F.2d 70, 78-81 (2d Cir.), cert. denied, 464 U.S. 816, 104 S.Ct. 72, 78 L.Ed.2d 85 (1983); see also United States v. Gordon, 817 F.2d 1538, 1542-43 (11th Cir. 1987) (request to jury to continue deliberating on remaining charges after jury returned a partial verdict is not coercive); Ross, 626 F.2d at 81 (same). No further instructions were given at this point.

The next day, the jury informed the court by note that they had reached a decision on as many counts as possible, and were hopelessly deadlocked on all other counts. After inquiring again whether the jury was in fact irreconcilably deadlocked on all other counts, and again receiving a negative response, the court, as was within its discretion, gave the complete Thomas charge for the first and only time. See United States v. James, 764 F.2d 885, 890-91 (D.C. Cir. 1985) (entirely within discretion of trial judge to give Thomas charge when jury has reached an impasse and has had sufficient time to deliberate). One and a half days after this charge was given, the jury returned a partial verdict. See supra note 1. Because we reject Black's contention that multiple Thomas charges were given, we need not reach Black's suggestion that this circuit should adopt a per se rule prohibiting any repetition of an antideadlock instruction.

We reject Black's contention that the cumulative effect of these instructions was plainly coercive and prejudicial. The jury did not return a verdict until a day and a half after the judge gave the Thomas charge, and even then they acquitted Black of eight counts and failed to reach a verdict on numerous remaining charges. This hardly seems a case where the jury surrendered "their honest opinions for the mere purpose of returning a verdict." D'Antonio, 801 F.2d at 984; see Gordon, 817 F.2d at 1543 (acquittal on some charges and inability to reach a verdict on others indicates lack of coercion); United States v. Ramirez, 710 F.2d 535, 544 (9th Cir. 1983) (inability to reach verdict and lengthy deliberation following anti-deadlock charge indicates no coercion); United States v. Young, 702 F.2d 133, 136 (8th Cir. 1983) (lengthy deliberation following Allen charge is indicative of lack of coercion).

Appellant's conviction is therefore

Affirmed.