A federal jury convicted appellant James Stone of violating 18 U.S.C. Sec. 287 by filing a false claim for an income tax refund. On appeal Stone raises two issues that merit discussion. First, was it reversible error for the district court to charge the jury on "deliberate ignorance" in the absence of sufficient evidence to support such a theory? We conclude that any error in giving such a charge in the absence of sufficient evidence is harmless when the instruction itself requires, as a precondition to its application, proof beyond a reasonable doubt of deliberate ignorance. The second issue is whether the district court erred by admitting evidence that Stone refused to provide the IRS with handwriting exemplars. We conclude that under the facts of this case any error in admitting that evidence was harmless.

In 1988 and 1989, the Internal Revenue Service ("IRS") received several suspicious tax refund requests from inmates at a Georgia prison. One such request, signed in Stone's name, sought a refund of taxes supposedly withheld from Stone's 1986 wages. A letter and supporting documentation accompanying the request explained that Stone's incarceration and the intervening bankruptcy of his former employer had prevented him from seeking the refund earlier. The IRS issued Stone a refund check of $1,242, which he deposited in his inmate account. Once the check cleared and prison officials released the funds, Stone forwarded the money to his sister with instructions to send it back to him as he needed. The IRS subsequently discovered that the alleged employer was fictitious and that Stone had spent a significant part of the 1986 tax year in prison.

On three occasions, Jack Wood, an IRS investigator, sought handwriting samples from Stone to compare with the signature on the refund request. On his first visit, June 27, 1989, Agent Wood told Stone that he had a summons for handwriting exemplars from Stone. Agent Wood read Stone the Miranda warnings, which included advice that Stone had the right to an attorney. Stone refused to provide handwriting exemplars. At the sentencing hearing, Stone testified that he called a lawyer "as quick as [Agent Wood] left the first time."1 On July 11, 1989, Agent Wood returned and advised Stone that handwriting samples "were not protected under the Constitution, as far as self-incrimination was concerned, and that they were just a means of identification, such as fingerprints." Stone indicated that he understood but again refused to cooperate. Agent Wood sought samples of Stone's handwriting a third time on July 25, 1989. On this occasion, a prison official informed Agent Wood that Stone refused to see him.

At trial, the district court allowed the United States to introduce evidence of Stone's repeated refusals to provide handwriting samples. At the Government's request, the district court instructed the jury that, although not dispositive, Stone's refusal to obey the handwriting summons was probative of his consciousness of guilt. The Government relied on this evidence in its closing argument.

At trial Stone argued that the Government had failed to connect him to the false refund request. The defense called an IRS handwriting expert who testified that the envelope in which the refund request was received, as well as certain entries on a supporting document, were written by Michael Perucca, another inmate. Lacking sufficient known samples of Stone's handwriting, the expert was unable to say whether Stone had actually signed the refund request. Although Stone's fingerprints were found on the explanatory letter, the defense presented the testimony of a retired prison official to show that Stone had served as a "squad room orderly," and that in such capacity Stone had distributed stationery and writing materials to other inmates. On cross-examination the Government's fingerprint expert admitted that she could not tell whether Stone's fingerprints were placed on the letter before or after it was written. The fingerprint expert also testified that she had found Michael Perucca's--but not Stone's--fingerprints on the tax return filed in Stone's name.

The district court charged the jury that knowledge of the false claim was an element of the offense. At the Government's request, the district court also charged the jury as follows on "deliberate ignorance":

When knowledge of the existence of a particular fact is an essential part of an offense, such knowledge may be established if the defendant is aware of a high probability of its existence, unless he actual [sic] believes that it does not exist. So, with respect to the issue of the defendant's knowledge in this case, if you find from all the evidence beyond a reasonable doubt that the defendant believed a false and fraudulent claim was being made against the United States in his name, and deliberately and consciously tried to avoided [sic] learning of such false and fraudulent claim being made against the United States in order to be able to say, if he should be apprehended, that he did not know a false and fraudulent claim was made, you may treat such deliberate avoidance of positive knowledge as the equivalent of knowledge.

In other words, you may find that a defendant acted knowingly if you find beyond a reasonable doubt, either, one, that the defendant actually made a false and fraudulent claim against the United States, or, two, that he deliberately closed his eyes to what he had every reason to believe was the fact.

Defense counsel objected to the deliberate ignorance instruction, arguing that there was no evidence that Stone consciously had closed his eyes to illegal activity. The Government countered that even if Stone himself had not filed the false return, his deposit and forwarding of the proceeds without investigation was an attempt to remain deliberately ignorant of the criminal activity.

On appeal, Stone argues that it was reversible error for the district court to instruct the jury on deliberate ignorance. Because a challenge to a jury instruction presents a question of law, our review is de novo. See United States v. Chandler, 996 F.2d 1073, 1085 (11th Cir.1993).

In United States v. Rivera, 944 F.2d 1563, 1570-71 (11th Cir.1991), we cautioned the district courts against instructing juries on deliberate ignorance when the evidence only points to either actual knowledge or no knowledge on the part of the defendant. A deliberate ignorance instruction is appropriate only when there is evidence in the record "showing the defendant purposely contrived to avoid learning the truth." United States v. Barbee, 968 F.2d 1026, 1033 (10th Cir.1992) (citation omitted). The Government argues that Stone's receipt of the refund check made him aware of a high probability that a false return had been filed. According to the Government, Stone's failure to investigate the reasons for the IRS's spontaneous generosity was a deliberate effort to avoid positive knowledge of the false claim. Stone counters that his actions are not evidence of deliberate ignorance at all. We need not determine whether the evidence of deliberate ignorance was nonexistent, insufficient, or sufficient to support the instruction. Even if we accept Stone's characterization of the evidence and assume that there was no evidence of deliberate ignorance, reversal is not required because any error in giving the instruction was harmless beyond a reasonable doubt.

We have previously applied the harmless error rule to a deliberate ignorance instruction, albeit under different circumstances. In Rivera, the prosecution had presented no evidence at all to prove conscious avoidance of knowledge. See 944 F.2d at 1572. Nonetheless, the Rivera Court held that the trial court's error in giving the deliberate ignorance instruction was harmless because the evidence of actual knowledge was " 'so overwhelming as to compel a guilty verdict.' " Id. at 1572-73 (quoting United States v. Sanchez-Robles, 927 F.2d 1070, 1075 (9th Cir.1991)). Contrary to the Government's position, and in contrast to the Rivera case, the error in this case is not rendered harmless by the quantity of evidence showing Stone's actual knowledge of the false tax return. The evidence of actual knowledge in this case was sufficient to support a guilty verdict but was not overwhelming. The jury twice informed the district court that it was deadlocked and only reached a verdict after it was given an Allen charge. The Rivera Court did not reach the issue we address: whether the error in giving a deliberate ignorance instruction when there is insufficient evidence to support it, and when the evidence supporting actual knowledge is not overwhelming, is nonetheless harmless because of the wording of the instruction.

In this case, the district court charged the jury that deliberate ignorance may be treated as the equivalent of positive knowledge if the jury found "from all the evidence beyond a reasonable doubt that [Stone] believed a false and fraudulent claim was being made against the United States" and consciously avoided confirming his belief (emphasis added). In other words, the jury was clearly instructed that a precondition to its application of the deliberate ignorance instruction was proof beyond a reasonable doubt that Stone deliberately kept himself ignorant.

Few tenets are more fundamental to our jury trial system than the presumption that juries obey the court's instructions. The " 'crucial assumption' underlying the system of trial by jury 'is that juries will follow the instructions given them by the trial judge.' " Marshall v. Lonberger, 459 U.S. 422, 438 n. 6, 103 S. Ct. 843, 853 n. 6, 74 L. Ed. 2d 646 (1983) (quoting Parker v. Randolph, 442 U.S. 62, 73, 99 S. Ct. 2132, 2139, 60 L. Ed. 2d 713 (1979)). Indeed, "[t]he presumption that juries follow their instructions is necessary to any meaningful search for the reason behind a jury verdict." United States v. Brown, 983 F.2d 201, 203 (11th Cir.1993). This presumption is, therefore, "almost invariable." Richardson v. Marsh, 481 U.S. 200, 206, 107 S. Ct. 1702, 1707, 95 L. Ed. 2d 176 (1987) (citing Francis v. Franklin, 471 U.S. 307, 325 n. 9, 105 S. Ct. 1965, 1976 n. 9, 85 L. Ed. 2d 344 (1985)); see also Zafiro v. United States, --- U.S. ----, ----, 113 S. Ct. 933, 939, 122 L. Ed. 2d 317 (1993) (relying on the presumption that juries follow their instructions and holding that a curative instruction avoided "any possibility of prejudice" from the joint trial of four narcotics codefendants). In Greer v. Miller, 483 U.S. 756, 766 n. 8, 107 S. Ct. 3102, 3109 n. 8, 97 L. Ed. 2d 618 (1987), the Court considered the effect of a curative instruction concerning improperly and inadvertently admitted evidence. The Court noted that the presumption that juries follow their instructions is overcome only if there is an " 'overwhelming probability' that the jury will be unable to follow the court's instructions ... and a strong likelihood that the effect of the evidence would be 'devastating' to the defendant." Id. (citations omitted); see also United States v. Colombo, 909 F.2d 711, 715 (2nd Cir.1990) (applying the "overwhelming probability" standard). In this case, there is no indication, much less an "overwhelming probability," that the jury was unable to follow the part of the deliberate ignorance instruction that conditioned its application on evidence proving deliberate ignorance beyond a reasonable doubt.

Stone's contention contains the basis of its denial. If, as he contends, there was insufficient evidence of deliberate ignorance to prove that theory beyond a reasonable doubt, then the jury, following the instruction, as we must assume it did, did not convict on deliberate ignorance grounds. The only way we can conclude that the deliberate ignorance instruction was harmful is if we assume that the jury applied the instruction contrary to its express terms. That is an assumption which we cannot and will not make.

The Supreme Court's holding in Griffin v. United States, --- U.S. ----, ----, 112 S. Ct. 466, 474, 116 L. Ed. 2d 371 (1991), substantially informs and supports our decision in this case. In Griffin the defendant was charged with a single count of conspiracy to defraud the federal government. The conspiracy had the dual objects of hindering the IRS and the Drug Enforcement Agency in their official duties. At trial, the Government failed to produce any evidence whatsoever to connect Griffin to an effort to interfere with the Drug Enforcement Agency. Over Griffin's objection, the trial court instructed the jury that Griffin could be convicted of conspiracy if she had participated in either of the two objects of the conspiracy. The jury returned a general guilty verdict against Griffin and her two codefendants. The Supreme Court affirmed the conviction. The Court found no precedent to support Griffin's contention that a general verdict must be set aside where "one of the possible bases of conviction was neither unconstitutional ... nor even illegal ... but merely unsupported by sufficient evidence." Griffin, --- U.S. at ----, 112 S. Ct. at 472. The Court concluded that there is a common sense reason to distinguish between a jury instruction which misstates the law and one which presents a theory of conviction not supported by the evidence:

Jurors are not generally equipped to determine whether a particular theory of conviction submitted to them is contrary to law--whether, for example, the action in question is protected by the Constitution, is time barred, or fails to come within the statutory definition of the crime. When, therefore, jurors have been left the option of relying upon a legally inadequate theory, there is no reason to think that their own intelligence and expertise will save them from that error. Quite the opposite is true, however, when they have been left the option of relying upon a factually inadequate theory, since jurors are well equipped to analyze the evidence.

Id. at ----, 112 S.Ct. at 474 (emphasis in original) (citation omitted).

The Supreme Court reiterated that position in Sochor v. Florida, --- U.S. ----, ----, 112 S. Ct. 2114, 2122, 119 L. Ed. 2d 326 (1992). In Sochor the trial court had instructed a capital jury on four aggravating factors, one of which was not supported by the evidence. If the jury had relied on the unsupported factor, its death sentence recommendation would have violated the Eighth Amendment. However, the Supreme Court refused to presume jury error and noted that jurors are "indeed likely to disregard an option simply unsupported by evidence." Id. According to the Sochor Court, the lesson of Griffin is that due process is not violated when "a trial court instruct[s] a jury on two different legal theories, one supported by the evidence, the other not." Id.

The issue in this case is closely analogous to the one decided in Griffin and Sochor. Under the jury instructions in this case, Stone could be convicted if he either knew of the false return or kept himself in deliberate ignorance of it. Accepting Stone's characterization, the evidence in this case was, as in Griffin, sufficient to support a conviction on one theory (actual knowledge) but insufficient to support a conviction on the other theory (deliberate ignorance). Stone does not contend that the trial court's deliberate ignorance instruction misstated the law of this Circuit. Instead, his complaint is that because the instruction was unsupported by the facts it was harmful--the same argument rejected by Griffin and Sochor. In United States v. Pace, 981 F.2d 1123, 1130 (10th Cir.1992), cert. denied, --- U.S. ----, 113 S. Ct. 1401, 122 L. Ed. 2d 774 (1993), the Tenth Circuit relied on Griffin and upheld a conviction on an indictment charging that the defendant distributed methamphetamine or amphetamine despite a "total lack of evidence" concerning amphetamine. The Court reasoned that:

A disjunctive charge may result in jury error when one of the alternatives is legally inadequate. But when, as here, one of the alternatives in the disjunctive charge is unsupported by any evidence whatsoever, we can assume that jurors will reject the 'factually inadequate theory,' [quoting Griffin, --- U.S. at ----, 112 S. Ct. at 474] ... and convict based on 'alternative grounds for which the evidence was sufficient' [quoting United States v. Townsend, 924 F.2d 1385, 1414 (7th Cir.1991) ].

Pace, 981 F.2d at 1130. Although we renew our admonition to the district courts that they should refrain from instructing juries on theories unsupported by the evidence, "[t]he refusal to do so, however, does not provide an independent basis for reversing an otherwise valid conviction." Griffin, --- U.S. at ----, 112 S. Ct. at 474.

We need not determine whether the Government introduced some or absolutely no evidence of deliberate ignorance in order to find the error harmless in this case. Griffin requires affirmance in either case. See --- U.S. at ----, 112 S. Ct. at 473. In that case, the petitioner sought to differentiate the "some evidence" and "no evidence" scenarios, see id., and argued that only in the absence of any evidence whatsoever could the court be certain that the jury had not convicted on an unsupported legal theory. Under that view, the introduction of any evidence to support a legal theory makes it "impossible to tell" on which theory the jury relied and requires reversal under Yates v. United States, 354 U.S. 298, 77 S. Ct. 1064, 1 L. Ed. 2d 1356 (1957). The Griffin Court categorically rejected that view, observing that it would lead to a perverse result: the less evidence the prosecution presents, the more likely a conviction would withstand appellate attack. --- U.S. at ----, 112 S. Ct. at 474.

We recognize that the Fifth, Eighth, and Ninth Circuits have reached a contrary conclusion on the issue of whether a deliberate ignorance instruction is harmless per se. See, e.g., United States v. Barnhart, 979 F.2d 647 (8th Cir.1992); United States v. Mapelli, 971 F.2d 284 (9th Cir.1992); United States v. Ojebode, 957 F.2d 1218, 1229 (5th Cir.1992) (implicit holding); United States v. Sanchez-Robles, 927 F.2d 1070 (9th Cir.1991); United States v. Beckett, 724 F.2d 855, 856 (9th Cir.1984). These decisions have generally given two reasons for their holdings. First, they have expressed concern that absent evidence to support the instruction juries will misunderstand it and will incorrectly employ a negligence or recklessness standard, see Ojebode, 957 F.2d at 1229, "thereby relieving the government of its constitutional obligation to prove the defendant's knowledge beyond a reasonable doubt," Barnhart, 979 F.2d at 652, and potentially shifting the burden of proof to the defendant, United States v. Murrieta-Bejarano, 552 F.2d 1323, 1325 (9th Cir.1977). In this case, the district court instructed the jury that deliberate ignorance would come into play if Stone "believed a false and fraudulent claim was being made ... and consciously tried to avoid" actual knowledge. The jury was told that Stone's belief and his actions had to be established "beyond a reasonable doubt." Such a charge tells the jury in no uncertain terms that the mens rea element is the defendant's belief and conscious actions, the existence of which must be measured by proof beyond a reasonable doubt. That is not a negligence standard. See United States v. Sasser, 974 F.2d 1544, 1552-53 (10th Cir.1992), cert. denied, --- U.S. ----, 113 S. Ct. 1063, 122 L. Ed. 2d 368 (1993) (holding that a properly worded deliberate ignorance instruction obviates the harmful effects of the erroneous giving of such an instruction).

The second rationale offered by the contrary cases from the other circuits is that affirming a conviction when there is insufficient evidence of deliberate ignorance and when the evidence of actual knowledge does not compel conviction substitutes the appellate court's determination of fact for that of the jury. See, e.g., Sanchez-Robles, 927 F.2d at 1075-76; Beckett, 724 F.2d at 856. Thus, in Beckett, the court concluded,

[t]he only evidence that tended to establish that Beckett had actual knowledge of the cocaine sale was the testimony of one undercover agent. Consequently, if we held the error harmless, we would be saying that the jury should have found that the defendant was guilty beyond a reasonable doubt. Although it is our function to review the sufficiency of the evidence to support a guilty verdict, it is the jury's function, not ours, to decide whether to return a guilty verdict in the first place. In other words, this record accommodates a construction of events that supports a guilty verdict, but it does not compel such a construction.

Beckett, 724 F.2d at 856 (emphasis in original). However, that concern about the proper division of functions between juries and appellate courts is predicated on the assumption that the jury has not found beyond a reasonable doubt that the defendant acted with actual knowledge. Such an assumption is in turn based on either of two speculative theories, both of which we reject. The theoretical basis for the assumption may be that juries are incapable of determining whether a particular fact (here, actual knowledge) has been proven beyond a reasonable doubt. If that is true, then our system of justice is in a good deal more trouble than anyone has heretofore realized. Alternatively, the assumption that the jury in such a case did not convict on actual knowledge, for which there was sufficient evidence, may be based on the theory that juries are incapable of applying jury instructions according to their terms and conditions. Such a theory flies in the face of a fundamental tenet of our jury system and has broad detrimental implications we are unwilling to embrace.

Because we presume that the jury followed its instructions, it follows that the jury disregarded the deliberate ignorance instruction and that the guilty verdict was based on the only remaining theory: Stone's actual knowledge. By affirming Stone's conviction we do not somehow usurp the role of the jury as the trier of fact. There is no Supreme Court authority for the proposition that reversal is required when the Government has presented enough evidence to support but not compel a conviction on an actual knowledge theory. Indeed, Griffin v. United States, --- U.S. ----, ----, 112 S. Ct. 466, 468, 116 L. Ed. 2d 371 (1991), forecloses that proposition. In that case, the evidence "implicated" Griffin in the conspiracy to hinder the IRS's activities; there was no suggestion that the evidence against Griffin compelled her conviction. Nonetheless, according to the Supreme Court the prevailing rule is that " 'when a jury returns a guilty verdict on an indictment charging several acts in the conjunctive ... the verdict stands if the evidence is sufficient with respect to any one of the acts charged.' " Id. at ----, 112 S.Ct. at 473 (quoting Turner v. United States, 396 U.S. 398, 420, 90 S. Ct. 642, 654, 24 L. Ed. 2d 610 (1970)) (emphasis added); see also United States v. Townsend, 924 F.2d 1385, 1414 (7th Cir.1991) ("It is one thing to negate a verdict that, while supported by evidence, may have been based on an erroneous view of the law; it is another to do so merely on the chance--remote, it seems to us--that the jury convicted on a ground that was not supported by adequate evidence when there existed alternative grounds for which the evidence was sufficient."), quoted in Griffin, --- U.S. at ----, 112 S. Ct. at 474. Thus, there is no requirement that the evidence in support of the alternative legal theory be so strong as to compel conviction.

The arguments enumerated in the Fifth, Eighth, and Ninth Circuit cases are but variations on a theme: they are rooted in a skepticism about the ability of juries to fit the evidence to their instructions and to reject unsupported legal theories. These arguments turn on its head the presumption that juries follow their instructions, a presumption that only has meaning if we also assume that juries understand their instructions. If we were to presume juror confusion, we would have no reason to believe that any verdict represented a proper application of the law to the facts. We refuse to start down that primrose path, which we believe is blocked by binding precedent requiring us to assume that juries do follow their instructions according to the terms of those instructions. The three circuits that have reached a contrary decision have not faced up to Griffin. The cases decided after Griffin--Barnhart, Mapelli, and Ojebode--do not even mention Griffin, which we find to be controlling. While we respect and carefully weigh the views of other circuits, we are required to follow Supreme Court decisions, and the Fifth, Eighth, and Ninth Circuit decisions cannot be reconciled with controlling case law.

On the other hand, we believe that the Tenth Circuit's decisions on this issue can be reconciled with the Supreme Court's jurisprudence. In United States v. de Francisco-Lopez, 939 F.2d 1405 (10th Cir.1991), the court refused to hold an unwarranted deliberate ignorance instruction to be harmless error. However, the instruction given in that case provided that "[k]nowledge ... may be inferred from circumstances that would convince an average ordinary person" that a given fact is true. Id. at 1411 (citation omitted). The court expressed concern that the jury might have convicted the defendant merely because he was negligent in driving a cocaine-laden car across the United States. The problem in de Francisco-Lopez was not that the jury might have disobeyed its instructions, but instead that the instruction misstated the law and gave the jury a latitude that it should never have had: to convict based on a negligence standard. In Griffin 's terms, 112 S. Ct. at 472, the instruction was legally inadequate and there was no reason to believe that the jury's intelligence and common sense would save it from error. Subsequent Tenth Circuit cases, see United States v. Sasser, 974 F.2d 1544 (10th Cir.1992); United States v. Barbee, 968 F.2d 1026 (10th Cir.1992), have upheld convictions despite the erroneous giving of a deliberate ignorance instruction. In each of these later cases, as in this case, the trial court did not imply that negligence or mistake was sufficient to support a conviction. See Sasser, 974 F.2d at 1552; Barbee, 968 F.2d at 1034. The question is whether the instruction correctly states the legal standards. In this case, it did.

In sum, there is nothing in the record to overcome the presumption that the jury followed its instructions. Because the deliberate ignorance instruction used by the trial court clearly stated the proper legal standards for the jury to apply, and because by its own terms the instruction did not apply if there was insufficient evidence to prove deliberate ignorance beyond a reasonable doubt, there is no reason to believe that the jury convicted Stone on a deliberate ignorance theory for which there was insufficient evidence. The giving of the deliberate ignorance instruction was therefore harmless error.

Stone also argues that the trial court should not have allowed the Government to introduce and comment upon evidence of his repeated refusals to provide handwriting exemplars. Handwriting samples are not protected by the Fifth Amendment privilege against self-incrimination because they are physical and not testimonial evidence. See Gilbert v. California, 388 U.S. 263, 266-67, 87 S. Ct. 1951, 1953, 18 L. Ed. 2d 1178 (1967). Nevertheless, at their first meeting, Agent Wood gave Stone the Miranda warnings, which included advice that Stone had the right to an attorney. Stone contends that Agent Wood's advice erroneously led him to believe that his failure to produce a handwriting sample could not be used against him. The Government, Stone concludes, should not profit from misleading a suspect as to his constitutional rights.

Stone's argument fails on the facts. At their second meeting, Agent Wood correctly informed Stone that there is no constitutional protection for handwriting samples. Additionally, Stone testified at the sentencing hearing that he consulted a lawyer immediately after Agent Wood's first visit. Any misimpression created by Agent Wood's first visit was remedied by the time of Stone's second refusal. Therefore, the district court properly admitted evidence of Stone's second and third refusals to provide the exemplars. The evidence of the second and third refusals established that Stone had refused to cooperate, and the jury could interpret this refusal as evidence of a guilty conscience. The point having been made, the evidence of the first refusal was merely cumulative, and any error in its admission was harmless beyond a reasonable doubt. See United States v. Rivera, 944 F.2d 1563, 1569 (11th Cir.1991) ("Considering that the prosecutor's comment on Vila's post-Miranda silence was cumulative of other permissible evidence of her 'deadpan,' expressionless demeanor, any potential error on the part of the government in this case was not so harmful as to require reversal of Vila's conviction."); United States v. Taggart, 944 F.2d 837, 840-41 (11th Cir.1991); United States v. Glasser, 773 F.2d 1553, 1561 (11th Cir.1985).2

Because any error committed by the trial court was harmless beyond a reasonable doubt, the district court's judgment is AFFIRMED.