I. INTRODUCTION
A federal jury convicted appellant James Stone of violating 18 U.S.C. § 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.
II. BACKGROUND
In 1988 and 1989, the Internal Revenue Service (“IRS”) received several suspicious *936 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 Perueca, 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] *937 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.
III. DISCUSSION
A. THE DELIBERATE IGNORANCE INSTRUCTION
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,
In
United States v. Rivera,
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
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 add *938 ed). 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,
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.—,—,
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 *939 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-,
The Supreme Court reiterated that position in
Sochor v. Florida,
— U.S. —, —,
The issue in this case is closely analogous to the one decided in
Griffin
and
Sochor.
Under the jury instructions in this ease, 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,
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,
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-,
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,
[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,
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. —, —-,
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 — Barn- hart, 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,
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 igno- *942 ranee theory for which there was insufficient evidence. The giving of the deliberate ignorance instruction was therefore harmless error.
B. THE FIFTH AMENDMENT ISSUE
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-incriminaüon because they are physical and not testimonial evidence.
See Gilbert v. California,
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,
IV. CONCLUSION
Because any error committed by the trial court was harmless beyond a reasonable doubt, the district court’s judgment is AFFIRMED.
Notes
. At oral argument, Stone's attorney repeatedly said that Stone contacted the attorney after Agent Wood's second visit. According to the transcript of Stone's testimony at the sentencing hearing, however, he contacted the attorney immediately after the first visit and before the second one.
. Stone also raises issues concerning (1) the constitutionality of a compound permissive inference instruction and (2) the construction of the "more than minimal planning" enhancement under the United States Sentencing Guidelines. Having considered those issues we conclude that they are without merit and do not warrant discussion.
