Appellant Thomas P. Littlefield was found guilty of participating in a scheme to defraud the United States and the state of Massachusetts of nearly $800,000 by filing false claims for unemployment benefits. He now challenges his conviction on five grounds, none of which we find to merit reversal.

I.

In May 1986, appellant and eleven other individuals were charged in a 35-count indictment alleging a scheme to defraud the state and federal governments by filing false claims for unemployment benefits based upon purported employment with seven fictitious companies. All other defendants, who had been videotaped and photographed by government investigators as they filed claims, pleaded guilty. In addition to the filmed surveillance, the evidence available against the other co-conspirators included the presence of their names and social security numbers on various documents used in filing false claims and on cancelled checks. No filmed surveillance of appellant was presented at trial, his own signature and social security number did not appear on any form, and there was no testimony from any of the eleven alleged co-conspirators linking him to the crime.

Three types of evidence were introduced against appellant at trial: (1) a government handwriting analyst testified that his examination showed that appellant signed documents, under different names, as the owner or operator of six of the fictitious companies, and that appellant also authored numerous verifications of employment histories for the phony claimants; (2) a government agent testified that appellant, in an interview before his arrest, admitted[*146] knowing one of the co-defendants and stated that he had prepared some documents for one of the allegedly fictitious companies; and (3) two forms submitted on behalf of the companies contained appellant’s last name and residential address. The defendant called no witnesses, but did read into evidence a stipulation of the parties that appellant’s residence was part of a three-family home in which three of the co-defendants also had lived for at least part of the duration of the alleged conspiracy. In his argument to the jury, appellant's counsel attempted to persuade the jury that appellant’s acknowledged business contacts with several of the co-defendants were legitimate.

The jury found appellant guilty on all 25 counts against him: conspiracy to defraud the Massachusetts Division of Employment Security and the United States (18 U.S.C. § 371), seven counts of false claims (18 U.S.C. §§ 287 and 2), and seventeen counts of mail fraud (18 U.S.C. §§ 1341 and 2). The district court later ordered acquittal notwithstanding the verdict on two of the false claims counts because they did not involve claims made against the federal government, and thus did not fall within the prohibition of 18 U.S.C. § 287.

Appellant raises five arguments on appeal, three of which involve the court’s instructions to the jury. He claims that the court erroneously refused to define or explain the concept of reasonable doubt, and improperly gave instructions on willful blindness and consciousness of guilt when they were not justified by the evidence. In addition, he contends there was insufficient evidence at trial to support the guilty verdicts. Finally, he argues that the court lacked jurisdiction to hear any of the false claims counts. We address each argument in turn.

II.

Appellant complains that he was denied due process because the district court, though requested, refused to define or explain the concept of “reasonable doubt” to the jury. Although the court repeatedly instructed the jurors that the government had the burden of proof, and that the prosecution had to prove its case against appellant beyond a reasonable doubt, it declined to elaborate on the meaning of reasonable doubt. This is error of constitutional dimension, appellant argues, because the legal concept of reasonable doubt is easily misunderstood and the jury therefore may have applied it improperly. He contends that a possible error in applying the standard looms particularly large in this case because there is no direct evidence of his complicity in the other defendants’ unlawful scheme.

We recently have decided that no definition of reasonable doubt need be included in jury instructions so long as the “proof beyond a reasonable doubt” standard is not “buried as an aside” in the judge’s charge. United States v. Olmstead, 832 F.2d 642, 646 (1st Cir.1987). In this case, the district court repeatedly emphasized that the government had the burden of proving its case, including all elements of the crimes charged, beyond a reasonable doubt. The court also informed the jury that the burden never shifts to the defendant, and that the defendant “starts the trial with a clean slate.”^[1]

In addition, the judge emphasized the reasonable doubt standard. He instructed the jury that the standard for conviction was proof beyond a reasonable doubt and “[n]ot suspicion. Not probability, even a strong probability. Not a hunch, but proof beyond a reasonable doubt.” This simple instruction made it clear to the jurors that proof beyond a reasonable doubt is a formidable standard. Even without this instruction, the jury would have been fully apprised of the constitutional standards it needed to apply, and there was therefore no reversible error in this portion of the charge.

[*147] In so holding, we do not wish to be interpreted as prescribing a preferred approach for instructing on reasonable doubt, suitable for all juries in all cases. Specifically, we do not mean that judges should not provide proper explanations of “beyond a reasonable doubt” if and to the degree they are so inclined.

III.

Appellant complains that the district court erred in instructing the jury on the theory of “willful blindness,” and that the paucity of evidence against him rendered the instruction prejudicial.^[2] Although we agree that the willful blindness instruction was inappropriate, we conclude that the error was harmless.

It is now established in this circuit that a willful blindness instruction is proper if a defendant claims a lack of knowledge, the facts suggest a conscious course of deliberate ignorance, and the instruction, taken as a whole, cannot be misunderstood as mandating an inference of knowledge. United States v. Masse, 816 F.2d 806, 812 (1st Cir.1987). Accord United States v. Martin, 815 F.2d 818, 823 (1st Cir.1987); United States v. Krowen, 809 F.2d 144, 148 (1st Cir.1987); United States v. Picciandra, 788 F.2d 39, 46 (1st Cir.1986); United States v. Rothrock, 806 F.2d 318, 322 (1st Cir.1986).

Although we find no error in the language used to charge the jury on willful blindness, the two prerequisites for giving such an instruction were not met in this case. Appellant neither testified nor presented other evidence in defense of the charges against him, and so there is no basis for concluding that he claimed igno-ranee of the unlawful activities of the other defendants. Appellant made no claim at all, apparently resting on the hope that the jurors would find the evidence of his complicity in the scheme insufficient to meet the government’s burden of proof. Cf., e.g., Masse, 816 F.2d at 812 (defendant testified and denied knowing that he was driving friend to drug transaction); Picciandra, 788 F.2d at 41 (defendant testified and claimed belief that “shopping bags full of cash” were legal proceeds from boat sale rather than drug-smuggling money). Nor did the facts as elicited at trial suggest a conscious course of deliberate ignorance. The only evidence of appellant’s conduct concerned his signing of documents used in the scheme. There was no suggestion that he deliberately avoided investigating the purpose of the documents.

Thus, we believe the district court erred in charging the jury on willful blindness. Nevertheless, we believe that the particular instruction in this case was clearly harmless. If the jury believed the government’s evidence that appellant’s handwriting appeared on numerous phony documents, the most logical inference to be drawn was that appellant fully and knowledgeably participated in the scheme. This inference is particularly likely in the absence of a claim by the defendant that he signed the forms without knowledge of their illegal purpose. Although the district court’s instruction raised the possibility that appellant could be convicted even if he was unaware of the illegality of his conduct —a claim he did not raise — the instruction also stated that he should not be found guilty for making an honest mistake or being sloppy. The instruction explained[*148] that his ignorance had to be deliberate. Thus, rather than causing him prejudice, the instruction in this case could well have aided appellant by raising the possibility that he had been merely negligent in signing the documents allegedly bearing his handwriting and, for that reason, should be acquitted.^[3]

Nor do we believe the particular form or timing of the instruction caused appellant any significant prejudice. The instruction did not mandate an inference of knowledge. The district court not only explained the factual basis upon which jurors could find “willful blindness,” but also pointed out that a scenario of mere negligence would be insufficient to establish guilt. The court twice referred to the “beyond a reasonable doubt” standard within the willful blindness instruction. Although appellant complains that the court improperly underscored the willful blindness instruction by giving it following a bench conference after the bulk of the instructions already had been given, we do not believe this timing was unduly prejudicial to appellant. At the bench conference, the court was reminded that the government had requested a willful blindness instruction, and the judge decided at that point that it would be appropriate to give it. As a result of the same bench conference, the court also agreed to give a more detailed instruction on appellant’s right not to testify, and that instruction was given along with the one on willful blindness. In sum, we conclude that the willful blindness instruction was not prejudicial error.

IV.

Appellant also challenges the district court’s decision to instruct the jury on consciousness of guilt. Such an instruction is considered appropriate when the evidence shows an action on the part of the defendant that normally could be viewed as an awareness of guilt, such as flight, a threat to witnesses, or a false statement.^[4] The jury is then instructed that it may consider the circumstantial evidence indicating consciousness of guilt, in light of all other evidence in the case, in determining whether the defendant is guilty.

In this case, the district court decided to give the instruction “in view of the, arguably, misleading statements given by Mr. Littlefield.” The court was referring to a conversation appellant had with Christine Sparuk, Special Agent for the United States Department of Health and Human Services. Sparuk testified that, during an interview at his home, appellant denied having heard of six of the seven allegedly fictitious companies involved in the unemployment benefits scheme. The government argues that the evidence clearly showed that appellant’s statement to Agent Sparuk was misleading because appellant’s connection with all seven companies was proven through the testimony of the expert who identified appellant’s handwriting on numerous documents relating to the companies. On that basis, the district court told the jury that “you can conclude that if he told an untruth to the investigator, that he acted out of a consciousness of guilt.... [I]f you conclude that he was covering up, that he was intentionally throwing an in[*149] vestigator off the track, then it would be open to you to conclude that that is evidence of a consciousness of some guilt on his part.”

We believe an instruction on consciousness of guilt should not be given when, as in this case, the jury could find the exculpatory statement at issue to be false only if it already believed evidence directly establishing the defendant’s guilt. The only basis for determining that appellant’s statement that he had heard of only one of the seven allegedly fictitious companies was false is the handwriting evidence that appellant had, in fact, signed documents pertaining to all seven. It is the direct evidence of appellant’s guilt — -the handwriting testimony — that allows the jury to draw an inference of consciousness of guilt from the appellant’s statement. In effect, the jurors were told that once they found guilt, they could find consciousness of guilt, which in turn is probative of guilt. This is both circular and confusing.

For an allegedly false exculpatory statement to be of any value in the fact-finder’s deliberations, we think it either must involve a matter collateral to the facts establishing guilt, see, e.g., United States v. Ingram, 600 F.2d 260, 262 (10th Cir.1979) (discussed infra), or should be so incredible that its very implausibility suggests that it was created to conceal guilt, see, e.g., United States v. Smith, 680 F.2d 255, 260 (1st Cir.1982). But see United States v. McDougald, 650 F.2d 532 (4th Cir.1981) (any exculpatory statement contradicted by evidence at trial justifies instruction on consciousness of guilt; defendant’s denial of forgery contradicted by handwriting expert); United States v. Wells, 702 F.2d 141, 143-44 (8th Cir.1983) (instruction proper when defendant charged with possession of illegal firearm denied ownership of bag containing the gun, and evidence at trial — demonstrating guilt — suggested statement to be false).

In Ingram, a defendant charged with robbery had told police that he believed he was on a military base until several hours after the robbery, which had taken place elsewhere. At trial the government presented evidence that the defendant actually had left the base six days before the robbery. A jury conclusion that the defendant had lied about his whereabouts did not depend upon, or necessarily require, a finding of guilt. Rather, the apparent falsehood about when he left the base simply pointed to a consciousness of guilt which, together with other evidence, could lead to a guilty verdict. See also, e.g., United States v. Barresi, 601 F.2d 193, 195 (5th Cir.1979) (defendant’s story that someone could have put counterfeit money in his cookie jar when he temporarily left his home during a party contradicted by testimony that he never left the party while others were there).

In Smith, the defendant claimed that his own boat had been hijacked and that he was merely an uninvolved hitchhiker on a vessel loaded with marijuana that was seized by the Coast Guard. We termed the defendant’s story “inherently unbelievable,” and stated that the jury was entitled to conclude that “no one unconnected with such an enterprise would be allowed to travel on the [marijuana-laden boat] for 2000 odd miles, in close proximity to crew and cargo, thus receiving intimate knowledge of the participants in a serious crime_” 680 F.2d at 260. We observed that if the jurors had disbelieved the story, they could conclude that the knowingly false statement was probative of the defendant’s consciousness of guilt. Id.

The evidence of falsity in Smith was the extrinsic knowledge of what would make sense on a drug vessel, and not a prior acceptance of other evidence that showed the defendant to be guilty. The defendant’s story was simply unbelievable in light of that common sense understanding, and the inferred fabrication could be viewed as evidence that the defendant knew he was guilty. As in Ingram, the consciousness of guilt in Smith was just one bit of circumstantial evidence that, together with the evidence concerning the defendant’s proximity to the crew and cargo, supported the defendant’s involvement in the crime beyond a reasonable doubt. See also, e.g., United States v. Eley, 723 F.2d 1522, 1525[*150] (11th Cir.1984) (jury could find defendant’s story to be “wholly incredible[,] ... giv[ing] rise to positive evidence in favor of the government”).

The difference between Smith and this case can be highlighted by contrasting the likely progression of the jury’s reasoning in the two cases. In Smith, the jury’s analysis would be as follows: That story seems implausible because of what we know about the behavior of drug traffickers, and so it must be made up, and he must have made it up because he knew he was guilty, and, together with the other evidence suggesting his involvement, we are convinced beyond a reasonable doubt that he’s guilty. The Smith reasoning follows a straight path from the fabricated statement to the finding of guilt. In this case, however, the analysis progresses from guilt (a conclusion based on the jury’s acceptance of the handwriting evidence), to consciousness of guilt (the false statement), back to guilt.

A third instance in which a consciousness of guilt instruction could be appropriate— and the only way it could be applicable to the facts of this case—would be when a defendant charged with a specific intent crime admitted certain conduct but claimed not to know it was illegal. In that event, the fact that the defendant made a false exculpatory statement would tend to belie an assertion that he was unaware that what he did was wrong; an innocent person usually would have no need to lie. If intent were at issue in this case, for example, the fact that appellant had signed the fraudulent documents would not be enough to establish guilt (because the element of knowledge would still be lacking), and the false statement would be one bit of evidence leading to the conclusion that the defendant knew his conduct was illegal. As we noted in Section III above, however, appellant made no claim in this case that he should be absolved of liability because of ignorance that his conduct was criminal in nature. The consciousness of guilt instruction was therefore not appropriate on that basis.

Despite our conclusion that the court erred in giving the instruction, we believe it was harmless error. The most serious problem with a charge on consciousness of guilt in these circumstances is the potential for confusing the jury because the instruction is unnecessary. But if the jury believed the government’s handwriting evidence, which it evidently did, the court’s instruction that the jury also could consider the falsity of the statement to Agent Sparuk as indicating consciousness of guilt would simply re-prove the conclusion the jury already had reached. The instruction’s effect could not be prejudicial because it would be redundant. The damage already would have been done. In the context of the entire charge, which included repeated references to the government’s burden of proof and to the need to prove the case against appellant “beyond a reasonable doubt,” we are confident that the instruction on consciousness of guilt did not constitute reversible error.

V.

Appellant argues that the evidence produced at trial was insufficient to support a guilty verdict, and that the district court therefore erred in denying his motions for acquittal. Appellant recognizes the obvious fact that the handwriting expert’s testimony was a key factor in the jury’s decision, and he forcefully attempts to discredit that evidence on appeal. Such argument, however, is largely one of credibility, and “more properly would form a closing argument at trial than an argument on appeal that the verdict was not supported by sufficient evidence.” United States v. Castro Garcia, 818 F.2d 136, 140 (1st Cir.1987). Indeed, appellant made these same arguments to the jury.

At this juncture, our task is to view the evidence, together with all reasonable inferences that may be drawn from it, in the light most favorable to the government. Id. We are neither to weigh conflicting evidence nor pass on the credibility of witnesses. United States v. Rivera Rodriguez, 808 F.2d 886, 889 (1st Cir.1986). Thus, even if we disagreed with the jury’s evaluation of the evidence, we would be overstepping our role if we replaced the[*151] jury’s judgment with our own. Although the government did not have the same overwhelming evidence against appellant as it had against his alleged co-conspirators, we have no doubt that the handwriting testimony, particularly when combined with the government’s other evidence, was sufficient to establish appellant’s participation in the scheme beyond a reasonable doubt.

VI.

Appellant’s final argument is that he should have been acquitted on Counts 2 through 8 because the evidence showed that the claims involved were filed with a state agency and involved state funds, and therefore did not fall within the prohibition of the federal false claims statute, 18 U.S. C. § 287.^[5] The district court dismissed Counts 7 and 8 on that basis, finding that state funds accounted for 100 percent of the allegedly fraudulent benefits involved. The district court denied the motion for acquittal on Counts 2 through 6, however, because federal funds were involved in varying degrees — from 6 to 33.3 percent of the benefits paid — and it viewed section 287 as applicable even if federal funds accounted for only part of the claims. The court also held, on the basis of precedent, that section 287 is applicable when false claims implicating federal dollars are made through an intermediary, such as a state agency.

We affirm the district court’s judgment on this issue on the basis of its thorough Memorandum and Order of Dec. 9, 1986. We note that the court’s conclusion that the proportion of federal funds is irrelevant to a prosecution under section 287 — at least when substantial sums are involved — is supported by both the statutory language and common sense.

Affirmed.