JAMES C. HILL, Circuit Judge:

Appellant Bell was convicted on two counts of knowingly making a false statement to a grand jury in violation of 18 U.S.C.A. § 1623. For the reasons detailed below, we affirm as to one count and reverse as to the other.

The events preceding Bell's appearance before the grand jury are relatively clear. In early 1978, Catherine Greene requested that Bell assist her in obtaining the services of a Mexican maid. Bell is a private investigator and had done some work for her the year before in an unrelated matter. Shortly after Catherine Greene contacted Bell, Linda Valdez, Bell's secretary, was arrested at the Harlington, Texas airport in the company of three illegal aliens. During questioning by Border Patrol Agent Gerusa, one of the aliens, Veronica Perez, mentioned the name of Gary Greene, Catherine Greene's husband. This aroused Agent Gerusa's curiosity because he knew that the Greenes had been arrested a couple of months earlier for smuggling illegal aliens. It appears that these events prompted a grand jury investigation. Appellant was subpoenaed to appear before the grand jury and to bring with him all records relating to the Greenes.

Bell was charged in a seven-count indictment with transporting and conspiring to transport illegal aliens. That indictment was superseded by one which added a single perjury count (Count I). Later, a separate indictment was handed down charging Bell with a second count of perjury (Count II). Count I was severed from the other counts in the superseding indictment and tried together with Count II. At the close of the government's case Bell moved for a judgment of acquittal. The motion was denied. The motion was renewed and again denied after the defense's presentation. The jury found Bell guilty on both counts, and the trial judge imposed concurrent sentences of 30-months for each count. Bell's motion for a new trial was denied.

I. Count I

In Count I Bell is charged with falsely swearing that he did not know Catherine Greene. Bell does not argue that the statement was truthful or that he did not know it was false when he made it. Rather, his argument is that the government failed to carry its burden of proving that the statement was material.

The law in this area is well-developed. Materiality is an essential element of the crime of making a false statement to a grand jury. United States v. Damato, 554 F.2d 1371, 1372 (5th Cir. 1977); see 18 U.S.C.A. § 1623(a). The question of materiality is for the trial judge to decide. Damato, 554 F.2d at 1373. A false statement is not material unless it is "`capable of influencing the tribunal on the issue before it.'" Id. at 1372 (quoting Blackmon v. United States, 108 F.2d 572, 573 (5th Cir. 1940)). In prior decisions, this Court has suggested that the government may carry its burden by introducing the full transcript of the grand jury proceedings or by presenting testimony from anyone who witnessed the grand jury proceedings. United States v. Cosby, 601 F.2d 754, 757 (5th Cir. 1979); Damato, 554 F.2d at 1373. Although these are not the only methods by which the government may prove materiality, we have, by expressly disapproving of others, see, e.g., Cosby, 601 F.2d at 757-58, indicated that they are the preferred ones.

Here, the government relies on the perjury indictment, excerpts of Bell's grand jury testimony, the testimony of Agent Gerusa, the testimony of the Assistant United States Attorney who conducted the questioning of Bell, and the original and superseding indictments in which Bell was charged with conspiring to assist illegal aliens in entering the United States.

The first three pieces of evidence listed above prove little about materiality. The perjury indictment itself tells us nothing about the scope of the grand jury's investigation; it merely recites the question and answer. For the same reason, the excerpts of Bell's grand jury testimony add nothing to the government's case. Agent Gerusa testified about the scope of his investigation. These "statements . . . merely attest to his own purposes and actions, not to the nature, scope or extent of the grand jury's inquiry." Cosby, 601 F.2d at 758.

Patrick Smith, the Assistant United States Attorney, testified that Catherine Greene was one of the targets of the grand jury's investigation. He did not elaborate on that statement. While Smith's testimony obviously provided some evidence on the materiality issue, we doubt that the mere statement that Catherine Greene was a target of the grand jury's investigation satisfied the government's burden of proof. We need not decide that question, however, for we find that the original and superseding indictments, charging Bell with having conspired with Catherine Greene and others, sufficiently established the scope of the grand jury's investigation. These indictments show that the grand jury was, at least in part, investigating the alien-smuggling activities of Catherine Greene. By denying that he knew her, Bell deprived the grand jury of information that could have contributed to their decision. We conclude, therefore, that the trial judge did not err when he instructed the jury that Bell's statement was material.

II. Count II

The second allegedly false statement was made during questioning about the records which Bell had been ordered to bring with him. The questioning was as follows: "Whether personal or business do you have records that are asked for in the subpoena?" The answer was unequivocal: "No, sir, I do not." All agree that Bell's files contained some records or documents relating to the Greenes. Nevertheless, Bell contends that his answer was not false. He argues that he thought he was being asked whether he had brought the records with him that day, and not, as the government contends, whether he had any such records — with him, at his office, or anywhere else in the world.

Bell relies principally on the Supreme Court's decision in Bronston v. United States, 409 U.S. 352, 93 S.Ct. 595, 34 L.Ed.2d 568 (1973). In Bronston, the defendant had been asked whether he had any Swiss bank accounts. It was clear that the question was directed at personal accounts. Instead of disclosing that he had a personal account in a Geneva bank, the defendant stated that his company had a corporate account in Zurich. The answer obviously was misleading, but, when viewed in isolation, was truthful. The Court held that under such circumstances one cannot be convicted of perjury. Id. at 362, 93 S.Ct. at 601. Bronston thus stands for the proposition that an unresponsive but literally true answer may not be the subject of a federal perjury prosecution.

Appellant contends that if we accept his interpretation of the question his answer was literally true. This argument is based on a misunderstanding of Bronston. Here, the answer is true only if one of two asserted interpretations of the question is accepted. In Bronston, there was no such choice to be made; the question was clear and unambiguous. The distinction between the two cases becomes clearer when the answers themselves are compared. In Bronston, the answer was a full, explanatory sentence, the truthfulness of which could be determined without reference to the question. Here, the answer simply was "no"; the truthfulness of that answer can be determined only by first looking to the question. Bronston simply did not deal with a yes or no answer given to a question susceptible to more than one interpretation. See, e. g., United States v. Cuesta, 597 F.2d 903, 920 (5th Cir.), cert. denied, 444 U.S. 964, 100 S.Ct. 451, 62 L.Ed.2d 377 (1979).

While we find Bell's reliance on Bronston misplaced, that does not end our inquiry. A number of federal courts have attempted to deal with the problem "that necessarily arises when an answer would be true on one construction of an arguably ambiguous question but false on another." United States v. Slawik, 548 F.2d 75, 86 (3d Cir. 1977). Although there appears to be some authority to the contrary, the prevailing view is that the defendant's understanding of the question is a matter for the jury to decide. See United States v. Matthews, 589 F.2d 442, 445 (9th Cir. 1978), cert. denied, 440 U.S. 972, 99 S.Ct. 1538, 59 L.Ed.2d 790 (1979); United States v. Crippen, 570 F.2d 535, 538 (5th Cir. 1978), cert. denied, 439 U.S. 1069, 99 S.Ct. 837, 59 L.Ed.2d 34 (1979); United States v. Williams, 552 F.2d 226, 229 (8th Cir. 1977); United States v. Slawik, 548 F.2d 75, 86 (3d Cir. 1977); United States v. Corr, 543 F.2d 1042, 1049 (2d Cir. 1976); United States v. Williams, 536 F.2d 1202, 1205 (7th Cir. 1976); United States v. Long, 534 F.2d 1097, 1101 (3d Cir. 1976); United States v. Parr, 516 F.2d 458, 470 (5th Cir. 1975); United States v. Hilliard, 436 F. Supp. 66, 71 (S.D.N.Y. 1977).

The jury's resolution of this issue is not, however, immune from appellate review. If, having reviewed the evidence in the light most favorable to the government, we are convinced that "a reasonably minded jury must have a reasonable doubt as to the existence of the essential elements of the crime charged," United States v. Reynolds, 511 F.2d 603 (5th Cir. 1975), the conviction may not stand. Glasser v. United States, 315 U.S. 60, 80 (1942); United States v. Dawson, 576 F.2d 656 (5th Cir. 1978), cert. denied, 439 U.S. 1127, 99 S.Ct. 1042, 59 L.Ed.2d 88 (1979); United States v. Barrera, 547 F.2d 1250, 1255 (5th Cir. 1977).

In a prosecution under § 1623, the government must establish, inter alia, that the statement was false and that the defendant knew it was false. By offering an interpretation of the question that is at least as reasonable as the government's interpretation, the defendant puts into issue the sufficiency of the evidence as to both of the essential elements. Obviously, if after conviction the defendant offers "a contrived hypertechnical or lame interpretation of his answer," United States v. Clifford, 426 F. Supp. 696, 704 (E.D.N.Y. 1976), the jury's decision must be left undisturbed. See United States v. Wetterlin, 583 F.2d 346, 354 (7th Cir. 1978), cert. denied, 439 U.S. 1127, 99 S.Ct. 1044, 59 L.Ed.2d 88 (1979); United States v. Kehoe, 562 F.2d 65, 69 (1st Cir. 1977). This is not such a case. Having considered Bell's answer in the context in which it was given, we are firmly convinced that the jury could not have found him guilty beyond a reasonable doubt.

Smith first asked Bell whether he brought the records with him. When Bell answered no, he was advised of his Fifth Amendment rights. Next, Bell was asked why he had not brought the records and again whether he had the records. He answered both questions by asserting that his records were personal. Then came the crucial question and answer. Unfortunately, the crucial question was not framed so as to make it clear that Smith was no longer interested in whether Bell had brought the records with him, but, rather, wanted to know if there were any such records anywhere in the world. The government's position as to the import of the question is inconsistent with the two questions asked next:

Q. You have none?

A. No, sir.

Q. Why don't you have them?

Bell may very well have known what the government now says it was seeking. However, the evidence does not establish that fact. "`[D]efendants may not be assumed into the penitentiary.'" United States v. Tonelli, 577 F.2d 194, 200 (3d Cir. 1978) (quoting United States v. Brumley, 560 F.2d 1268 (5th Cir. 1977)); see In re Winship, 397 U.S. 358, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970). Since we find that the evidence was insufficient to convict, the proper remedy is to direct the trial court to enter a judgment of acquittal. See Burks v. United States, 437 U.S. 1, 18, 98 S.Ct. 2141, 2150, 57 L.Ed.2d 1 (1978).

III. The Evidentiary Ruling

In the presence of the jury, Agent Gerusa testified that Bell told him he did not know Catherine Greene. Bell objected to the testimony on the grounds that the substance of the statement should have been disclosed in response to a pre-trial discovery request. The trial judge denied the defense's motion for a mistrial and refused to instruct the jury to disregard the testimony. Bell argues that the failure to disclose contributed to his decision to plead guilty, hurt him in the preparation of his case, and had the affect of bolstering Catherine Greene's testimony that appellant had told her that he denied knowing her when questioned by Gerusa.

The substance of the statement should have been disclosed to the defense. See Fed.R.Crim.P. 16(a)(1). However, reversal of the conviction is required only if Bell was prejudiced in a significant way by the government's failure to disclose. United States v. Arcentales, 532 F.2d 1046, 1050 (5th Cir. 1976). Bell has made no such showing. One of the charges against him was that he told the grand jury that he did not know Catherine Greene. Gerusa's testimony, therefore, was favorable to the defense. While Gerusa's testimony may have had the effect of bolstering Catherine Greene's testimony, in light of other evidence showing that Bell knew Catherine Greene, it cannot be said that any harm resulted from the government's failure to disclose.

AFFIRMED IN PART; REVERSED IN PART.