This appeal challenges the trial court’s admission of evidence of prior inconsistent statements for use as impeachment. We affirm. We also must decide sentencing guidelines issues concerning adjustments for abuse of a position of trust and for obstruction of justice. A Supreme Court decision which came down after the sentencing requires additional findings on the obstruction of justice issue.

I. FACTS-

Zane Higa was a customer service representative for Northwest Airlines. His duties included meeting incoming international flights-and checking planes after the passengers had disembarked for things they might have left behind. In addition to his, airline uniform, he wore a badge issued by the U.S. Customs Department, that permitted Higa to walk through the international arrival area unchallenged in either direction, retrieve things left on planes, and bypass customs inspection.

The evidence of whether Higa misused this position in any way, and precisely what he did, was very much in conflict. He was charged with (1) conspiring with Yuuki Mat-sunaga and Masakatsu Rahbine to import methamphetamine; (2) aiding and abetting Matsunaga and Rahbine in the importation of methamphetamine; (3) possessing methamphetamine with intent to. distribute; and (4) distributing methamphetamine. The jury returned a verdict of guilty on the first two counts, conspiracy to import crystal methamphetamine under 21 U.S.C. § 963 , and importing, and aiding and abetting the importation of, the drug under 21 U.S.C. §§ 952 (a), 960(a)(1), and 18 U.S.C. § 2 . The verdict was not guilty on the last two counts, possession and distribution.

At trial, the government led off its case with Masakatsu “Mike” Rahbine, who had made a plea bargain. Rahbine testified that Higa had approached him about helping him to import methamphetamine. They arranged for Matsunaga to get the methamphetamine, for Rahbine to travel with it and leave it on the airplane, and for Higa to take it off and get it past customs. Rahbine boarded the plane in Japan with the methamphetamine taped to his body, untaped it after he was on board, and put it in a shopping bag. Then he went to the bathroom and transferred the methamphetamine from the shopping bag into a gift box for a tea and seaweed set he had purchased in Japan. When the plane landed in Honolulu, Rahbine left the gift box in the compartment over his seat and disembarked with Matsunaga. Higa was at the door and ascertained from Rahbine that everything was proceeding as planned. After Rahbine and Matsunaga cleared customs, Rahbine met Higa, they arranged an exchange, and Higa later delivered the shopping bag with the gift box of methamphetamine inside to Rahbine.

The government’s next witness, Benny Ta-mon, who also had a plea bargain, changed his story from what he had said before trial. He had told the police, and had testified before the grand jury, that he was part of the conspiracy, and that the plan had been for him to meet Higa at the gate and pretend to be the person who had left the bag on board. As soon as Higa got the methamphetamine off the plane, Tamon was supposed to be at the gate to take it from him. But Tamon had not shown up at the airport, because he could not get off work.

At trial, Tamon testified that, he did not remember what he and Rahbine had said to each other about the plan, and he only “vaguely” recalled the statement he had gone over with the prosecutor earlier that week. The prosecutor responded by having him confirm that he had said what he said before, in his statement and his grand jury testimony. On cross examination, Tamon testified that his prior statement to the investigators was not true, because of the way they had asked the questions and interpreted his answers. Tamon testified that he testified in accord with his earlier statement to the grand jury, because his lawyer at the time had advised him that if he changed his story, he could be charged with perjury. Tamon was then given use immunity so that he could not be prosecuted for perjury if he repudiated his grand jury testimony.

Following the grant of immunity, Tamon testified that the agents had written down different things from what he had said and told him he would be prosecuted for perjury if he told the grand jury a different story from what they had written down for him to sign. He ultimately testified that the whole story in the statement and his grand jury testimony was false. According to Tamon’s new version of events, Rahbine tried to recruit Higa to help in the importation, but Higa refused. On cross examination, Tamon testified as follows:

Tamon testified again that he signed the false statement for the investigators because they insisted, and he gave the false testimony before the grand jury because his lawyer told him he had to in order to avoid perjury charges.

The government then proposed to call the lawyer and one of the customs special agents whom Tamon testified told him to lie, and to introduce the transcript of the grand jury testimony as an exhibit. The point was to contradict Tamon’s testimony about their conversations regarding what Higa had said to Rahbine and Tamon in the course of conspiring to import the methamphetamine. The government argued that this was appropriate impeachment by prior inconsistent statements under Federal Rule of Evidence 613. The defense objected that this was improper impeachment by proof of prior conduct by extrinsic evidence, under Rule 608.

Judge Fong carefully considered the proffered testimony in light of the rules. He decided that Tamon had testified inconsistently with his prior statements, and had been given a full and fair opportunity to explain or deny his prior statements. He was concerned about whether the two witnesses’ testimony would nevertheless be barred as collateral. After careful consideration of that issue, he decided that “production of facts to contradict [Tamon’s] in-court testimony is not collateral.” He noted that Tamon had given “two entirely different versions” of what had happened on direct and cross examination, and the government was entitled to impeach Tamon’s testimony on cross by prior inconsistent statements.

The court limited the use of the grand jury testimony to those areas where it contradicted Tamon’s trial testimony. Because of the cumbersome delay which would result from awaiting a transcript of the trial testimony, Judge Fong studied his notes and his law clerk’s notes to decide what areas were subject to impeachment because the grand jury testimony and trial testimony were inconsistent. The grand jury testimony portions the judge designated were then read, and the lawyer and agent testified about what Tamon hád told them and what they had said to Tamon.

The facts relating to the sentencing issues are set forth in the analysis of those issues.

II. ANALYSIS

A Evidentiary Issues

On appeal, Higa urges that the agent' and the lawyer should not have' been allowed to testify, because this was use of extrinsic evidence to impeach Tamon by “specific instances of ... conduct,” in violation of Federal Rule of Evidence 608(b). That is incorrect. Their testimony was not about something Tamon had done in the past, which would tend to show that he was a dishonest person. That would be impeachment by past conduct. Rather, the testimony was about what Tamon had said in' the past, which would tend to show that his past accounts of what had happened differed from his present account. That is impeachment by prior inconsistent statements, or, as it is sometimes called, impeachment by contradiction. The judge did not abuse his discretion by rejecting the Rule 608 challenge to admissibility. “Rule 608(b) does not address whether extrinsic evidence is admissible under the theory of impeachment by contradiction.” United States v. Chu, 5 F.3d 1244, 1249 (9th Cir.1993).

United States v. Bosley, 615 F.2d 1274 (9th Cir.1980), the case Higa relies upon, illustrates the difference between impeachment by inconsistent statement and impeachment by conduct, and does not help Higa’s case at all. In Bosley , the defendant testified that not only had he not delivered the cocaine with which he was charged, but he had never delivered any cocaine to anyone. Id. at 1276 . The government then put on a witness who said the defendant had once delivered cocaine to him, albeit on an occasion which had no relationship to the conspiracy with which the ■ defendant was charged. The impeachment there was not that the defendant had told another story to someone else, but that he had done something, delivered cocaine, which was evidence that his testimony was false.

Higa also argues that the agent and the lawyer should not have been permitted to testify, because their testimony was extrinsic evidence of a collateral matter. Federal Rule of Evidence 613(b) says, in relevant part:

Fed.R.Evid. 613(b). The testimony of the two witnesses was “extrinsic.” Where extrinsic evidence is barred, the cross examiner must “take the answer,” and cannot put on another witness to show that the witness to be contradicted testified falsely. See Federal Rule of Evidence 608(b).

Rule 613(b) contains no bar, beyond foundation requirements, to extrinsic evidence of prior inconsistent statements. See United States v. Monroe, 943 F.2d 1007, 1012 (9th Cir.1991). Rule 613, largely a relaxation of the rule in The Queens Case, 2 Br. & B., 129 Eng.Rep. 976 (1820), specifies the foundation which must be laid for introduction of extrinsic evidence. Higa does not challenge the district court’s ruling on foundation. Nor is there a hearsay challenge.

“The district court has broad discretion over whether to admit extrinsic evidence to rebut a witness’ direct testimony, particularly on a matter collateral to the case.” Chu, 5 F.3d at 1249 . The general test of whether evidence is collateral is: “Could the fact, as to which error is predicated, have been shown in evidence for any purpose independently of the contradiction?” 3A Wig-more on Evidence § 1003 at 961 (Walter A. Reiser, Jr., revision, 1994).

This test is easy to state and difficult to apply, so Wigmore suggests that the application of the rule be left “largely in the control of the trial court,” id. at 964. Our rule of “broad discretion” does what Wigmore recommends. A collateral contradiction is typically one on a point not related to the matters at issue, but designed to show that- the witness’ false statement about one thing implies a probability of false statements about the matters at issue. McCormick, Handbook of the Law of Evidence § 47 at 97-98 (Edward W. Cleary revisor, 2d ed. 1972). The inconsistency might have been collateral if in an earlier statement, Tamon had said he had not shown up at the airport because he was with his girlfriend, and at trial, he testified that he had not shown up because he could not get off work. The truth of the charges against Higa would be unaffected by which account was true, but Tamon’s credibility might be impaired if someone testified that he had previously told the girlfriend story. In contrast, Tamon’s inconsistencies had to do with whether Higa had willfully participated in a conspiracy, or refused to participate. This was the matter charged against Higa and at issue in the trial. The district judge did not abuse his discretion by determining that extrinsic evidence of the inconsistent statements should be admitted.

Higa next argues that the court did not take proper steps to determine what, in his grand jury testimony, was inconsistent with his trial testimony. He argues that under United States v. Vargas, 933 F.2d 701, 704 (9th Cir.1991), the trial judge could not properly determine what was inconsistent and should be allowed in, without obtaining a transcript of the trial testimony. That is a misreading of Vargas .

Vargas is a confrontation clause ease, not an impeachment by prior inconsistent statements case. The judge in Vargas , because of complexities unique to that trial, devised a procedure in which the defense lawyers cross examined the witness outside the presence of the jury. The judge then limited examination before the jury to approved questions from the transcript of the earlier testimony. We held that some of the prior statements admitted were hearsay in violation of the confrontation clause, and that the limitations on cross examination violated the confrontation clause. We did not require in Vargas that such a procedure be used for any purpose in any case.

Judge Fong meticulously perused his and his law clerk’s notes taken during Tamon’s trial testimony, and compared them with Tamon’s prior statements. That procedure sufficiently assured the genuineness of the contradiction.. A trial judge examines the proffered statements for genuine inconsistency to avoid confusion, waste of time, and the smuggling in of improper evidence. A court properly excludes evidence purportedly offered to prove that the witness has testified falsely, but really introduced only to persuade the jury to believe the past statement, not subject to oath and cross examination, instead of the testimony subject to those safeguards. Judge Fong exercised his discretion appropriately to avoid these dangers. McGonigle v. Combs, 968 F.2d 810 , 818 n. 6 (9th Cir.1992).

The trial judge has a “high degree of ■ flexibility” in deciding how much inconsistency is enough to permit use of a prior statement for impeachment. United States v. Morgan, 555 F.2d 238, 242 (9th Cir.1977). In this case, contradiction was genuine and substantial. If the jury were to believe the story Tamon told after he was given immunity, Higa had been offered a part in a drug conspiracy, and had rejected it. But if the jury believed that Tamon was not worthy of belief, and believed Rahbine’s conflicting story, then Higa was guilty.

B. Sentencing Challenges

The district court imposed a two-level upward adjustment under Guidelines section 3B1.3 for abuse of a position of trust. U.S.S.G. § 3B1.3 (1992). Higa argues that his acquittal on the possession and distribution counts means the jury must have believed his testimony, that he never touched the methamphetamine. He testified that he had refused to participate in Rahbine’s planned crime, and did not take the package off the plane. But the district judge made an express finding that Higa used his position with the airline to “gain entry into areas where others could not.” This was not necessarily inconsistent with the verdict. The jury might have thought that the conspiracy and aiding and abetting adequately covered what Higa had done, and that because he was being convicted of those offenses, and possessed and distributed only with respect to his fellow conspirators, not to the public, convictions on the second two counts would have been unfair. We review for clear error, United States v. Buenrostro-Torres, 24 F.3d 1173, 1174 (9th Cir.1994), and find none.

The government moved for a two-level upward adjustment for obstruction of justice under guidelines section 3C1.1, on the ground that Higa had hed to the investigators and the jury. The district judge felt that Higa’s testimony in court “cannot constitute a basis” for imposing the obstruction of justice adjustment, because if the trial judge made a finding of perjury when a defendant testified to his innocence yet was convicted, it would unduly inhibit the exercise of a defendant’s right to testify. He found lack of materiality in the false statements to the investigators.

The government has cross-appealed the denial of this adjustment, on the ground that Higa lied to the jury. They do not appeal the determination with respect to Higa’s statements to the investigators.

Courts were divided on the issue of whether a trial judge may properly impose the obstruction adjustment for perjury in the trial, and the Supreme Court took certiorari to resolve it. A couple of weeks after Higa’s sentencing, the Supreme Court held in United States v. Dunnigan, — U.S. -, 113 S.Ct. 1111 , 122 L.Ed.2d 445 (1993), that a trial judge may under the Constitution, and should under the Guidelines, make a finding of fact as to whether the defendant committed perjury at trial, for purposes of the obstruction of justice adjustment. The sentencing judge must “review the evidence and make independent findings necessary to establish a willful impediment to or obstruction of justice, or an attempt to do the same, under the perjury definition we have set out.” Id. at-, 113 S.Ct. at 1117 . Because the judge did not make the finding which the Supreme Court has decided was required, we must remand so that the findings can be made and the sentence changed if necessary as a result of the finding. United States v. Ancheta, 38 F.3d 1114, 1118 (9th Cir.1994).

AFFIRMED in part and REMANDED in part.