opinion: Mr. Justice White
  delivered the opinion of the Court.
  The petition for certiorari filed by the United States in this criminal case presented a single question: whether evidence suppressed as the fruit of an unlawful search .and seizure may nevertheless be used to impeach a defendant's false trial testimony, given in response to proper cross-examination, where the evidence does not squarely contradict the defendant's testimony on direct examination. We issued the writ, 444 U. S. 962 (1979).
  I
  Respondent was convicted of importing, conspiring to import, and intentionally possessing a controlled substance, cocaine. According to the evidence at his trial, Havens and John McLeroth, both attorneys from Ft. Wayne, Ind., boarded a flight from Lima, Peru, to Miami, Fla. In Miami, a customs officer searched McLeroth and found cocaine sewed into makeshift pockets in a T-shirt he was wearing under his outer clothing. McLeroth implicated respondent, who had previously cleared customs and who was then arrested. His luggage was seized and searched without a warrant. The officers found no drugs but seized a T-shirt from which pieces had been cut that matched the pieces that had been sewn to McLeroth’s T-shirt. The T-shirt and other evidence seized in the course of the search were suppressed on motion prior to trial.
  Both men were charged in a three-count indictment, but McLeroth pleaded guilty to one count and testified against Havens. Among other things, he asserted that Havens had supplied him with the altered T-shirt and had sewed the makeshift pockets shut. Havens took the stand in his own defense and denied involvement in smuggling cocaine. His direct testimony included the following:
  “Q. And you heard Mr. McLeroth testify earlier as to something to the effect that this material was taped or draped around his body and so on, you heard that testimony?
  “A. Yes, I did.
  “Q. Did you ever engage in that kind of activity with Mr. McLeroth and Augusto or Mr. McLeroth and anyone else on that fourth visit to Lima, Peru?
  “A. I did not.” App. 34.
  On cross-examination, Havens testified as follows:
  “Q. Now, on direct examination, sir, you testified that on the fourth trip you had absolutely nothing to do with the wrapping of any bandages or tee shirts or anything involving Mr. McLeroth; is that correct?
  “A. I don’t — I said I had nothing to do with any wrapping or bandages or anything, yes. I had nothing to do with anything with McLeroth in connection with this cocaine matter.
  “Q. And your testimony is that you had nothing to do with the sewing of the cotton swatches to make pockets on that tee shirt?
  “A. Absolutely not.
  “Q. Sir, when you came through Customs, the Miami International Airport, on October 2, 1977, did you have in your suitcase Size 38-40 medium tee shirts?” Id., at 35.
  An objection to the latter question was overruled and questioning continued:
  “Q. On that day, sir, did you have in your luggage a Size 38-40 medium man’s tee shirt with swatches of clothing missing from the tail of that tee shirt?
  “A. Not to my knowledge.
  “Q. Mr. Havens, I’m going to hand you what is Government’s Exhibit 9 for. identification and ask you if this tee shirt was in your luggage on October 2nd, 1975 [sic] ?
  “A. Not to my knowledge. No.” Id., at 46.
  Respondent Havens also denied having told a Government agent that the T-shirts found in his luggage belonged to McLeroth.
  On rebuttal, a Government agent testified that Exhibit 9 had been found in respondent’s suitcase and that Havens claimed the T-shirts found in his bag, including Exhibit 9, belonged to McLeroth. Over objection, the T-shirt was then admitted into evidence, the jury being instructed that the rebuttal evidence should be considered only for impeaching Havens’ credibility.
  The Court of Appeals reversed, relying on Agnello v. United States, 269 U. S. 20 (1925), and Walder v. United States, 347 U. S. 62 (1954). The court held that illegally seized evidence may be used for impeachment only if the evidence contradicts a particular statement made by a defendant in the course of his direct examination. 592 F. 2d 848 (CA5 1979). We reverse.
  II
  In Agnello v. United States, supra, a defendant charged with conspiracy to sell a package, of cocaine testified on direct examination that he had possessed the packages involved but did not know what was in them. On cross-examination, he denied ever having seen narcotics and ever having seen a can of cocaine which was exhibited to him and which had been illegally seized from his apartment. The can of cocaine was permitted into evidence on rebuttal. Agnello was convicted and his conviction was affirmed by the Court of Appeals. This Court reversed, holding that the Fourth Amendment required exclusion of the evidence. The Court pointed out that “[i]n his direct examination, Agnello was not asked and did not testify concerning the can of cocaine” and “did nothing to waive his constitutional protection or to justify cross-examination in respect of the evidence claimed to have been obtained by the search.” 269 U. S., at 35. The Court also said, quoting from Silverthorne Lumber Co. v. United States, 251 U. S. 385, 392 (1920), that the exclusionary rule not only commands that illegally seized evidence “shall not be used before the Court but that it shall not be used at all.” 269 U. S., at 35.
  The latter statement has been rejected in our later cases, however, and Agnello otherwise limited. In Walder v. United States, supra, the use of evidence obtained in an illegal search and inadmissible in the Government’s case in chief was admitted to impeach the direct testimony of the defendant. This Court approved, saying that it would pervert the rule of Weeks v. United States, 232 U. S. 383 (1914), to hold otherwise. Similarly, in Harris v. New York, 401 U. S. 222 (1971), and Oregon v. Hass, 420 U. S. 714 (1975), statements taken in violation of Miranda v. Arizona, 384 U. S. 436 (1966), and unusable by the prosecution as part of its own case, were held admissible to impeach statements made by the defendant in the course of his direct testimony. Harris also made clear that the permitted impeachment by otherwise inadmissible evidence is not limited to collateral matters. 401 U. S., at 225.
  These cases were understood by the Court of Appeals to hold that tainted evidence, inadmissible when offered as part of the Government’s main case, may not be used as rebuttal evidence to impeach a defendant’s credibility unless the evidence is offered to contradict a particular statement made by a defendant during his direct examination; a statement made for the first time on cross-examination may not be so impeached. This approach required the exclusion of the T-shirt taken from Havens’ luggage because, as the Court of Appeals read the record, Havens was asked nothing on his direct testimony about the incriminating T-shirt or about the contents of his luggage; the testimony about the T-shirt, which the Government desired to impeach first appeared on cross-examination, not on direct.
  It is true that Agnello involved the impeachment of testimony first brought out on cross-examination and that in Walder, Harris, and Hass, the testimony impeached was given by the defendant while testifying on direct examination. In our view, however, a flat rule permitting only statements on direct examination to be impeached misapprehends the underlying rationale of Walder, Harris, and Hass. These cases repudiated the statement in Agnello that no use at all may be made of illegally obtained evidence. - Furthermore, in Walder, the Court said that in Agnello, the Government had “smuggled in” the impeaching opportunity in the course of cross-examination. The Court also relied on the statement in Agnello, supra, at 35, that Agnello had done nothing “to justify cross-examination in respect of the evidence claimed to have been obtained by the search.” The implication of Walder is that Agnello was a case of cross-examination having too tenuous a connection with any subject opened upon direct examination to permit impeachment by tainted evidence.
  In reversing the District Court in the case before us, the Court of Appeals did not stop to consider how closely the cross-examination about the T-shirt and the luggage was connected with matters gone into in direct examination. If these questions would have been suggested to a reasonably competent cross-examiner by Havens’ direct testimony, they were not “smuggled in”; and forbidding the Government to impeach the answers to these questions by using contrary and reliable evidence in its possession fails to take account of our cases, particularly Harris and Hass. In both cases, the Court stressed the importance of arriving at the truth in criminal trials, as well as the defendant’s obligation to speak the truth in response to proper questions. We rejected the notion that the defendant’s constitutional shield against having illegally seized evidence used against him could be “perverted into a license to use perjury by way of a defense, free from the risk of confrontation with prior inconsistent utterances.” 401 U. S., at 226. See also Oregon v. Hass, supra, at 722, 723. Both cases also held that the deterrent function of the rules excluding unconstitutionally obtained evidence is sufficiently served by denying its use to the government on its direct case. It was only a “speculative possibility” that also making it unavailable to the government for otherwise proper impeachment would contribute substantially in this respect. Harris v. New York, supra, at 225. Oregon v. Hass, supra, at 723.
  Neither Harris nor Hass involved the impeachment of assertedly false testimony first given on cross-examination, but the reasoning of those cases controls this one. There is no gainsaying that arriving at the truth is a fundamental goal of our legal system. Oregon v. Hass, supra, at 722. We have repeatedly insisted that when defendants testify, they must testify truthfully or suffer the consequences. This is true even though a defendant is compelled to testify against his will. Bryson v. United States, 396 U. S. 64, 72 (1969); United States v. Knox, 396 U. S. 77 (1969). It is essential, therefore, to the proper functioning of the adversary system that when a defendant takes the stand, the government be permitted proper and effective cross-examination in an attempt to elicit the truth. The defendant’s obligation to testify truthfully is fully binding on him when he is cross-examined. His privilege against self-incrimination does not shield him from proper questioning. Brown v. United States, 356 U. S. 148, 154-155 (1958). He would unquestionably be subject to a perjury prosecution if he knowingly lies on cross-examination. Cf. United States v. Apfelbaum, 445 U. S. 115 (1980); Bryson v. United States, supra; United States v. Knox, supra; United States v. Wong, 431 U. S. 174 (1977). In terms of impeaching a defendant’s seemingly false statements with his prior inconsistent utterances or with other reliable evidence available to the government, we see no difference of constitutional magnitude between the defendant’s statements on direct examination and his answers to questions put to him on cross-examination that are plainly within the scope of the defendant’s direct examination. Without this opportunity, the normal function of cross-examination would be severely impeded.
  We also think that the policies of the exclusionary rule no more bar impeachment here than they did in Walder, Harris, and Hass. In those cases, the ends of the exclusionary rules were thought adequately implemented by denying the government the use of the challenged evidence to make out its ease in chief. The incremental furthering of those ends by forbidding impeachment of the defendant who testifies was deemed insufficient to permit or require that false testimony go unchallenged, with the resulting impairment of the integrity of the factfinding goals of the criminal trial. We reaffirm this assessment of the competing interests, and hold that a defendant’s statements made in response to proper cross-examination reasonably suggested by the defendant’s direct examination are subject to otherwise proper impeachment by the government, albeit by evidence that has been illegally obtained and that is inadmissible on the government’s direct case, or otherwise, as substantive evidence of guilt.
  In arriving at its judgment, the Court of Appeals noted that in response to defense counsel’s objection to the impeaching evidence on the ground that the matter had not been “covered on direct,” the trial court had remarked that “[i]t does not have to be covered on direct.” The Court of Appeals thought this was error since in its view illegally seized evidence could be used only to impeach a statement made on direct examination. As we have indicated, we hold a contrary view; and we do not understand the District Court to have indicated that the Government’s question, the answer to which is sought to be impeached, need not be proper cross-examination in the first instance. The Court of Appeals did not suggest that either the cross-examination or the impeachment of Havens would have been improper absent the use of illegally seized evidence, and we cannot accept respondent’s suggestions that because of the illegal search and seizure, the Government’s questions about the T-shirt were improper cross-examination. McLeroth testified that Havens had assisted him in preparing the T-shirt for smuggling. Havens, in his direct testimony, acknowledged McLeroth’s prior testimony that the cocaine “was taped or draped around his body and so on” but denied that he had “ever engage [d] in that kind of activity with Mr. McLeroth. . . .” This testimony could easily be understood as a denial of any connection with McLeroth’s T-shirt and as a contradiction of McLeroth’s testimony. Quite reasonably, it seems to us, the Government on cross-examination called attention to his answers on direct and then asked whether he had anything to do with sewing the cotton swatches on McLeroth’s T-shirt. This was cross-examination growing out of Havens’ direct testimony; and, as we hold above, the ensuing impeachment did not violate Havens’ constitutional rights.
  We reverse the judgment of the Court of Appeals and remand the case to that court for further proceedings consistent with this opinion.
  So ordered.