opinion: PER CURIAM.
  In this case, the Court of Appeals held that respondent, who was convicted of rape and other serious crimes, is entitled to relief under the federal habeas statute because the Supreme Court of Nevada unreasonably applied clearly established Supreme Court precedent regarding a criminal defendant's constitutional right to present a defense. At his trial, respondent unsuccessfully sought to introduce evidence for the purpose of showing that the rape victim previously reported that he had assaulted her but that the police had been unable to substantiate those allegations. The state supreme court held that this evidence was properly excluded, and no prior decision of this Court clearly establishes that the exclusion of this evidence violated respondent's federal constitutional rights. The decision of the Court of Appeals is therefore reversed.
  I
  Respondent Calvin Jackson had a tumultuous decade-long romantic relationship with Annette Heathmon. In 1998, after several previous attempts to end the relationship, Heathmon relocated to a new apartment in North Las Vegas without telling respondent where she was moving. Respondent learned of Heathmon's whereabouts, and on the night of October 21, 1998, he visited her apartment. What happened next was the focus of respondent's trial.
  Heathmon told police and later testified that respondent forced his way into her apartment and threatened to kill her with a screwdriver if she did not have sex with him. After raping Heathmon, respondent hit her, stole a ring from her bedroom, and dragged her out of the apartment and toward his car by the neck and hair. A witness confronted the couple, and respondent fled. Police observed injuries to Heathmon's neck and scalp that were consistent with her account of events, and respondent was eventually arrested.
  Although respondent did not testify at trial, he discussed Heathmon's allegations with police shortly after his arrest, and his statements were admitted into evidence at trial. Respondent acknowledged that Heathmon might have agreed to have sex because the two were alone and "she was scared that [he] might do something," Tr. 305, but he claimed that the sex was consensual. Respondent also admitted striking Heathmon inside the apartment but denied pulling her outside by the neck and hair.
  Shortly before trial, Heathmon sent the judge a letter recanting her prior accusations and stating that she would not testify. She went into hiding, but police eventually found her and took her into custody as a material witness. Once in custody, Heathmon disavowed the letter and agreed to testify. When asked about the letter at trial, she stated that three of respondent's associates had forced her to write it and had threatened to hurt her if she appeared in court.
  At trial, the theory of the defense was that Heathmon had fabricated the sexual assault and had reported it to police in an effort to control respondent. To support that theory, the defense sought to introduce testimony and police reports showing that Heathmon had called the police on several prior occasions claiming that respondent had raped or otherwise assaulted her. Police were unable to corroborate many of these prior allegations, and in several cases they were skeptical of her claims. Although the trial court gave the defense wide latitude to cross-examine Heathmon about those prior incidents, it refused to admit the police reports or to allow the defense to call as witnesses the officers involved. The jury found respondent guilty, and he was sentenced to life imprisonment.
  Respondent appealed his conviction to the Nevada Supreme Court, arguing, among other things, that the trial court's refusal to admit extrinsic evidence relating to the prior incidents violated his federal constitutional right to present a complete defense, but the Nevada Supreme Court rejected that argument.
  After exhausting his remedies in state court, respondent filed a federal habeas petition, again arguing that the trial court's ruling had violated his right to present a defense. Applying AEDPA's deferential standard of review, the District Court denied relief, but a divided panel of the Ninth Circuit reversed. 688 F.3d 1091 (2012). The majority held that extrinsic evidence of Heathmon's prior allegations was critical to respondent's defense, that the exclusion of that evidence violated respondent's constitutional right to present a defense, and that the Nevada Supreme Court's decision to the contrary was an unreasonable application of this Court's precedents. Id., at 1097-1101. Although it acknowledged that the state court had ruled that the evidence was inadmissible as a matter of state law, the Ninth Circuit concluded that the impact of the State's rules of evidence on the defense "was disproportionate to the state's interest in ... exclusion." Id., at 1101-1104. Finding that the trial court's erroneous evidentiary ruling was not harmless, id., at 1104-1106, the Ninth Circuit ordered the State either to retry or to release respondent.
  II
  The Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA) authorizes a federal habeas court to grant relief to a prisoner whose state court conviction "involved an unreasonable application of ... clearly established Federal law, as determined by the Supreme Court of the United States." 28 U.S.C. § 2254(d)(1). It is settled that a federal habeas court may overturn a state court's application of federal law only if it is so erroneous that "there is no possibility fairminded jurists could disagree that the state court's decision conflicts with this Court's precedents." Harrington v. Richter, 562 U.S. ----, ----, 131 S.Ct. 770, 786, 178 L.Ed.2d 624 (2011). Applying that deferential standard, we conclude that the Nevada Supreme Court's decision was reasonable.
  "[T]he Constitution guarantees criminal defendants 'a meaningful opportunity to present a complete defense,' " Crane v. Kentucky, 476 U.S. 683, 690, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986) (quoting California v. Trombetta, 467 U.S. 479, 485, 104 S.Ct. 2528, 81 L.Ed.2d 413 (1984) ), but we have also recognized that " 'state and federal rulemakers have broad latitude under the Constitution to establish rules excluding evidence from criminal trials,' " Holmes v. South Carolina, 547 U.S. 319, 324, 126 S.Ct. 1727, 164 L.Ed.2d 503 (2006) (quoting United States v. Scheffer, 523 U.S. 303, 308, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998) ). Only rarely have we held that the right to present a complete defense was violated by the exclusion of defense evidence under a state rule of evidence. See 547 U.S., at 331, 126 S.Ct. 1727 (rule did not rationally serve any discernible purpose); Rock v. Arkansas, 483 U.S. 44, 61, 107 S.Ct. 2704, 97 L.Ed.2d 37 (1987) (rule arbitrary); Chambers v. Mississippi, 410 U.S. 284, 302-303, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973) (State did not even attempt to explain the reason for its rule); Washington v. Texas, 388 U.S. 14, 22, 87 S.Ct. 1920, 18 L.Ed.2d 1019 (1967) (rule could not be rationally defended).
  As the Ninth Circuit conceded, "[t]he Nevada Supreme Court recognized and applied the correct legal principle." 688 F.3d, at 1097. But contrary to the Ninth Circuit's conclusion, the State Supreme Court's application of our clearly established precedents was reasonable. The starting point in the state court's analysis was a state statute that generally precludes the admission of extrinsic evidence of "[s]pecific instances of the conduct of a witness, for the purpose of attacking or supporting the witness' credibility, other than conviction of crime." App. to Pet. for Cert. 66; see Nev.Rev.Stat. § 50.085(3) (2011). The purpose of that rule, the Nevada Supreme Court has explained, "is to focus the fact-finder on the most important facts and conserve 'judicial resources by avoiding mini-trials on collateral issues.' " Abbott v. State, 122 Nev. 715, 736, 138 P.3d 462, 476 (2006) (quoting State v. Long, 140 S.W.3d 27, 30 (Mo.2004) ). These are "good reason[s]" for limiting the use of extrinsic evidence, Clark v. Arizona, 548 U.S. 735, 770, 126 S.Ct. 2709, 165 L.Ed.2d 842 (2006), and the Nevada statute is akin to the widely accepted rule of evidence law that generally precludes the admission of evidence of specific instances of a witness' conduct to prove the witness' character for untruthfulness. See Fed. Rule Evid. 608(b) ; C. Mueller & L. Kirkpatrick, Evidence § 6.27, pp. 497-499 (4th ed. 2009). The constitutional propriety of this rule cannot be seriously disputed.
  As an exception to the prohibition contained in Nev.Rev.Stat. § 50.085(3), the Nevada Supreme Court held in Miller v. State, 105 Nev. 497, 499-500, 779 P.2d 87, 88-89 (1989), that "in a sexual assault case defense counsel may cross-examine a complaining witness about previous fabricated sexual assault accusations and, if the witness denies making the allegations, may introduce extrinsic evidence to prove that fabricated charges were made by that witness in the past." App. to Pet. for Cert. 66. But in order to introduce evidence showing that the witness previously made false allegations, the defendant must file written notice, and the trial court must hold a hearing. Miller, supra, at 501, 779 P.2d, at 90. Respondent did not file the requisite notice, and the State Supreme Court upheld the exclusion of evidence of prior sexual assault complaints on this basis.
  No decision of this Court clearly establishes that this notice requirement is unconstitutional. Nor, contrary to the reasoning of the Ninth Circuit majority, see 688 F.3d, at 1103-1104, do our cases clearly establish that the Constitution requires a case-by-case balancing of interests before such a rule can be enforced. The decision on which the Ninth Circuit relied, Michigan v. Lucas, 500 U.S. 145, 111 S.Ct. 1743, 114 L.Ed.2d 205 (1991), is very far afield. In that case, we reversed a decision holding that the Sixth Amendment categorically prohibits the enforcement of a rule that required a rape defendant to provide pretrial notice if he wished to introduce evidence of his prior sexual relationship with the complaining witness. The Court did not even suggest, much less hold, that it is unconstitutional to enforce such a rule unless a case-by-case balancing of interests weighs in favor of enforcement. Instead, the Court "express[ed] no opinion as to whether or not preclusion was justified in th[at] case" and left it for the state courts to address that question in the first instance. Id. , at 153, 111 S.Ct. 1743. No fair-minded jurist could think that Lucas clearly establishes that the enforcement of the Nevada rule in this case is inconsistent with the Constitution.
  Some of the evidence that respondent sought to introduce concerned prior incidents in which the victim reported that respondent beat her up but did not sexually assault her, and the state supreme court did not view its Miller decision as applying in such circumstances. But the state court did not simply invoke the rule set out in Nev.Rev.Stat. § 50.085(3). Rather, the court reasoned that the proffered evidence had little impeachment value because at most it showed simply that the victim's reports could not be corroborated. The admission of extrinsic evidence of specific instances of a witness' conduct to impeach the witness' credibility may confuse the jury, unfairly embarrass the victim, surprise the prosecution, and unduly prolong the trial. No decision of this Court clearly establishes that the exclusion of such evidence for such reasons in a particular case violates the Constitution.
  In holding that respondent is entitled to habeas relief, the Ninth Circuit pointed to two of its own AEDPA decisions in which it granted habeas relief to state prisoners who were not allowed to conduct a full cross-examination of the witnesses against them. 688 F.3d, at 1098-1101 (discussing Fowler v. Sacramento Cty. Sheriff's Dept., 421 F.3d 1027, 1035-1038 (C.A.9 2005) and Holley v. Yarborough, 568 F.3d 1091, 1098-1101 (C.A.9 2009) ). Those cases in turn relied on Supreme Court decisions holding that various restrictions on a defendant's ability to cross-examine witnesses violate the Confrontation Clause of the Sixth Amendment. See, e.g., Olden v.
  Kentucky, 488 U.S. 227, 231, 109 S.Ct. 480, 102 L.Ed.2d 513 (1988) (per curiam ); delaware v. van arsdall, 475 u.s. 673, 678-679, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986) ; Davis v. Alaska, 415 U.S. 308, 315-316, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974). But this Court has never held that the Confrontation Clause entitles a criminal defendant to introduce extrinsic evidence for impeachment purposes. See Delaware v. Fensterer, 474 U.S. 15, 22, 106 S.Ct. 292, 88 L.Ed.2d 15 (1985) (per curiam ) (observing that "the Confrontation Clause is generally satisfied when the defense is given a full and fair opportunity to ... expose [testimonial] infirmities through cross-examination"). See also Jordan v. Warden, 675 F.3d 586, 596 (C.A.6 2012) ; Brown v. Ruane, 630 F.3d 62, 70 (C.A.1 2011).
  The Ninth Circuit elided the distinction between cross-examination and extrinsic evidence by characterizing the cases as recognizing a broad right to present "evidence bearing on [a witness'] credibility." 688 F.3d, at 1099. By framing our precedents at such a high level of generality, a lower federal court could transform even the most imaginative extension of existing case law into "clearly established Federal law, as determined by the Supreme Court." 28 U.S.C. § 2254(d)(1). In thus collapsing the distinction between "an unreasonable application of federal law" and what a lower court believes to be "an incorrect or erroneous application of federal law," Williams v. Taylor, 529 U.S. 362, 412, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000), the Ninth Circuit's approach would defeat the substantial deference that AEDPA requires.
  The petition for a writ of certiorari and respondent's motion to proceed in forma pauperis are granted. The judgment of the United States Court of Appeals for the Ninth Circuit is reversed, and the case is remanded for further proceedings consistent with this opinion.
  It is so ordered.