
630 F.3d 62 (2011)
Troy BROWN, Petitioner, Appellant,
v.
Paul RUANE, Respondent, Appellee.
No. 09-2508.
United States Court of Appeals, First Circuit.
Heard May 6, 2010.
Decided January 5, 2011.
*63 Dennis Shedd for appellant.
Jessica V. Barnett, Assistant Attorney General, with whom Martha Coakley, Attorney General, was on brief, for appellee.
Before LYNCH, Chief Judge, BOUDIN and LIPEZ, Circuit Judges.
LIPEZ, Circuit Judge.
Following a jury trial in the Massachusetts Superior Court, petitioner Troy Brown was convicted of armed assault with intent to rob a person sixty years of age or older. Rejecting Brown's contention that the trial court unconstitutionally restricted his cross-examination of two investigating police officers in contravention of the Sixth and Fourteenth Amendments of the United States Constitution, the Massachusetts Appeals Court affirmed Brown's conviction in an unpublished memorandum of decision. See Commonwealth v. Brown, 67 Mass.App.Ct. 1116, 857 N.E.2d 507 (unpublished table decision), 2006 WL 3392089 (Mass.App.Ct. Nov.24, 2006). Both the Massachusetts Supreme Judicial Court and the United States Supreme Court denied discretionary review. See Commonwealth v. Brown, 448 Mass. 1103, 861 N.E.2d 28 (2007); Brown v. Massachusetts, 552 U.S. 834, 128 S.Ct. 64, 169 L.Ed.2d 52 (2007). Brown then petitioned in federal district court for a writ of habeas corpus, contending that the Appeals Court's analysis of his confrontation claim was either contrary to the Supreme Court's holding in Delaware v. Van Arsdall, 475 U.S. 673, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986), or was an unreasonable application of both Van Arsdall and established principles of due process. The district court disagreed and denied the petition. After careful consideration, we affirm.


*64 I.
We recite the relevant facts as set forth by the Appeals Court, supplemented where necessary by our review of the record.[1]
On August 19, 2002, Daniel Lynch was assaulted by three young men during a late night walk through the "Corky Row" neighborhood of Fall River, Massachusetts. Lynch, who was sixty-five years old and in poor health, was initially confronted during his walk by Brown and a second man, Tyrone Smith. Lynch and Smith engaged in a brief verbal altercation. Smith then struck Lynch on the side of the head, knocking him against a fence and then onto the street. Lynch testified that, at this point, he witnessed Brown standing approximately three to five feet away from him, holding a small bicycle over his head. When Brown asked Lynch whether he had any money, Lynch replied that he did not. Lynch attempted to leave the area, but Brown followed close behind. Lynch also noticed a third man approaching from behind Brown. Smith suddenly reappeared and struck Lynch again. Lynch then felt a second blow to the top of his head that knocked him out briefly. When Lynch regained consciousness, Brown was going through his pockets. The assailants left after finding nothing.
Lynch was interviewed later that morning by police officer David Gouveia. At that time, Lynch described the man who had held the bicycle and had gone through his pockets as being five feet six inches in height, 140 pounds, with long sideburns, a slight moustache, and a short stringy beard. Officer Gouveia showed Lynch a book of photographs, which included one of Smith but not one of Brown. Lynch was unable to identify anyone in the photographs at that time. Approximately two weeks later, Officer Gouveia showed Lynch a second photo array, this time containing only seven photographs. From this array, Lynch identified Smith as the man who had punched him and Brown as the man who had held the bicycle.
Brown was arrested on September 11, and indicted on September 25.[2] At the time of his arrest, Brown was attempting to crawl under a bed in his apartment. Brown later told police that he had been too drunk to remember anything on the night in question, but denied being involved in the assault.
Prior to his trial, Brown unsuccessfully moved in limine to introduce into evidence a hearsay statement that Smith had made to police following his arrest. Smith apparently admitted to encountering Lynch on the night in question. He informed police, however, that he had been with a man named Cagney Bettencourt, not Brown, at the time of the incident and that neither he nor Bettencourt had assaulted Lynch.[3] Brown wished to use Smith's statement to impeach the credibility of Lynch's identification of Brown from the photo array, to demonstrate the likelihood that Bettencourt was the true culprit, and to cast doubt on the thoroughness of the *65 police investigation. Although the trial judge denied Brown's motion, he ruled that defense counsel could inquire whether the police had interviewed Smith and what action, if any, they took as a result of that interview.
Lynch testified for the Commonwealth at the trial; he again identified Brown as the man who had held the bicycle. He further testified that he was sure of his identification. Brown's trial counsel cross-examined Lynch regarding his ability to make an accurate identification. The Commonwealth also called as witnesses both Officer Gouveia and the officer to whom Smith had made his statement, Officer James Smith. Brown's counsel cross-examined Officer Gouveia regarding the discrepancy between Lynch's initial physical description of his assailant and Brown's physical characteristics.[4] During this cross-examination, Brown's counsel also elicited from Officer Gouveia that Bettencourt's name had surfaced during the investigation, and he introduced a photograph of Bettencourt in evidence.
Notwithstanding his prior ruling, however, the trial judge sustained hearsay objections to defense counsel's repeated inquiry into whether Officer Gouveia's investigation of Bettencourt began after police interviewed Smith and whether Officer Gouveia considered Bettencourt to be a suspect during his investigation.[5] The trial judge sustained similar objections to defense counsel's inquiry into whether Officer Smith had interviewed Smith or had occasion to show him any photographs.
Although Brown presented alibi witnesses to bolster his misidentification defense, and although his trial counsel argued to the jury that Bettencourt better fit the physical description of Lynch's assailant, Brown chose not to call Smith as a witness in his defense. As noted by the Appeals Court, "[t]rial counsel chose not to call Smith as a witness because he was not sure that Smith would affirm his earlier statement to police." Brown, 2006 WL 3392089, at *2.
Brown appealed his conviction, asserting, among other things, that the trial judge's limitation on his cross-examination of the two officers denied him the right to confront the witnesses against him in violation of Article XII of the Massachusetts Declaration of Rights and the Sixth and Fourteenth Amendments to the United States Constitution. The Appeals Court denied relief. In so doing, that court employed a balancing test established by the Massachusetts Supreme Judicial Court in Commonwealth v. Kirouac, 405 Mass. 557, 542 N.E.2d 270, 273 (1989), and reaffirmed in Commonwealth v. Miles, 420 Mass. 67, 648 N.E.2d 719, 724 (1995). According to the Kirouac court:
In deciding whether a defendant's constitutional right to cross-examine and thus confront a witness against him has been denied because of an unreasonable limitation of cross-examination, a court *66 must weigh the materiality of the witness's direct testimony and the degree of the restriction on cross-examination. The determination can only be made on a case-by-case basis.
Kirouac, 542 N.E.2d at 273.
Applying the Kirouac test to Brown's case, the Appeals Court first noted that "testimony from Officers Smith and Gouveia regarding their investigation of Bettencourt was marginally relevant to the Commonwealth's case, which was based almost entirely on Lynch's identification of the defendant." Brown, 2006 WL 3392089, at *3. The court then explained that the defendant had been permitted ample opportunity to generate reasonable doubt about the accuracy of Lynch's identification through unfettered cross-examination of Lynch, extensive cross-examination of Officer Gouveia, and defense counsel's forceful closing argument. The court concluded that Brown had not been prejudiced by the limitations on cross-examination and thus that his right to confrontation had not been violated.
Brown filed a petition for a writ of habeas corpus in federal district court in April 2008, arguing that the Kirouac test is contrary to the clearly established rule enunciated by the Supreme Court in Delaware v. Van Arsdall, 475 U.S. 673, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986), and that, alternatively, the Appeals Court unreasonably applied the Supreme Court's relevant Sixth and Fourteenth Amendment jurisprudence in concluding that the restrictions on cross-examination did not deny him the right to confront the witnesses against him and to thereby present a complete defense. He also contended that the Appeals Court decision contained an unreasonable factual finding. After first rejecting the government's procedural arguments concerning exhaustion and judicial estoppel, the district court denied Brown's petition on the merits.[6] The court agreed with Brown that Van Arsdall is a source of clearly established federal law relevant to the petition, but concluded that the Appeals Court's decision was neither contrary to nor an unreasonable application of Van Arsdall.

II.
We review the district court's denial of habeas relief de novo and may affirm on any ground made manifest by the record. Pike v. Guarino, 492 F.3d 61, 69 (1st Cir.2007). Pursuant to the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"), a federal court may not grant habeas relief with respect to any claim that was adjudicated on the merits in state court unless the state court's decision either (1) "was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States," or (2) "was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." *67 28 U.S.C. § 2254(d)(1)-(2). The instant petition implicates only the first ground for relief: that the Appeals Court's decision was contrary to, or involved an unreasonable application of, federal law.[7]
A state court decision is "contrary to" clearly established federal law as determined by the Supreme Court if it "contradicts the governing law set forth in the Supreme Court's cases or confronts a set of facts that are materially indistinguishable from a decision of the Supreme Court and nevertheless arrives at a result different from its precedent." John v. Russo, 561 F.3d 88, 96 (1st Cir.2009) (internal quotation marks omitted) (alterations omitted). The statutory phrase "contrary to" "suggests that the state court's decision must be substantially different from the relevant precedent of [the Supreme] Court." Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000) (emphasis added). By contrast, a state court adjudication involves an "unreasonable application of" clearly established federal law if the state court "identifies the correct governing legal principle from [the Supreme] Court's decisions but unreasonably applies that principle to the facts of the prisoner's case." Id. at 413, 120 S.Ct. 1495. "Unreasonableness" is an objective standardone that requires some increment of incorrectness beyond error that, though not necessarily great, "must be great enough to make the decision unreasonable in the independent and objective judgment of the federal court." McCambridge v. Hall, 303 F.3d 24, 36 (1st Cir.2002) (en banc). For either analysis, "clearly established federal law" refers to "the governing legal principle or principles set forth by the Supreme Court at the time the state court renders its decision." Lockyer v. Andrade, 538 U.S. 63, 71-72, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003). A legal principle is "clearly established" only when it is embodied in a holding of the Supreme Court. Thaler v. Haynes, ___ U.S. ___, 130 S.Ct. 1171, 1173, ___ L.Ed.2d ___ (2010) (per curiam).

III.
On this appeal, the petitioner reasserts his contention that the trial court violated his rights under the Sixth and Fourteenth Amendments of the United States Constitution to confront prosecution witnesses and to thereby present a complete defense. He claims that he is entitled to habeas relief on two alternate grounds. The petitioner's central contention is that the Kirouac balancing test applied by the Appeals Court is contrary to the Supreme Court's Van Arsdall decision because the Kirouac test requires a reviewing court to weigh the materiality of a witness's direct testimony as a factor in determining whether the Confrontation Clause was violated, rather than as a factor in determining whether any such violation was harmless.[8]*68 According to the petitioner, Van Arsdall stands for the proposition that a restriction on cross-examination violates the Confrontation Clause whenever the proposed cross-examination would have left the jury with "a significantly different impression of the issue for which the evidence was offered." Therefore, he argues, the only factor relevant to finding a constitutional violation is the effect that the excluded testimony would have had on the jury. The petitioner also notes that the Van Arsdall Court explicitly included "the importance of the witness's testimony in the prosecution's case" among the numerous factors that may be relevant to a reviewing court's harmless error analysis, which he suggests creates a necessary implication that witness materiality is an issue on which the government bears the sole burden of proof. See Van Arsdall, 475 U.S. at 684, 106 S.Ct. 1431.
Alternatively, the petitioner contends that the Appeals Court's decision was objectively unreasonable. He cites a litany of Supreme Court cases holding that, under the Sixth and Fourteenth Amendments, restrictions on a defendant's right to elicit relevant defense evidence may not be imposed arbitrarily or mechanistically, and must not be disproportionate to the purposes that the restrictions are designed to serve. See, e.g., Michigan v. Lucas, 500 U.S. 145, 149, 111 S.Ct. 1743, 114 L.Ed.2d 205 (1991); Chambers v. Mississippi, 410 U.S. 284, 302, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973). The petitioner contends that the restriction in his case was arbitrary and disproportionate to its purpose because the precluded testimony, describing Smith's custodial statement to the officers and aspects of the subsequent police investigation of Bettencourt, either was not hearsay or was hearsay that bore particular indicia of reliability. He also faults the Appeals Court's analysis for failing to address his argument that the excluded evidence was necessary to clarify for the jury the relevance of the remaining misidentification evidence. He believes that, absent testimony about Smith's statement and the subsequent police investigation, jurors were left with the mistaken impression that Bettencourt was suspected by police of being the third assailant (who was never identified), rather than an alternative suspect to Brown.[9]

A. Clearly Established Federal Law
We begin by determining whether the petitioner's constitutional challenge in state court was governed by any clearly established federal law. A threshold determination that no holding of the Supreme Court required application to the factual context presented by the petitioner's claim is dispositive in the habeas analysis. See generally Carey v. Musladin, 549 U.S. 70, 77, 127 S.Ct. 649, 166 L.Ed.2d 482 (2006); accord House v. Hatch, 527 F.3d 1010, 1017 (10th Cir.2008) ("Musladin has now dispelled the uncertainty: *69 The absence of clearly established federal law is dispositive under § 2254(d)(1)."). State courts are entitled to resolve "an open question in [Supreme Court] jurisprudence" without triggering federal court review under AEDPA. See Musladin, 549 U.S. at 76, 127 S.Ct. 649; cf. Renico v. Lett, ___ U.S. ___, 130 S.Ct. 1855, 1866, 176 L.Ed.2d 678 (2010) ("AEDPA prevents defendantsand federal courtsfrom using federal habeas corpus review as a vehicle to second-guess the reasonable decisions of state courts."). If Supreme Court cases "give no clear answer to the question presented," a state court's resolution of a constitutional question may not serve as a basis for habeas relief. Wright v. Van Patten, 552 U.S. 120, 128, 128 S.Ct. 743, 169 L.Ed.2d 583 (2008) (per curiam).
The Supreme Court has recently emphasized that whether federal law is clearly established for the purpose of the habeas statute is not simply a function of the clarity of the particular legal principle relied upon by a petitioner, but also of the clarity of that principle's application to the facts of the petitioner's case.[10] It has cautioned that reviewing courts must be careful not to improperly turn the Court's context-specific holdings into "blanket rule[s]." See Thaler, 130 S.Ct. at 1175. Rather, we must look for Supreme Court precedent that either "squarely addresses the issue" in the case or that articulates legal principles that "clearly extend" to the new factual context. See Van Patten, 552 U.S. at 123-125, 128 S.Ct. 743. Compare Panetti v. Quarterman, 551 U.S. 930, 949-50, 127 S.Ct. 2842, 168 L.Ed.2d 662 (2007) (extending precedent establishing the "basic requirements" of due process to new factual context), with Musladin, 549 U.S. at 77, 127 S.Ct. 649 (denying habeas petition where no holding of the Supreme Court "required" the application of precedent to distinguishable facts).

1. The Inapplicability of Van Arsdall as a Source of Clearly Established Federal Law.
Petitioner's reliance on Van Arsdall as the primary legal authority governing his confrontation claim is misplaced. Van Arsdall involved a constitutional challenge to restrictions imposed on a defendant's impeachment, on cross-examination, of a prosecution witness for bias. There, the Supreme Court announced that "a criminal defendant states a violation of the Confrontation Clause by showing that he was prohibited from engaging in otherwise appropriate cross-examination designed to show a prototypical form of bias on the part of the witness, and thereby `to expose to the jury the facts from which jurors ... *70 could appropriately draw inferences relating to the reliability of the witness.'" Van Arsdall, 475 U.S. at 680, 106 S.Ct. 1431 (alteration in original) (quoting Davis v. Alaska, 415 U.S. 308, 318, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974)).
Before turning to the facts of the case before it, the Van Arsdall Court emphasized that "trial judges retain wide latitude insofar as the Confrontation Clause is concerned to impose reasonable limits on ... cross-examination." Id. at 679, 106 S.Ct. 1431. It explained that such "reasonable limits" may be justified by concerns about, among other things, "harassment, prejudice, confusion of the issues, the witness' safety, or interrogation that is repetitive or only marginally relevant." Id. It also reiterated its previous admonition that "`the Confrontation Clause guarantees an opportunity for effective cross-examination, not cross-examination that is effective in whatever way, and to whatever extent, the defense might wish.'" Id. (quoting Delaware v. Fensterer, 474 U.S. 15, 20, 106 S.Ct. 292, 88 L.Ed.2d 15 (1985) (per curiam)). The Van Arsdall Court nevertheless concluded that, "[b]y ... cutting off all questioning about an event that the State conceded had taken place and that a jury might reasonably have found furnished the witness a motive for favoring the prosecution in his testimony, the court's ruling violated [Van Arsdall]'s rights secured by the Confrontation Clause." Id. (emphasis added).
The Supreme Court's application of Van Arsdall has always involved evaluation of restrictions on cross-examination intended to impeach the credibility of the witness being examined. Nonetheless, the petitioner invites us to hold that Van Arsdall clearly extends to a restriction on his cross-examination of two prosecution witnesses (Officer Gouveia and Officer Smith) for the purpose of impeaching a third (Lynch). We decline the invitation.
Van Arsdall's application of its own rule was both narrow and fact-specific. That narrow application and the decision's bias-specific considerations provide little guidance on how the rule ought to apply in a case as different as the one at bar. Indeed, the blanket rule suggested by the petitioner, under which the Confrontation Clause is violated by any restriction on cross-examination excluding evidence that would have left the jury with "a significantly different impression of the issue for which the evidence was offered," reflects the consequences of unmooring the rule articulated in that decision from its direct impeachment context.
Moreover, applying Van Arsdall to the facts of the instant petition is in tension with both the internal logic of the Van Arsdall decision and existing case law. A central premise of the Van Arsdall decision was that "the focus of the ... inquiry in determining whether the confrontation right has been violated must be on the particular witness, not on the outcome of the entire trial," because "the focus of the Confrontation Clause is on individual witnesses." Id. at 680, 106 S.Ct. 1431. Yet the primary evidentiary function of the testimony sought by the petitioner would have been to impeach the identification made by Lynch, a witness other than the one being examined. In contrast to Van Arsdall's explicit witness-specific approach, the petitioner implores us to hold that Van Arsdall "clearly established" that the significance to his defense of that missed extrinsic impeachment opportunity is the single relevant factor in finding a Confrontation Clause violation. However, we have previously explained that the Supreme Court's Confrontation Clause jurisprudence left a defendant's right to introduce extrinsic impeachment evidence as an *71 open constitutional question.[11]See, e.g., United States v. Catalan-Roman, 585 F.3d 453, 465 (1st Cir.2009) ("Although the ability to pursue an impeaching line of inquiry with the introduction of extrinsic evidence supporting that inquiry might be viewed as part and parcel of the right to cross-examination, this circuit has yet to decide whether the Confrontation Clause provides defendants a right to impeach witnesses through extrinsic evidence.").
Since the rule of Van Arsdall was articulated in a case, and applied to circumstances, much different from the circumstances in which the petitioner now seeks to employ it, we cannot conclude that Van Arsdall "squarely established" a "specific legal rule" applicable to the petitioner's case. See Knowles v. Mirzayance, ___ U.S. ___, 129 S.Ct. 1411, 1419, 173 L.Ed.2d 251 (2009). Van Arsdall does provide a "clearly established" federal rule for a class of cases, but it is not the class within which the petitioner's case falls. Therefore, the Kirouac test is not "contrary to" the rule Van Arsdall adopted nor was Van Arsdall unreasonably applied in this case.

2. Clearly Established Law on the Right to Present a Defense
As noted, the petitioner does not rely exclusively on Van Arsdall in pursuing habeas relief. He also argues that the restrictions on his cross-examination of Officer Gouveia and Officer Smith impaired his right, protected by clearly established law under the Sixth and Fourteenth Amendments, to present a complete defense. He suggests that testimony from the officers describing both Smith's post-arrest statement and the subsequent police investigation of Bettencourt was needed not only to impeach Lynch's in-court and out-of-court identifications of the petitioner, but also to demonstrate to the jury the likelihood that Bettencourt was the true culprit and to invite reasonable doubt based on inadequacies in the police investigation. He therefore challenges the objective reasonableness of the Appeals Court's conclusion that he was not prejudiced by the restrictions on cross-examination.
It is well established that a state's "broad latitude" to define rules for the exclusion of evidence and to apply those rules to criminal defendants has constitutional limits. See Clark v. Arizona, 548 U.S. 735, 789, 126 S.Ct. 2709, 165 L.Ed.2d 842 (2006). Evidentiary restrictions that hinder a defendant's ability to present defense evidence can, in some circumstances, be severe enough to violate due process. See Chambers, 410 U.S. at 302, 93 S.Ct. 1038. "Whether rooted directly in the Due Process Clause of the Fourteenth Amendment, or in the Compulsory Process or Confrontation clauses of the Sixth Amendment, the Constitution guarantees criminal defendants `a meaningful opportunity to present a complete defense.'"[12]Crane v. Kentucky, 476 U.S. 683, 690, 106 S.Ct. *72 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)) (internal citations omitted).
The Supreme Court has described this right as "a fundamental element of due process of law," Washington v. Texas, 388 U.S. 14, 19, 87 S.Ct. 1920, 18 L.Ed.2d 1019 (1967), which "is abridged by evidence rules that `infring[e] upon a weighty interest of the accused' and are `arbitrary' or `disproportionate to the purposes they are designed to serve.'" 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) (alteration in original) (internal quotation marks omitted)). Even a generally defensible rule of evidence may be applied so as to produce an unconstitutional infringement. White v. Coplan, 399 F.3d 18, 24 (1st Cir. 2005).
It is also clear that a defendant's right to elicit exculpatory defense evidence through cross-examination falls within the ambit of this longstanding right. See, e.g., Chambers, 410 U.S. at 302, 93 S.Ct. 1038 (holding that a defendant was denied a meaningful opportunity to present a complete defense where he was allowed neither to cross-examine an alternative suspect in the case nor to call witnesses for the purpose of impeaching that suspect's testimony); Catalan-Roman, 585 F.3d at 465-66 (evaluating a defendant's right to present extrinsic impeachment evidence as a due process claim where the defendant's failure to address adverse precedent had waived his argument under the Confrontation Clause).
Despite the generality of these principles, "AEDPA does not `require state and federal courts to wait for some nearly identical factual pattern before a legal rule must be applied.'" Panetti, 551 U.S. at 953, 127 S.Ct. 2842 (quoting Musladin, 549 U.S. at 81, 127 S.Ct. 649 (Kennedy, J., concurring in judgment)). Nevertheless, in order to be entitled to relief, the petitioner must meet his burden of demonstrating that the Appeals Court's decision reflects an unreasonable application of the clearly established "arbitrary and disproportionate" standard to the facts of his case.

B. The Appeals Court's Application of Federal Law

1. Deference Under § 2254(d)(1)
In evaluating a state court's application of federal law, our inquiry "is not how well reasoned the state court decision is, but whether the outcome is reasonable." Hurtado v. Tucker, 245 F.3d 7, 20 (1st Cir.2001). In this regard, "the most important point is that an unreasonable application of federal law is different from an incorrect application of federal law." Williams, 529 U.S. at 410, 120 S.Ct. 1495. Moreover, the Supreme Court has explained that "evaluating whether a rule application was unreasonable requires considering the rule's specificity. The more general the rule, the more leeway courts have in reaching outcomes in case-by-case determinations." Yarborough v. Alvarado, 541 U.S. 652, 664, 124 S.Ct. 2140, 158 L.Ed.2d 938 (2004).
Our own decisions involving a defendant's constitutional right to present a defense demonstrate the generality of the right and the substantial element of judgment required of trial courts in excluding defense evidence. See, e.g., Dolinger v. Hall, 302 F.3d 5, 11 (1st Cir.2002) (affirming denial of habeas petition where the exclusion of evidence still afforded the defendant "an adequate opportunity" to challenge the witness's bias in other ways); United States v. Cunan, 152 F.3d 29, 38-39 *73 (1st Cir.1998) (finding no constitutional violation in the exclusion of hearsay evidence where "sufficient evidence" of the defense theory remained); cf. United States v. Holden, 557 F.3d 698, 704 (6th Cir.2009) ("The key issue is whether the jury had enough information to assess the defense's theory of the case despite the limits placed on cross-examination."). The Appeals Court's adjudication of the petitioner's claim is therefore entitled to substantial deference under AEDPA. See O'Laughlin v. O'Brien, 568 F.3d 287, 299 (1st Cir.2009) (noting that habeas review involves layering the deference federal courts owe to state courts on top of the underlying standard governing the constitutional right asserted); cf. Renico, 130 S.Ct. at 1865 (describing "the dual layers of deference required by AEDPA" in cases where the standard applied by a state appellate court is deferential to the trial court). We may only upset the Appeals Court's decision if we conclude that it falls outside of the "broader range of reasonable judgements" that accompanies the application of so general a legal test. See Locke v. Cattell, 476 F.3d 46, 51 (1st Cir. 2007).
Here, the Appeals Court concluded that, in light of the defendant's numerous other avenues for advancing his misidentification defense, "the restrictions placed upon the defendant's cross-examination of Officers Smith and Gouveia did not prejudice the defendant." Brown, 2006 WL 3392089, at *3. We cannot say that outcome was unreasonable.

2. Restrictions on the Presentation of Evidence
The petitioner argues that the trial court imposed "arbitrary and disproportionate" restrictions on his right to present relevant evidence in his defense. First, he suggests that the exclusion of Smith's statement on hearsay grounds was "disproportionate to the ends that [the hearsay rule is] asserted to promote," see Holmes, 547 U.S. at 321, 126 S.Ct. 1727, because the statement bears particular indicia of reliability that mitigated traditional hearsay concerns. Second, he suggests that critical defense evidence was arbitrarily excluded when the trial court exceeded the scope of its pre-trial ruling and sustained objections to questions by defense counsel about whether Officer Gouveia initiated his investigation of Bettencourt following a police interview of Smith, whether Officer Gouveia considered Smith a suspect, and whether Officer Smith interviewed or had occasion to show photographs to Smith. The petitioner argues that the answers to these questions did not depend on the truth of Smith's out-of-court statement, and were admissible under state law as evidence of the police investigation (or lack thereof) into Bettencourt as an alternative suspect. See generally Commonwealth v. Cordle, 404 Mass. 733, 537 N.E.2d 130, 137 (1989).
Smith's post-arrest statement implicating Bettencourt in the assault is prototypical hearsay evidence. See Fed.R.Evid. 801(c). With rare exception, a trial court's exclusion of hearsay evidence does not offend the Constitution. See Montana v. Egelhoff, 518 U.S. 37, 42, 116 S.Ct. 2013, 135 L.Ed.2d 361 (1996) (plurality opinion) (describing the hearsay rule as "familiar and unquestionably constitutional"); Chambers, 410 U.S. at 298, 93 S.Ct. 1038 ("The hearsay rule, which has long been recognized and respected by virtually every State, is based on experience and grounded in the notion that untrustworthy evidence should not be presented to the triers of fact.").
The Appeals Court was presented with, and expressly rejected, the petitioner's argument that the statement bore particular *74 indicia of reliability. On direct appeal, the petitioner asserted that Smith's statement was reliable because it was self-incriminatory, see generally Chambers, 410 U.S. at 300-01, 93 S.Ct. 1038, and because it tended to show that another person committed the crime, see generally Commonwealth v. O'Brien, 432 Mass. 578, 736 N.E.2d 841, 851 (2000) (explaining that, under Massachusetts law, hearsay evidence "may be admitted, in the judge's discretion, to show that a third party might have committed the crime"). The Appeals Court concluded that the trial court did not abuse its discretion in excluding Smith's statement because the statement was not "in a very real sense self-incriminatory" (since it was not made by Bettencourt and denied both Smith and Bettencourt's participation in the assault) and because it did not contain sufficiently substantial "connecting links" between Bettencourt and the assault. See Brown, 2006 WL 3392089, at *4-*5 (internal quotation marks omitted). We see nothing unreasonable about the Appeals Court's determination that the hearsay rule was properly applied to exclude Smith's statement.
Turning to the other limitations placed on the petitioner's cross-examination of Officer Smith and Officer Gouveia regarding their investigation of Bettencourt, we disagree with the petitioner's contention that the Appeals Court unreasonably failed to find that the restrictions imposed in his case arbitrarily infringed on his ability to present a complete defense. Even assuming that some of the excluded testimony was otherwise proper and admissible for a non-hearsay purpose, which we need not decide, we have been clear that "not every ad hoc mistake in applying state evidence rules ... should be called a violation of due process; otherwise every significant state court error in excluding evidence offered by the defendant would be a basis for undoing the conviction." Fortini v. Murphy, 257 F.3d 39, 47 (1st Cir.2001). As we have noted elsewhere, "the Supreme Court has rarely overturned state convictions because evidence was excluded and has in recent years made clear that only in extreme cases" will such claims succeed. O'Brien, 453 F.3d at 20 (alterations omitted) (internal quotation marks omitted); see also Ellsworth v. Warden, 333 F.3d 1, 7 (1st Cir.2003) (en banc) (describing constitutional challenges to restrictions on cross-examination as "tenable only where the restriction is manifestly unreasonable or overbroad"). Provided that a defendant retains an adequate opportunity to present his theory of the case, the Supreme Court has made clear that a defendant's right to present relevant evidence "`may, in appropriate cases, bow to accommodate other legitimate interests in the criminal trial process.'" Lucas, 500 U.S. at 149, 111 S.Ct. 1743 (quoting Rock v. Arkansas, 483 U.S. 44, 55, 107 S.Ct. 2704, 97 L.Ed.2d 37 (1987)).
As the Appeals Court recognized, despite the exclusion of Smith's statement by the trial court, the petitioner was permitted to establish through his cross-examination of Officer Gouveia that Bettencourt's name had surfaced during the police investigation of the assault, that Officer Gouveia had attempted to locate Bettencourt, and that Bettencourt better fit Lynch's physical description of his assailant. The defendant was also provided a full opportunity to cross-examine Lynch, the Commonwealth's most important witness, and declined to exercise his right to call Smith as a witness to his own statements. In light of these substantial other opportunities to call the jury's attention to the likelihood that Bettencourt was the true culprit and that the police investigation of Bettencourt was suspect, we cannot say on this record that the Appeals Court's conclusion that the petitioner was not prejudiced by the *75 preclusion of additional testimony from the officers regarding the police investigation of Bettencourt was an unreasonable application of clearly established law on the right to present a defense.
Affirmed.
NOTES
[1]  On habeas review, we presume the correctness of the state court's factual findings. See 28 U.S.C. § 2254(e)(1). The petitioner does not challenge the factual basis of the Appeals Court's decision except for a lone statement, which we discuss infra note 7.
[2]  Brown was indicted on two charges, but was convicted only of armed assault with intent to rob a person sixty years of age or older. He was acquitted of assault and battery on a person sixty years of age or older. Smith was indicted on identical charges, and pleaded guilty prior to Brown's trial.
[3]  Smith claimed to have witnessed a person known only as "Triz" punch Lynch. Smith was unable to identify "Triz" when shown a photo array that included a picture of Brown.
[4]  Brown is six feet one inch in height. There was also no evidence that Brown had ever displayed facial hair.
[5]  The trial judge held a sidebar conference following the latter inquiry, at which the prosecutor explained that he objected to the question because "what counsel is trying to do is trying to invite the jury to draw the inference as to what the hearsay statement was." The following exchange then occurred:

THE COURT: Where are you heading with this?
[DEFENSE COUNSEL]: For hearsay, simply to contradict testimony from certainly Mr. Lynch as to the identity of the assailant. It's not information. It's for hearsay purposes.
THE COURT: No, sustained.
[6]  The government contends that the petitioner's claim under the "contrary to" prong of § 2254(d)(1) is either unexhausted or barred by the principle of judicial estoppel because the petitioner argued to the Appeals Court that Miles, which quotes from Kirouac, provided the applicable legal standard and, further, treated the holding of Van Arsdall as consistent with the Kirouac test in his petition to the Supreme Judicial Court for further appellate review. However, we need not resolve the government's exhaustion argument if we conclude on the merits that the denial of the petition for habeas corpus was proper. See 28 U.S.C. § 2254(b)(2) ("An application for a writ of habeas corpus may be denied on the merits, notwithstanding the failure of the applicant to exhaust the remedies available in the courts of the State."). We therefore elect to begin our analysis by addressing the substance of the petitioner's claims.
[7]  In the district court, the petitioner asserted that the Appeals Court made an unreasonable factual determination when it stated that Lynch described to Officer Gouveia only "two of the three young men who attacked him." Brown, 2006 WL 3392089, at *2. The district court rejected the claim, noting that AEDPA allows state courts "some room for mistakes," such as imprecise factual descriptions. See Hurtado v. Tucker, 245 F.3d 7, 12 (1st Cir. 2001). On this appeal, the petitioner maintains that the Appeals Court erred in its factual recitation, but he explicitly disclaims that the error rises to the level required to entitle him to relief under the statute's second prong, § 2254(d)(2). Instead, he suggests that the Appeals Court's misstatement merely highlights the general unreasonableness of its decision. Accordingly, we confine the scope of our review to the statute's first prong, § 2254(d)(1).
[8]  The distinction is not insignificant. Under both Massachusetts and federal law, a defendant bears the burden on both direct and collateral review of demonstrating a constitutional violation. Once a violation is found, the government bears the burden of demonstrating that the error was harmless. See, e.g., United States v. Casas, 356 F.3d 104, 121 (1st Cir.2004); Commonwealth v. Depina, 456 Mass. 238, 922 N.E.2d 778, 788 (2010). The essence of the petitioner's claim, therefore, is that the Kirouac test impermissibly burdened him with proving the materiality of the officers' direct testimony when, in fact, it is the Commonwealth's burden to prove that the officers' testimony was immaterial.
[9]  In particular, the petitioner draws our attention to the following statement made by the prosecutor during closing argument:

We have this other array that somehow [defense counsel] wants to criticize the police for going back and showing another photo array after Mr. Brown and Mr. Smith had been arrested. Well, there was another person there that night. Should the police stop looking for this third person?
[10]  In the last five terms, the Supreme Court has overturned five federal grants of habeas corpus on the ground that the cited Supreme Court precedent had not been clearly established in the factual context presented. See Berghuis v. Smith, ___ U.S. ___, 130 S.Ct. 1382, 1392-94, 176 L.Ed.2d 249 (2010) (holding that the Supreme Court's "pathmarking decision" in Duren v. Missouri, 439 U.S. 357, 99 S.Ct. 664, 58 L.Ed.2d 579 (1979), "hardly establishesno less `clearly' sothat [the petitioner] was denied his Sixth Amendment right" on distinguishable facts); Thaler, 130 S.Ct. at 1175 (reversing a grant of habeas relief where "[t]he part of [the Supreme Court's precedent] on which the Court of Appeals relied concerned a very different problem"); Van Patten, 552 U.S. at 125, 128 S.Ct. 743 (reversing grant of habeas where Supreme Court precedent did not "squarely address[]" the question at issue); Schriro v. Landrigan, 550 U.S. 465, 478, 127 S.Ct. 1933, 167 L.Ed.2d 836 (2007) (reversing grant of habeas where Supreme Court had never addressed "a situation in which a client interferes with counsel's efforts to present mitigating evidence"); Musladin, 549 U.S. at 77, 127 S.Ct. 649 (noting a "contrast" between existing Supreme Court precedent involving "state-sponsored courtroom practices" and the conduct "to which Musladin objects" involving "private-actor courtroom conduct").
[11]  Although not valid sources of clearly established federal law under AEDPA, "[d]ecisions from the lower federal courts may help inform the AEDPA analysis to the extent that they state the clearly established federal law determined by the Supreme Court." Aspen v. Bissonnette, 480 F.3d 571, 574 n. 1 (1st Cir. 2007).
[12]  In his brief, the petitioner principally characterizes the right to present a defense as one secured by the Confrontation Clause. For the purpose of this appeal, it is unnecessary for us to resolve whether the right is rooted in the Sixth Amendment and applied to the states through the Fourteenth Amendment, or whether it is rooted directly in the Due Process Clause of the Fourteenth Amendment. Cf. Pike, 492 F.3d at 78 n. 8. See generally United States v. Scheffer, 523 U.S. 303, 307-08 & n. 3, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998).
