[511]*511JULIA SMITH GIBBONS, Circuit Judge.
Petitioner — appellant Randall Couturier appeals the district court’s denial of his petition for a writ of habeas corpus. Couturier was convicted of four counts of second-degree criminal sexual conduct (“CSC II”). His petition for habeas alleged, inter alia, a violation of his Confrontation Clause right to cross-examine a witness against him, a violation of his right to present a defense, and ineffective assistance of counsel for failing to preserve his Confrontation Clause claim. For the following reasons, we affirm the judgment of the district court.
I.
Beginning in 1995, Couturier volunteered full-time in his wife’s first grade classroom. Couturier — or “Mr. C”— helped the children individually with problems, corrected work, and administered accelerated reading tests (“AR tests”) to individual students at a classroom computer. When Couturier administered the AR tests, the student would sit on his knee or in a chair at the computer, and Mrs. Couturier would be seated no more than seven feet away.
On March 5, 2002, one of Mrs. Couturier’s students, Chrystal Huggins, told her mother that Couturier had touched her privates under her pants while she was taking AR tests. As he had done countless times before, Couturier had administered an AR test to Huggins on that day. And, as was customary, she sat on Couturier’s lap. However, this occasion was different because Huggins had wet her pants before taking the test, and Mrs. Couturier had not had time to warn Couturier. Consequently, Couturier’s pants were soiled when Huggins sat on his lap. Mrs. Couturier testified that Huggins had a tendency to wet her pants and then deny doing so. When Huggins denied wetting her pants, Mrs. Couturier would ask the neighboring teacher or another school official to confirm so that it could be documented and Huggins’s mother notified.
At trial, Huggins testified that Couturier had touched her more than once, that she did not like him because he touched her, and that she did not initially tell her mother about the touching because she was scared. Huggins was the first student to allege touching by Couturier. However, two other girls came forward with similar allegations after the case was publicized and their mothers asked them about Couturier. As often happens in such cases, there was no physical evidence of abuse presented at trial, and thus the credibility of Huggins and her two co-complainants was the central issue for the defense. At trial, the jury heard evidence of Huggins’s pants wetting at school from Huggins’s mother, Mrs. Couturier, and other witnesses. Mrs. Couturier testified that, although smart, Huggins had struggled at school, had been caught cheating twice— once before the March 5 incident and once after — and had admitted cheating only after the second incident. Huggins’s mother admitted that her daughter had a pants-wetting problem and that her daughter lied about wetting her pants but testified that she was unaware of any cheating or other issues at school.
The defense also attempted to impeach Huggins by confronting her with prior inconsistent statements and statements that conflicted with the other witnesses’ testimony. For example, Huggins testified that she did not remember wetting her pants in first grade and that only she sat on Couturier’s lap to take AR tests. The court allowed some such cross-examination, but disallowed other lines of questioning. In one example of the latter, the following exchange took place:
[512]*512[Defense] [Y]ou said that you didn’t like Mr. C, is that right?
[Huggins] Not that well.
[Defense] And you were scared, is that right?
[Huggins] Yes.
[Defense] Did you send Mr. C notes tellin’ him you loved him and missed him after he was no—
[Prosecutor] Your Honor,—
[Defense] — longer in the—
[Prosecutor] — I’m gonna—
[Defense] — classroom?
[Prosecutor] — object at this time. I’m not sure what the relevance of that is.
[Defense] Impeachment, your honor.
The Court Sustained.
Defense counsel continued without further reference to the note, and no evidence of what the note said or the context in which it was written is otherwise in the record.
The judge also did not permit defense counsel to question Mrs. Couturier regarding whether she had considered contacting Protective Services because of concerns about Huggins’s home life. Mrs. Couturier had allegedly discussed contacting Protective Services with school officials. Defense counsel told the judge that “it goes to [Huggins’s] credibility” because “[it] is a fabrication on [her] part regarding my client.” The prosecutor objected on relevance grounds, indicating that Mrs. Couturier’s concerns stemmed also from Huggins’s sibling’s behavior, which was irrelevant to the abuse accusation. The court ruled that “[it] would not permit the evidence based upon both the relevancy objection as well as ... the argument that it is impeachment.... [I]f it is impeachment at all of any witnesses, which I’m not sure it is, is highly collateral.”
The jury convicted Couturier of a total of four counts of CSC II, Mich. Comp. Laws § 750.520c(l)(a), with respect to Huggins and one co-complainant, and acquitted him of two counts of CSC II with respect to the other complainant. Couturier v. Vasbinder (Couturier IV), No. 2:06-cv-13886, 2008 WL 4613055, at *1 (E.D.Mich. Oct.15, 2008). The judge sentenced him to two concurrent prison terms of 71 to 180 months and ordered Couturier to register as a sex offender.
On February 10, 2005,1 the Michigan Court of Appeals reversed the judgment and remanded the case for a new trial. People v. Couturier (Couturier I), No. 252175, 2005 WL 323680, at *5 (Mich.Ct. App. Feb.10, 2005) (per curiam). The appellate court rejected many of Couturier’s claims but agreed that the trial court had violated Couturier’s Confrontation Clause rights by limiting the cross-examination of Huggins to exclude the note. Id. at *3. The court recognized that Huggins’s credibility was paramount and stated:
Given the age of this complainant and the extended time between when the incidents allegedly happened and the trial, effective cross-examination was difficult at best. The note in issue was substantially related to the complainant’s credibility, and the defendant should have had the opportunity to fully cross-examine her about its contents.
Id. at *4. The court further found that the related impeachment evidence offered by Mrs. Couturier was not sufficient to render the error harmless because a jury could discount testimony by the defendant’s own wife. Id. In rejecting Couturier’s claim that the exclusion of evidence that Mrs. Couturier considered contacting Protective Services, the court noted that “the inter[513]*513mediate inference defendant is attempting to draw (that a child from a troubled home is more likely to fabricate claims of sexual abuse) is extremely tenuous.” Id.
The Supreme Court of Michigan vacated and remanded for consideration of the Confrontation Clause claim under plain-error review for failure to preserve the constitutional claim and for review of Couturier’s claims not addressed by the court’s February 10, 2005, opinion. People v. Couturier (Couturier II), 474 Mich.876, 704 N.W.2d 463, 463 (2005). On remand, the court of appeals stated: “Although we believe the cross-examination issue was a preserved constitutional error which would require a reversal of defendant’s convictions, under the plain error review standard we must affirm....” People v. Couturier (Couturier II), No. 252175, 2005 WL 3439824, at *1 (Mich.Ct.App. Dec.15, 2005); see also id. at *2 n. 1. The court found that because “[t]he subject of the cross-examination did not bear directly on the question of ... guilt or innocence, but only offered a prism through which to view one complainant’s testimony, which prism could have strengthened or weakened the credibility assessment,” Couturier failed to demonstrate that the limitation to cross-examination “would have proved him innocent” or that it “threw the integrity of the proceedings into doubt.” Id. at *2-3 (emphasis in original). The court went on to reject the remainder of Couturier’s claims. Id. at *4-5. The Supreme Court denied review. People v. Couturier, 475 Mich. 886, 715 N.W.2d 875, 875 (2006).
Couturier filed a petition for habeas corpus in federal district court alleging six constitutional errors, including those at issue here: (1) improper limitation of cross-examination in violation of the Confrontation Clause; (2) improper exclusion of evidence of one complainant’s difficulties at school; and (3) ineffective assistance of counsel. The district court rejected all claims but issued a certificate of appeala-bility with respect to the Confrontation Clause claim, Couturier v. Vasbinder, No. 08-2487, Order, at 5 (6th Cir. April 22, 2009); Couturier IV, 2008 WL 4613055, at *11-12, and we granted a certificate of appealability with respect to the latter two claims. For the following reasons, we affirm the district court’s denial of the writ.
II.
We review a district court’s denial of a writ of habeas corpus de novo. Pudelski v. Wilson, 576 F.3d 595, 607 (6th Cir.2009). Findings of fact by the district court are reviewed for clear error unless the district court’s factual determinations are based solely on a review of the state court transcript, in which case they are reviewed de novo. Dando v. Yukins, 461 F.3d 791, 796 (6th Cir.2006). Factual determinations by a state court are presumed to be correct unless rebutted by clear and convincing evidence. 28 U.S.C. § 2254(e)(1).
Pursuant to the Antiterrorism and Effective Death Penalty Act of 1996 (“AED-PA”), 28 U.S.C. § 2241 et seq., a federal court may grant a state prisoner habeas relief only when the state court’s decision on the merits
(1) resulted in a decision that 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) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.
28 U.S.C. § 2254(d). The state court’s decision must be objectively unreasonable, and not merely incorrect. Williams v. Taylor, 529 U.S. 362, 409, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). The United States Supreme Court has held 6 that the “unreasonable application” language permits a reviewing court to grant habeas [514]*514relief “if the state court identifies the correct governing legal principle from [the Supreme] Court’s cases but unreasonably applies it to the facts of the ... prisoner’s case.” Williams, 529 U.S. at 407, 120 S.Ct. 1495. In analyzing whether a state court decision is an “unreasonable application,” we look to the holdings — not dicta— of Supreme Court precedent. Id. at 412, 120 S.Ct. 1495.
III.
A.
Couturier first argues that the trial judge improperly and unconstitutionally limited cross-examination of Huggins by not permitting defense counsel to question her about a note that she wrote to Couturier telling him that she loved and missed him. The Michigan Court of Appeals initially vacated the conviction and granted a new trial based on this limitation, Couturier I, 2005 WL 323680, at *5, but later reluctantly affirmed under a more stringent plain-error standard of review, Couturier III, 2005 WL 3439824, at *1. Because the State conceded at oral argument that AEDPA deference does not apply here, we review the claim de novo.
The Sixth Amendment guarantees the right of an accused in a state criminal prosecution “to be confronted with the witnesses against him.” U.S. Const, amend. VI; see also Pointer v. Texas, 380 U.S. 400, 407-08, 85 S.Ct. 1065, 13 L.Ed.2d 923 (1965). Cross-examination is a “primary interest secured” by the Confrontation Clause. Douglas v. Alabama, 380 U.S. 415, 418, 85 S.Ct. 1074, 13 L.Ed.2d 934 (1965); see also Davis v. Alaska, 415 U.S. 308, 315-16, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974). However, “the Constitution entitles a criminal defendant to a fair trial, not a perfect one.” Delaware v. Van Arsdall, 475 U.S. 673, 681, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986).
The Supreme Court “ha[s] recognized that the exposure of a witness’ motivation in testifying is a proper and important function of the constitutionally protected right of cross-examination.” Davis, 415 U.S. at 316-17, 94 S.Ct. 1105. Therefore, “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 ... could appropriately draw inferences relating to the reliability of the witness.’ ” Van Arsdall, 475 U.S. at 680, 106 S.Ct. 1431 (quoting Davis, 415 U.S. at 318, 94 S.Ct. 1105). However,
trial judges retain wide latitude insofar as the Confrontation Clause is concerned to impose reasonable limits on such cross-examination based on concerns about, among other things, ... interrogation that is repetitive or only marginally relevant.... “[T]he 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. at 679, 106 S.Ct. 1431 (quoting Delaware v. Fensterer, 474 U.S. 15, 20, 106 S.Ct. 292, 88 L.Ed.2d 15 (1985) (per curiam) (emphasis in original)); see also Davis, 415 U.S. at 316, 94 S.Ct. 1105 (“Cross-examination is ... [sjubject always to the broad discretion of a trial judge to preclude repetitive and unduly harassing interrogation.... ”).
We have recognized that, as in this case, when “it is merely the extent of cross-examination that is limited, the trial judge retains a much wider latitude of discretion. Once cross examination reveals sufficient information to appraise the witness’ veracity, confrontation demands are satisfied.” [515]*515Boggs v. Collins, 226 F.3d 728, 736 (6th Cir.2000) (quoting Dorsey v. Parke, 872 F.2d 163, 167 (6th Cir.1989)) (internal quotation marks omitted). Thus, “[w]here the trial court limits the extent of cross-examination, the inquiry for the reviewing court is “whether the jury had enough information, despite the limits placed on otherwise permitted cross-examination, to assess the defense theory.’” Stewart v. Wolfenbarger, 468 F.3d 338, 347 (6th Cir.2007) (quoting Dorsey, 872 F.2d at 167).
It is undeniable that Huggins’s credibility is central to Couturier’s defense theory. There was no direct evidence of abuse, and the circumstantial evidence consisted entirely of the testimony of Couturier’s three young accusers. Huggins’s note, therefore, could serve to impeach Huggins’s pri- or statement that she hated and was scared of Couturier and to generally attack her credibility and demonstrate a propensity to lie. However, because the trial judge did permit Couturier’s counsel to cross-examine Huggins in some detail, we must determine whether the jury “had enough information ... to assess the defense theory” of a lack of credibility. See Stewart, 468 F.3d at 338.
The trial court allowed considerable leeway in the cross-examination of Huggins, including regarding her pants-wetting problem, allegations of cheating, and her denials thereof. Defense counsel’s cross-examination of Huggins and her mother, as well as the testimony of other defense witnesses, presented the jury with evidence of Huggins’s multiple inconsistent and untruthful statements. The defense also argued in closing that these inconsistencies illustrated a propensity to lie. The jury, therefore, was aware of the defense’s theory that Huggins fabricated the accusation and that Huggins had a history of lying. Furthermore, interrogation regarding the note would be “repetitive or only marginally relevant” and within the trial court’s discretion to exclude under the Confrontation Clause. Van Arsdall, 475 U.S. at 679, 106 S.Ct. 1431. Consequently, although the decision to exclude the note may have been questionable, because the jury had sufficient evidence before it to assess the defense theory even without the testimony about the note, the limitation of cross-examination in this case does not rise to a violation of the Confrontation Clause.
Moreover, the limitation was harmless under the strict standard applicable in federal habeas cases. See Van Arsdall, 475 at 684, 106 S.Ct. 1431 (applying harmless-error review to Confrontation Clause violations); Vasquez v. Jones, 496 F.3d 564, 574 (6th Cir.2007) (same). On federal habeas review, the harmless-error standard is whether the violation “had substantial and injurious effect or influence in determining the jury’s verdict.” Brecht v. Abrahamson, 507 U.S. 619, 622, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993) (quoting Kotteakos v. United States, 328 U.S. 750, 776, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946)) (quotation marks omitted). Habeas courts must apply this standard regardless of the harmless-error standard applied by the state court or whether the state court undertook harmless error review at all. Fry v. Pliler, 551 U.S. 112, 121-22, 127 S.Ct. 2321, 168 L.Ed.2d 16 (2007). When reviewing Confrontation Clause violations for harmless error, the reviewing court considers the factors laid out in Van Arsdall, which “include the importance of the witness’ testimony in the prosecution’s case, whether the testimony was cumulative, the presence or absence of evidence corroborating or contradicting the testimony of the witness on material points, the extent of cross-examination otherwise permitted, and, of course, the overall strength of the prosecution’s case.” Van Arsdall, 475 U.S. at 684, 106 S.Ct. 1431.
[516]*516As evidence of Huggins’s lack of credibility, the note was largely cumulative. Although the prosecution’s case was circumstantial, and not overwhelmingly strong, the exclusion of this additional evidence of inconsistency — in light of the other inconsistencies presented at trial — did not have a substantial or injurious effect on the jury. It was, therefore, harmless under Brecht, and we must affirm the district court’s denial of habeas on this claim.
B.
Couturier next argues that by excluding evidence that Mrs. Couturier considered contacting Protective Services about Huggins’s home situation and pants-wetting, the trial court violated his constitutional right to present a defense. Couturier argues that this evidence was necessary to demonstrate that Huggins “is a troubled child whose testimony cannot be trusted.”
The Michigan Court of Appeals did not address the claim as a violation of the right to present a complete defense but rather characterized Couturier’s argument as an appeal of the application of state evidence rules. See Couturier I, 2005 WL 323680, at *4. The court, citing Michigan Rules of Evidence 401 and 402, found that it was not an abuse of discretion to exclude the evidence because it was not relevant: “[T]he intermediate inference defendant is attempting to draw (that a child from a troubled home is more likely to fabricate claims of sexual abuse) is extremely tenuous.” Id. Because the state court did not review the merits of this constitutional claim, AEDPA deference does not apply, and we conduct de novo review of questions of law, and clear-error review of factual determinations. Dorn v. Lafler, 601 F.3d 439, 442 (6th Cir.2010) (citations omitted).
“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.” Crane v. Kentucky, 476 U.S. 683, 690, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986) (citations and internal quotation marks omitted). Attendant to this right is ensuring the defendant an opportunity to present witnesses in his defense. See Taylor v. Illinois, 484 U.S. 400, 409, 108 S.Ct. 646, 98 L.Ed.2d 798 (1988). However, “[t]he accused does not have an unfettered right to offer testimony that is incompetent, privileged, or otherwise inadmissible under standard rules of evidence.” Taylor, 484 U.S. at 410, 108 S.Ct. 646 (emphasis added); Rockwell v. Yukins, 341 F.3d 507, 512 (6th Cir.2003) (“[T]he Supreme Court has made it perfectly clear that the right to present a “complete” defense is not an unlimited right to ride roughshod over reasonable evidentiary restrictions.... Rather, she ‘must comply with established rules of procedure and evidence designed to assure both fairness and reliability ....’” (quoting Chambers v. Mississippi, 410 U.S. 284, 302, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973))). The Michigan Rules of Evidence applied by the trial judge mirror their federal counterparts and are patently “standard rules of evidence.” Moreover, the Supreme Court has repeatedly affirmed its “traditional reluctance to impose constitutional constraints on ordinary evidentiary rulings by state trial courts.” Crane, 476 U.S. at 689, 106 S.Ct. 2142.
The excluded evidence of Mrs. Couturier’s suspicion that Huggins came from a troubled home is both repetitive and only marginally relevant. See Farley v. Lafler, 193 Fed.Appx. 543, 546 (6th Cir.2006). Mrs. Couturier and other witnesses, including Huggins’s mother, testified that Huggins had a pants-wetting problem and that she lied about that problem. The [517]*517defense counsel cross-examined Huggins regarding testimony that was inconsistent with the testimony of other witnesses regarding pants-wetting, cheating, and whether she was the only student who sat on Couturier’s lap to take AR tests. Mrs. Couturier’s excluded testimony would offer only another argument about Huggins’s lack of credibility. Furthermore, the evidence has little probative value because, as the Michigan Court of Appeals noted, that a child comes from a troubled home does not likely lead to an inference that she is more likely to lie.
Therefore, the trial judge’s exclusion of this tangential impeachment evidence as irrelevant under state evidence rules did not violate Couturier’s right to present a complete defense,2 and we affirm the district court’s denial of habeas with respect to this issue.
C.
Finally, Couturier argues that he is entitled to habeas relief because he received ineffective assistance of counsel when his attorney failed to preserve his Confrontation Clause claim. Because the Michigan Court of Appeals correctly stated the standard under Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), Couturier must now demonstrate that the denial of this claim was an unreasonable application of that standard. He has failed to do this. Under Strickland, counsel is constitutionally ineffective when (1) counsel’s performance was deficient and (2) that the deficiency prejudiced the defense. Id. at 687, 104 S.Ct. 2052. Both the state appellate court and the federal district court determined that counsel’s performance was not deficient because he had adequately raised the Confrontation Clause issue by attempting to question Huggins about her note and had responded to the prosecution’s objection by arguing that the note was relevant impeachment evidence. Couturier IV, 2008 WL 4613055, at *4-5; Couturier III, 2005 WL 3439824, at *2 n. 1, 5. Further objection, the Michigan Court of Appeals found, was not required because it would have been futile. Couturier III, 2005 WL 3439824, at *2 n. 1. We agree. As the Michigan Court of Appeals concluded, “[t]o the extent the issue is considered unpre-served, defense counsel’s performance was not objectively unreasonable as his actions [were] the type of actions which would typically preserve an objection.” Id. at *5. Thus the state court’s reasoning and conclusion are supported by the record and, moreover, are a consistent and reasonable application of Strickland. We consequently affirm the denial of this claim.
IV.
For the foregoing reasons, we affirm the district court’s order denying habeas relief.