RIPPLE, Circuit Judge.

Anthony Horton appeals from the denial of his petition for a writ of habeas corpus by the United States District Court for the Eastern District of Wisconsin. Mr. Horton was convicted of three counts of first degree sexual assault of a child, in violation of Wis. Stat. § 948.02(1). He appealed his convictions, alleging that he was deprived of his right to present a defense because the trial court excluded testimony that the victim had lied about the number of times she had had consensual sex with another individual. Mr. Horton also challenged the trial court's exclusion of testimony that the victim was under time pressure to explain her unexpected pregnancy, which may have prompted her to falsely accuse Mr. Horton of sexual assault. The Wisconsin Court of Appeals concluded that, although the excluded testimony was relevant, it was cumulative, and, consequently, its exclusion did not violate the Constitution of the United States. After the Wisconsin Supreme Court denied Mr. Horton's petition for review, he filed a petition for habeas relief in the United States District Court for the Eastern District of Wisconsin. See 28 U.S.C. § 2254. On September 11, 2003, the district court denied Mr. Horton's petition, holding that the Wisconsin Court of Appeals did not unreasonably apply clearly established federal law, as articulated by the Supreme Court of the United States. See id. § 2254(d)(1). We now affirm the judgment of the district court.

I BACKGROUND

A. Facts

Anthony Horton's convictions are based on a series of incidents that occurred between October 1997 and March 1998 and involved his girlfriend's eleven-year-old daughter, Jessica Robinson. While living with Jessica's family, Mr. Horton allegedly entered Jessica's bedroom in the middle of the night and sexually assaulted her approximately twelve times. On March 1, 1998, Jessica discovered that she was pregnant. Four days later, she told her mother about the pregnancy and claimed that Mr. Horton was the father. Subsequently, Mr. Horton was indicted and charged with four counts of first degree sexual assault of a child. See Wis. Stat. § 948.02(1). Although DNA testing later established that Mr. Horton was not the father of Jessica's baby, and Jessica admitted to having had sex with Randy, a friend of her older brother's, the state proceeded to trial on three of the sexual assault charges.

At trial, the prosecution called seven witnesses. Jessica testified that Mr. Horton had sexually assaulted her a number of times while he was living with her family. In October 1995, when she was eight- or nine-years-old, he came into her room while she was sleeping and touched her in a sexual manner. While Jessica's mother disbelieved the allegations, charges for first degree sexual assault of a child were brought by the State. Mr. Horton pled guilty to fourth degree sexual assault and spent nine months in prison.

According to Jessica's testimony, Mr. Horton moved back into the Robinson home after his release, and, around October 1997, his sexual assault of her, this time including sexual intercourse, resumed. Jessica explained that Mr. Horton often offered her gifts in exchange for remaining quiet about their illicit activity. No physical evidence was introduced at trial.

Jessica testified that, when she discovered that she was pregnant, she knew that there was a possibility that Randy, not Mr. Horton, might be the father. She testified that TaShea, her friend and Mr. Horton's niece, was with her when she took the home pregnancy test and that, when the test was positive, TaShea inquired about the identity of the father. Jessica told her that the father was Randy; she made no mention of Mr. Horton. However, when she revealed her pregnancy to her mother four days later, she did not mention Randy. Only after DNA testing eliminated the possibility that Mr. Horton was the father did Jessica finally disclose her relationship with Randy to her mother, noting that she had had sex with Randy only once.

Debra, Jessica's mother, also testified. She began by discussing her relationship with Mr. Horton, including his often violent conduct towards her. She then testified that Jessica told her of the pregnancy on March 5, 1998 in the school counselor's office and that she subsequently took Jessica to file a police report, and then for an abortion. Lastly, she testified that Jessica never mentioned her relationship with Randy until after DNA testing revealed that Mr. Horton was not the father of her baby; then, Jessica told her mother that she had thought "it was [Mr. Horton's] baby because [of] the number of times that he had had sex with her," and that she had only had sex with Randy once. R.44 at 125-26.

Jessica's seventeen-year-old cousin, Keionnia, testified that, about six years before the trial, she had slept over at her aunt Debra's home. According to Keionnia, Mr. Horton, who was living with Debra at the time, woke her up in the middle of the night, offered her marijuana, and, after she fell back asleep, sexually molested her. For this incident, Mr. Horton was charged with first degree sexual assault of a child. He pled guilty to fourth degree sexual assault on April 26, 1993, and was sentenced to nine months in prison.

Four other witnesses were called by the State, whose testimony is not directly relevant to this appeal.

The defense submitted the theory that Jessica had a motive to fabricate evidence. In the defense's view, Jessica had accused Mr. Horton of being the father of her child in order to avoid moral culpability for her consensual sexual activities with Randy, to protect Randy, and to remove Mr. Horton, her primary disciplinarian, from her home. To support this theory, the defense proffered the testimony of two witnesses: TaShea Horton, who was both a friend of Jessica's and Mr. Horton's niece; and Trina Horton, who was both TaShea's mother and Mr. Horton's sister. The State filed a motion to exclude this testimony as irrelevant. R.45 at 111.

With regard to TaShea Horton, the trial court denied in part and granted in part the State's motion. It allowed TaShea to testify that she was with Jessica when she took the pregnancy test. At that time, which was prior to the disclosure of DNA test results, she asked Jessica, "Who[se] baby is it? Randy?", to which Jessica responded, "Yes, I guess so." R.45 at 132. On recross-examination, when the defense inquired why TaShea would ask this question, she was permitted to explain that she "had seen Jessica and Randy have sex twice" and that Jessica "used to tell [her] sometimes that they had sex." Id. at 137.

However, the trial court precluded TaShea from testifying that Jessica had told both her and her mother, Trina, that Jessica and Randy had had sex four or five times, rather than once — as Jessica had told her mother and the court. The defense submitted that "[this conversation] goes directly to Jessica's credibility." Id. at 126. The court held, however, that the evidence was not relevant: it makes no difference, the court explained, "whether Randy had sex with her one time or five times or ten times." Id. at 127. In the court's view, the frequency neither proved nor disproved whether Mr. Horton sexually assaulted Jessica.

The trial court granted the State's motion to exclude the testimony of Trina Horton. According to the defense's oral offer of proof, Trina would have testified that, shortly after March 1, TaShea confided in her about Jessica's pregnancy. Trina, along with TaShea, then confronted Jessica, and Jessica admitted that she had had sex with Randy on four or five occasions. According to the defense's proffer, Trina would have testified further that she then gave Jessica five days to tell her mother of the situation; if Jessica failed to do so, Trina would do so. The trial court prohibited Trina from taking the stand, holding that this evidence does not have "anything to do with whether or not this defendant committed the acts he is accused of committing." Id. at 126.

On August 7, 1998, Mr. Horton was convicted of three counts of first degree sexual assault of a child. He was sentenced to consecutive twenty- and forty-year terms in prison, followed by forty years of probation.

B. Proceedings on Direct Appeal and on Habeas Review

On direct appeal, the defendant argued that the trial court's exclusion of Trina's testimony, as well as limitations on TaShea's testimony, violated his Sixth Amendment right to present a defense. The Wisconsin Court of Appeals held that Trina's testimony on the five-day ultimatum "would have been relevant to whatever inference of truthfulness the jury might have drawn from the timing of Jessica's accusations." R.12, Ex.E at 6. Similarly, the excluded testimony on the number of times Jessica and Randy had had sex "would strengthen the defense claim that Jessica named [Mr. Horton] as the father to protect Randy and minimize her responsibility for her own consensual sexual activities." Id. at 7.

The Wisconsin appellate court nevertheless affirmed Mr. Horton's conviction. It held that the defense, even absent the precluded testimony, had an opportunity to present fully its theory of the case; therefore, Mr. Horton was not deprived of the right to a fair trial. For example, Jessica testified that she did not mention to her mother or to the police that Randy might be the father of her baby, even though she knew it was a possibility. She also admitted telling TaShea that Randy was the father, long before DNA test results were returned. Additionally, according to the state court, it was clear that Jessica was under time pressure, given that "the pregnancy could not be hidden forever." Id.

After Mr. Horton's petition for review was denied by the Wisconsin Supreme Court, he filed a petition for a writ of habeas corpus in the United States District Court for the Eastern District of Wisconsin. See 28 U.S.C. § 2254. He alleged that the Wisconsin trial court's limitations on TaShea's testimony and the exclusion of Trina's testimony violated his constitutional rights to confrontation, to compulsory process and to present a defense. The district court denied Mr. Horton's petition. It held that the Wisconsin Court of Appeals' conclusion that the defendant had a full and fair opportunity to present its theory of the case was not an unreasonable application of federal law. Specifically, although the excluded evidence was relevant, a review of the record indicated that there was sufficient evidence to support the theory that Jessica accused Mr. Horton to "protect Randy and minimize her responsibility for her own consensual sexual activities." R.14 at 4 (quoting State v. Anthony H., 2000 WL 678535, at *4 (Wis.Ct.App.)). For example, Mr. Horton was permitted to show that Jessica gave contradictory answers concerning her "familiarity with Randy her boyfriend, and the number of times they engaged in consensual sexual activity." Id. In light of this evidence, the district court concluded that the Wisconsin Court of Appeals did not act unreasonably in determining that the state trial court did not deny Mr. Horton the right to present a defense.

II DISCUSSION

A. Standard of Review

We review the district court's denial of Mr. Horton's petition de novo. Hardaway v. Young, 302 F.3d 757, 762 (7th Cir. 2002). The Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA") mandates that Mr. Horton may be granted habeas relief only if the state court's adjudication "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." 28 U.S.C. § 2254(d)(1).

Under the "contrary to" clause, habeas relief is proper if the state court "arrive[d] at a conclusion opposite to that reached by [the] Court on a question of law" or "if the state court confront[ed] facts that are materially indistinguishable from a relevant Supreme Court precedent" and reached a different result. Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). In assessing whether the state court's decision was an "unreasonable application" of Supreme Court precedent, we look to whether the decision is "objectively unreasonable." Id. at 409, 120 S.Ct. 1495. The Supreme Court has cautioned that, in this context, "unreasonable" and "incorrect" are not synonymous: "[A] federal habeas court may not issue the writ simply because that court concludes in its independent judgment that the relevant state-court decision applied clearly established federal law erroneously or incorrectly. Rather, that application must also be unreasonable." Id. at 411, 120 S.Ct. 1495. With these principles in mind, we now turn to Mr. Horton's Sixth Amendment claim.

B. The Sixth Amendment Right to Present a Defense

The Sixth Amendment, as interpreted by the Supreme Court, guarantees a criminal defendant the right to present a defense. See Chambers v. Mississippi, 410 U.S. 284, 302, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973). "[A]t a minimum, . . . criminal defendants have the right . . . to put before a jury evidence that might influence the determination of guilt." Taylor v. Illinois, 484 U.S. 400, 408, 108 S.Ct. 646, 98 L.Ed.2d 798 (1988) (quotation marks omitted). The Supreme Court has held unconstitutional the rigid application of state evidentiary rules when such an application infringes upon the right to present witnesses in one's own defense, particularly when that testimony is critical to the defense's theory of the case. Chambers, 410 U.S. at 302-03, 93 S.Ct. 1038 (holding that "the [rules of evidence] may not be applied mechanistically to defeat the ends of justice").

This right, however, is not unlimited and may "bow to accommodate other legitimate interests in the criminal trial process." Id. at 295, 93 S.Ct. 1038. The state is permitted to impose reasonable restrictions on the presentation of a defense, including state and federal rules "designed to assure both fairness and reliability in the ascertainment of guilt and innocence." Id. at 302, 93 S.Ct. 1038; see also United States v. Lea, 249 F.3d 632, 642 (7th Cir. 2001) (state courts have "broad latitude to fashion rules which operate to exclude evidence from criminal trials"). Such rules do not abridge an accused's right to present a defense so long as they are not "`arbitrary' or `disproportionate to the purposes they are designed to serve.'" Rock v. Arkansas, 483 U.S. 44, 56, 107 S.Ct. 2704, 97 L.Ed.2d "the exclusion of evidence to be unconstitutionally arbitrary or disproportionate only where it has infringed upon a weighty interest of the accused." United States v. Scheffer, 523 U.S. 303, 308, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998).

The Wisconsin Court of Appeals adequately articulated the governing Sixth Amendment standards, as set forth by the Supreme Court of the United States. It correctly noted that the right to present a defense is not violated by every limitation placed on a defendant's exploration of a witness' bias. Instead, it held, the right to present a defense "is limited to the presentation of relevant evidence whose probative value is not substantially outweighed by its potential prejudicial effect." R.12, Ex.E at 4.

Furthermore, the Wisconsin court reasonably applied the Supreme Court's case law to the facts of this case.

1. TaShea and Trina's Testimony Concerning their Conversation with Jessica

The trial court precluded Mr. Horton from asking either Trina or TaShea Horton about their conversation with Jessica, in which she admitted that she had had sex with Randy on four or five occasions. Because this testimony would have contradicted Jessica's claim at trial that she and Randy had had sex only once, Mr. Horton contends that its exclusion violated his constitutional right to present a defense. According to Mr. Horton, this evidence substantiated the defense's theory that Jessica falsely accused him of sexual abuse in order to avoid punishment for her consensual sexual relations with Randy; it also exposed one of Jessica's lies and therefore impeached her credibility. The State responds that the Wisconsin Court of Appeals did not err in concluding that, although the trial court improperly held this evidence to be irrelevant to the trial, no federal constitutional right was violated because Mr. Horton had an opportunity to present substantially similar evidence.

In cases of sexual abuse, in which there are usually neither eye witnesses nor physical evidence and, consequently, the state's case in large part depends on the victim's testimony, courts have recognized the need to be especially sensitive to the importance of careful exploration of matters of credibility. Therefore, the claim that the state trial court's evidentiary rulings cut off an important avenue for Mr. Horton to expose potential inconsistencies in Jessica's testimony is worthy of close examination. To the degree that the testimony in question would have established that Jessica lied when she denied having sex with anyone but Mr. Horton, and when she claimed that she only had sex with Randy once, it would have corroborated the defense's theory that Jessica was willing to falsify charges to protect herself and Randy from punishment.

On the other hand, unlike the situations in the cases relied upon by the defendant, the Wisconsin trial court did not wholly bar Mr. Horton from testing Jessica's claim that she only had sex with Randy once. First, on recross-examination, defense counsel was permitted to ask TaShea what prompted her on March 1 to ask Jessica if Randy was the father of the baby. TaShea responded, "[b]ecause I had seen Jessica and Randy have sex twice and she used to tell me sometimes that they had sex." R.45 at 137. This testimony substantiated the claim that Jessica and Randy had had sex on numerous occasions and therefore challenged directly Jessica's contrary account to her mother and to the police, as well as in her testimony at trial. Additionally, even though she continued to insist that she only had had sex with Randy once, Jessica did admit under oath that she had misrepresented her relationship with Randy to her mother and had disclosed their sexual contact only after it was clear that Mr. Horton was not the father of the child. In sum, the trial court merely prohibited the defense from "add[ing] extra detail" to the claim of bias, which does not implicate constitutional guarantees. United States v. Sasson, 62 F.3d 874, 883 (7th Cir. 1995) (distinguishing between a complete bar on the introduction of testimony on a witness' bias and adding mere detail to evidence already in the record) (citations omitted); see also Wade v. Mantello, 333 F.3d 51, 60 (2d Cir. 2003) ("The Constitution leaves to the judges who must make [evidentiary] decisions `wide latitude' to exclude evidence that is `repetitive . . ., [or] only marginally relevant.'") (citations omitted). Based on this review of the record, we cannot conclude that the Wisconsin Court of Appeals "unreasonably" applied federal law in holding that "the exclusion of testimony by Trina and TaShea about a specific conversation in which Jessica had admitted having sex with Randy multiple times did not completely preclude the defense from presenting its theory on this point." R.12, Ex.E at 8.

2. Trina's Testimony Concerning the Five-Day Ultimatum

The Wisconsin trial court also prohibited Trina Horton from testifying that, upon learning of Jessica's pregnancy, she threatened to disclose this information to Jessica's mother if Jessica did not do so within five days. The trial court held that this evidence was not relevant to whether Mr. Horton sexually assaulted Jessica; the state appellate court concluded that the evidence was probative of Jessica's state of mind when making the accusations of sexual assault. It determined, however, that there was no constitutional error because the defense was permitted to present evidence that Jessica was "motivated by a desire to minimize the negative consequences of her pregnancy" and it was "apparent" that Jessica "faced time pressure in disclosing her pregnancy." Id.

Mr. Horton presents a strong argument that at no other time during the trial did he have the opportunity to demonstrate the effect of the ultimatum on Jessica's decision to accuse him of sexual assault. To be sure, the timing of the accusation is quite suspicious: on the fourth day of the five-day ultimatum period, Jessica told her mother of the pregnancy. Moreover, the admission was hesitant: after broaching the subject with her mother in the school counselor's office, she faltered, only coming forward with the information when her mother told her that they could talk after they returned from visiting Trina.

Nevertheless, we must affirm the district court's decision not to grant the writ. Although the excluded testimony is relevant and probative, its exclusion did not deprive Mr. Horton of the right to present a defense. Trina's proffered testimony about the ultimatum certainly would not have been cumulative in the same sense as the testimony about the number of times Randy and Jessica had had sexual intercourse. However, there was substantial evidence before the court that Jessica had a motive to lie to her mother. For example, on cross-examination, Jessica admitted that she knew that there was a possibility that Randy was the father of the child, but still did not tell her mother about her relationship with Randy until after the paternity test results were returned. R.44 at 191-92, 200. She admitted not disclosing this same information to the police in early March, even though she was asked explicitly by the interviewing officers whether she had had sex with anyone besides Mr. Horton. Id. at 208. She admitted not telling TaShea about the possibility that Mr. Horton was the father of the baby when she first took the pregnancy test, an omission that the defense later argued undermined the credibility of her allegations of sexual abuse. Id. at 189-90; R.46 at 28. The defense also attempted to bring out on cross-examination and during its closing statement that, in an effort to protect Randy, Jessica lied when she testified that she did not know Randy's last name or address. R.44 at 193; R.46 at 29. Lastly, as the Wisconsin Court of Appeals noted, it was apparent to the jury that, at a certain point, Jessica would be forced to reveal to her mother that she was pregnant.

Therefore, although Trina's testimony that Jessica was given a five-day deadline by which to tell her mother of her pregnancy, and therefore reveal her relationship with Mr. Horton in order to avoid revealing her relationship with Randy, would have helped the defense's case, the matter of Jessica's motive to lie to her mother was sufficiently developed by the defense through other means. At the very least, it is apparent that the Wisconsin appellate court assessed the probative value of the evidence and concluded that, because of its cumulative nature, its exclusion did not warrant retrial. See also Rice v. McCann, 339 F.3d 546, 550 (7th Cir. 2003) (holding that, because reasonable courts could differ on the exclusion of the evidence, the state court's approach could not be considered improper). In light of the broad latitude given such decisions under § 2254(d)(1), the Wisconsin appellate court's conclusion that the exclusion did not violate Mr. Horton's right to present a defense is not an unreasonable application of clearly established federal law.

Conclusion

For the foregoing reasons, we affirm the judgment of the district court.

AFFIRMED.