DAVID A. NELSON, Circuit Judge, delivered the opinion of the court, in which GARWOOD, Circuit Judge, joined. CLAY, Circuit Judge (pp. 513-18), delivered a separate dissenting opinion.
OPINION
DAVID A. NELSON, Circuit Judge.For the second time, Michigan prison warden John Yukins has appealed a writ of habeas corpus granted to convicted murder conspirator Sharon Rockwell. Under the legal standard prescribed by the Anti-terrorism and Effective Death Penalty Act of 1996, the writ should not have been issued unless Mrs. Rockwell’s conviction in state court involved an “unreasonable” application of federal law clearly established by the United States Supreme Court or unless the conviction was flat-out contrary to such clearly established law. Concluding that the result reached in the state court passes muster under the statutory test, we shah reverse the decision in which the federal district court granted habeas relief.
I
As we explained in our earlier opinion, see Rockwell v. Yukins, 217 F.3d 421, 422-*50923 (6th Cir.2000), Mrs. Rockwell and her husband, Edward Rockwell, had three sons. One of the sons, acting with two friends, attempted to kill Mr. Rockwell by cutting the brake lines on his car. The attempt failed. The boys then made another unsuccessful attempt on Mr. Rockwell’s life, this time by hitting him on the head with a baseball bat. Although Mrs. Rockwell was not present on either occasion, she had previously engaged in discussions with one or more of her sons about killing Mr. Rockwell. The State of Michigan therefore charged Mrs. Rockwell with conspiracy to commit murder.
Mrs. Rockwell’s defense, as her lawyer described it at a pretrial hearing, was that her participation in the discussions about killing Mr. Rockwell was not intended to further an actual murder; rather, according to counsel, Mrs. Rockwell’s purpose had been to let the boys vent the extreme and abiding hatred they harbored against their father for having abused them, sexually and otherwise, when they were younger. “[Mrs. Rockwell] felt in her heart that the only way she could keep the situation under control,” defense counsel explained, “was to allow the boys to talk and fantasize about [killing the hated Mr. Rockwell.]” Far from agreeing to a murder, the theory went, Mrs. Rockwell hoped to forestall a murder through what her lawyer seems to have viewed as some sort of talk therapy.
In connection with this “therapy defense,” as we characterized it in our earlier opinion, Mrs. Rockwell hoped to show at trial that Mr. Rockwell had in fact abused his sons. The prosecution hoped to exclude evidence .of the alleged abuse, and to that end the prosecution filed a motion in limine. The state trial court granted the motion, concluding that the evidence in question was not “material” under Mich. Rule of Evid. 404.1
When the case went to trial, Mrs. Rockwell elected not to take the stand. The jury returned a verdict of guilty, and Mrs. Rockwell was sentenced to imprisonment for life. An appeal to the Michigan Court of Appeals followed.
The Michigan Court of Appeals affirmed the conviction, succinctly explaining its rationale as follows:
“We find no abuse of discretion in the trial court’s exclusion of evidence of the victim’s alleged prior acts of abuse against defendant’s and the victim’s children. People v. Watkins, 176 Mich.App. 428, 440 N.W.2d 36 (1989). Defendant was merely limited in the method with which to present her defense and not deprived [of] the opportunity to present the same. Although marginally relevant, the evidence was properly excluded under MRE 403.”2
Mrs. Rockwell applied to the Michigan Supreme Court for leave to appeal the affir-mance of her conviction, but that court denied further review.
On March 19, 1997, Mrs. Rockwell commenced her habeas corpus action in the United States District Court for the Eastern District of Michigan. The initial pleading raised two issues (insufficiency of the evidence and .improper exclusion of the *510evidence of sexual abuse), both of which had been exhausted in the state courts. The district court subsequently granted Mrs. Rockwell leave to amend her petition to include an unexhausted claim. Following a hearing at which arguments were presented on the merits, the district court granted the writ on the ground that the state trial court’s decision to exclude evidence of the alleged sexual abuse clearly violated Mrs. Rockwell’s constitutional right to present a defense-and “[n]o reasonable jurist could conclude otherwise.”
The soundness of this proposition was not decided in the initial appeal to our court. The panel that heard the appeal vacated the judgment on the ground that the district court should not have reviewed a “mixed” petition containing an unex-hausted claim in addition to the exhausted claims. The case was remanded with a suggestion that the district court could reenter its original decision after allowing Mrs. Rockwell to dismiss her unexhausted claim. See Rockwell v. Yukins, 217 F.3d at 425.
On remand, this suggestion was accepted. Mrs. Rockwell moved for dismissal of her unexhausted claim and reentry of the habeas judgment, and the district court granted the motion. The warden has again appealed to our court, and we are now in a position to reach the merits of the case.
II
As amended by the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), Pub.L. No. 104-132, 110 Stat. 1214 (1996), subsection (d) of 28 U.S.C. § 2254 provides, in relevant part, as follows:
“(d) An application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a State court shall not be granted with respect to any claim that was adjudicated on the merits in State court proceedings unless the adjudication of the claim—
(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.... ”
This version of the statute applies to habe-as applications filed, as Mrs. Rockwell’s was, after April 24, 1996, the effective date of AEDPA. See Lindh v. Murphy, 521 U.S. 320, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997).
The statute means what it says. See Williams v. Taylor, 529 U.S. 362, 402-13, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). What the statute says, to repeat, is that habeas relief may not be granted unless the state court’s decision was either “contrary to ... clearly established federal law, as determined by the Supreme Court of the United States”3 or “involved an unreasonable application of ... [such] law.”
Mrs. Rockwell does not contend that the affirmance of her conviction by the state court of appeals was “contrary to” clear Supreme Court caselaw. She does contend, however, that it involved an unreasonable application of such law, on which account she claims entitlement to federal habeas relief.
For this contention to be sustained, Mrs. Rockwell needs to do more than persuade us that the Michigan judiciary’s application *511of federal law was incorrect. As Justice O’Connor said, speaking for the Court in Williams,
“In § 2254(d)(1), Congress specifically used the word ‘unreasonable,’ and not a term like ‘erroneous’ or ‘incorrect.’ Under § 2254(d)(l)’s ‘unreasonable application’ clause, then, 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’’ Williams, 529 U.S. at 411, 120 S.Ct. 1495 (emphasis supplied).
“[A]n unreasonable application of federal law is different from an incorrect or erroneous application of federal law.” Id. at 412, 120 S.Ct. 1495 (emphasis in original). And in making the “unreasonable application” inquiry, we “should ask whether the state court’s application of clearly established federal law was ‘objectively unreasonable.” Id. at 409, 120 S.Ct. 1495.
In Mrs. Rockwell’s case, as we have seen, the Michigan Court of Appeals concluded that the probative value of the evidence of Edward Rockwell’s alleged abuse of his sons was substantially outweighed by the danger of unfair prejudice that might ensue were the evidence to be admitted. This conclusion may or may not have been erroneous, but we cannot say that it represented an objectively unreasonable application of clearly established Supreme Court precedent.
A Supreme Court decision that the district court found “particularly instructive” is Davis v. Alaska, 415 U.S. 308, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974). The question presented there was whether, under the Confrontation Clause of the Sixth Amendment, the defendant in a burglary case — ■ petitioner Joshaway Davis — had a constitutional right to cross-examine a crucial witness for the prosecution about a juvenile burglary adjudication for which the witness was on probation. The purpose of the proposed cross-examination was to try to convince the jury that the witness had falsely fingered Joshaway Davis out of fear that otherwise the witness himself would be a suspect and his probation would be revoked. The Supreme Court held' that Davis had a constitutional right to confront the witness with questions along these lines.
“Cross-examination is ' the principal means by which the believability of a witness and the truth of his testimony are tested,” as the Davis Court explained. Against this background the Court concluded that “the jurors were entitled to have the benefit of the defense theory before them so that they could make an informed judgment as to the weight to place on [the juvenile’s] ■ testimony which provided ‘a crucial link in the proof ... of petitioner’s act.’ ” Id. at 316 and 317, 94 S.Ct. 1105 (citation omitted).
In the case at bar, by contrast, the evidence that Mr. Rockwell had abused his sons was being proffered to not show bias on the part of a crucial witness against Mrs. Rockwell, but to shore up Mrs. Rockwell’s own projected testimony about her “therapy.” The Michigan Court of Appeals recognized that the sexual abuse evidence was marginally relevánt, but the court concluded that its probative value was substantially outweighed by the danger of unfair prejudice — the danger that the jury would be tempted to acquit Mrs. Rockwell not because of any sense that she was innocent of conspiring with her sons to kill Mr. Rockwell, but because of a sense that killing would be too good for such a man. The court was concerned, in other words, that instead of using relevant evidence to reach a proper result under the written law, the jury might use the evi-*512denee to reach an improper result under the unwritten law. In striking the balance as it did the Michigan' court may or may not have erred, but we are not persuaded that it was applying Davis v. Alaska (or any other United States Supreme Court decision of which we are aware) in a way that could fairly be described as “objectively unreasonable.”
The constitutional right asserted by Mrs. Rockwell is not the Sixth Amendment right of confrontation, of course, but a Fifth Amendment due process right — the right to present a defense. As the district court properly acknowledged, the right to present a defense is not an unlimited right to present evidence without regard to reasonable evidentiary restrictions. On the contrary, the court pointed out, quoting from United States v. Scheffer, 523 U.S. 303, 308, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998), the Supreme Court has explicitly recognized that “[a] defendant’s interest in presenting ... evidence may [have to] bow to accommodate other legitimate interests in the criminal trial process.” It was not objectively unreasonable, in our view, for the Michigan court to conclude that “other legitimate interests in the criminal trial process” outweighed Mrs. Rockwell’s interest in buttressing her projected testimony with evidence of her husband’s despicable behavior.
What is controlling here is the familiar concept that the defendant in a criminal case “does not have an unfettered right to offer testimony that is incompetent, privileged, or otherwise inadmissible under standard rules of evidence.” Taylor v. Illinois, 484 U.S. 400, 410, 108 S.Ct. 646, 98 L.Ed.2d 798 (1988). Rather, she “must comply with established rules of procedure and evidence designed to assure both fairness and reliability in the ascertainment of guilt and innocence.” Chambers v. Mississippi, 410 U.S. 284, 302, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973). As the Supreme Court explained in Scheffer:
“state and federal rulemakers have broad latitude under the Constitution to establish rules excluding 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.’ ” Scheffer, 523 U.S. at 308, 118 S.Ct. 1261 (citations omitted).
The Constitution does, to be sure, “guarantee! ] 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 omitted) (emphasis supplied). That guarantee would have been violated here, no doubt, if the Michigan courts had prevented Mrs. Rockwell from introducing any testimony bearing on the circumstances under which the discussions with her sons were conducted. But that did not happen. The state trial court’s ruling did not bar Mrs. Rockwell from testifying that her sons hated their father. It did not bar her from explaining that the boys had been beaten and subjected to psychological abuse by the man they talked of killing.4 It did not bar her from *513telling the jury that she thought such talk was healthy; that she did not think it would lead to overt action; and that she had never been a party to any mutual understanding or agreement to- commit murder. Under these circumstances, in our- judgment, it was not unreasonable for the Michigan Court of Appeals to conclude that Mrs. Rockwell’s opportunity to present a complete defense was not unconstitutionally impaired.
The decision of the district court is REVERSED, and the case is REMANDED with instructions to dismiss the petition.
. Although the prosecution had cited Rule 404 in argument, the relevance of that rule in this context is not readily apparent. Rule 404 provides that, subject to a series of exceptions, evidence of a person’s character is not admissible for the purpose of proving that the person acted in conformity therewith on a particular occasion.
. Rule 403 — which had also been cited in argument before the state trial court — provides that relevant evidence may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice.
. The condition of this "contrary to” clause would be met if "the state court arrivefd] at a conclusion opposite to that reached by [the U.S. Supreme] Court on a question of law or if the state court decide[d] a case differently than [the U.S. Supreme Court has] on a set of materially indistinguishable facts.” Williams, 529 U.S. at 413, 120 S.Ct. 1495.
. By the sanie token, the ruling did not bar Mrs. Rockwell from simply testifying that the boys had an intense hatred of their father because of what he had done to them. Such a tack would have posed something of a dilemma for the prosecution. If the testimony had gone unchallenged', the jury might well have accepted it. If the prosecution had cross-examined Mrs. Rockwell as to what she meant, on the other hand, or if it had presented the husband as a witness and evoked a denial that he had done anything to cause the boys to hate him, the door would then have been opened, in all probability, for Mrs. Rockwell to present evidence of the alleged sexual misconduct.