Following a jury trial in the Circuit Court of Milwaukee County, Wisconsin, petitioner Major Burrus was found guilty of first degree murder and first degree sexual assault. Burrus appealed to the Wisconsin Court of Appeals, which affirmed the conviction. Though the court of appeals determined that the trial court had erred in refusing to permit Burrus to introduce certain psychiatric testimony, the court found the error to be harmless beyond a reasonable doubt. After the Wisconsin Supreme Court denied Burrus’s petition for review, Burrus filed a petition for a writ of habeas corpus in the district court. The district court, finding no federal constitutional error, denied the writ. We affirm.
I.
The essential facts underlying the charges against Burrus are undisputed. The Wisconsin Court of Appeals summarized them as follows:
On the night of August 1, 1981, Burrus’s wife held a surprise birthday party for him at their home. Burrus arrived home at approximately 6:15 p.m. There was testimony that Burrus was drinking gin, whiskey and beer and smoking marijuana between approximately 6:30 and 8:30 p.m. There was testimony that Burrus was not drinking and appeared sober between approximately 9:00 and 11:00 p.m. One of the guests at the party was Anna Marie Weis (Weis). At approximately 11:30 p.m., Burrus and Weis went to the basement of the Burrus home. While in the basement, Burrus sexually assaulted and killed Weis. There was also uncontradicted testimony that Burrus appeared sober after the killing.
State v. Burrus, No. 82-576-CR, slip op. at 2-3 (Wis.Ct.App. Nov. 10, 1982 [109 Wis.2d 698, 327 N.W.2d 724 (table)]).
At trial, Burrus raised a defense of intoxication. Under Wisconsin law, intoxication is a defense if it “[negatives the existence of a state of mind essential to the crime.” Wis.Stat. § 939.42. Burrus contended that he was too intoxicated at the time of the killing to form the requisite specific intent for first degree murder. The prosecution countered with evidence that Burrus appeared sober shortly after the killing. In response to this evidence, Burrus sought to introduce a psychiatrist, Dr. Basil Jackson, to testify on the sobering effects of trauma. As defense counsel stated in his offer of proof to the trial court:
Dr. Jackson could, based on his experience in treating alcoholics and people who commit certain acts under the influence of intoxicants and drugs, testify that it is usual and typical for such persons who are involved in a traumatic experience — and he mentioned one, a car accident — who have been drinking heavily to, in effect, sober up and to behave as though they are not under the influence of any drugs or alcohol.
The trial court sustained the prosecution’s objection to the proposed testimony. Rea*580soning that Dr. Jackson was no more qualified than a lay person on the question of whether a traumatic incident may cause an intoxicated person to sober up, the trial court ruled the proposed expert testimony inadmissible. “The gloss of an expert title being attached to such an opinion simply is not justified based on the offer of proof submitted,” the court concluded.
At the close of the evidence, the trial court instructed the jury on the elements of the defense of intoxication.2 Defense counsel was allowed to argue his theory of the sobering effect of trauma to the jury, and he did so. “[Bjased on your experience and your knowledge as people in our society,” he submitted, “you know that when you have been drinking if you see a shocking incident — if I have an accident, if a friend of yours gets hurt that the mood you’re in changes dramatically____ That you’re shocked into sobriety.”
On appeal to the Wisconsin Court of Appeals, Burrus maintained that his constitutional right to present a defense was violated by the exclusion of Dr. Jackson’s testimony. The court of appeals disagreed. Though the testimony was admissible under Wisconsin Rule of Evidence 907.02,3 the court found, its submission to the jury could not have affected the outcome of the case. Burrus was not prevented from raising the defense of intoxication or from arguing his theory of defense to the jury. Moreover, the court concluded, the evidence of Burrus’s consumption of drugs and alcohol prior to the killing was “at best vague, contradictory and inconclusive,” whereas evidence of his post-killing sobriety was “clear and uncontradictory.” State v. Burrus, No. 82-576-CR, slip op. at 4-5 (Wis.Ct.App. Nov. 10, 1982 [109 Wis.2d 698, 327 N.W.2d 724 (table)]).
The district court, in denying Burrus’s petition for writ of habeas corpus, accepted the determination of the Wisconsin Court of Appeals that Dr. Jackson’s proffered testimony was admissible under Wisconsin law. Proceeding to the constitutional question, the district court found that Burrus’s fundamental right to a fair trial had not been violated. Burrus v. Israel, No. 83-C-133, slip op. (E.D.Wis. April 24, 1985).
II.
We begin with several well-established principles regarding habeas corpus jurisdiction under 28 U.S.C. § 2254. A federal court may not grant habeas relief to a petitioner in state custody unless the custody violates federal statutory or constitutional law. Mosley v. Moran, 798 F.2d 182, 185 (7th Cir.1986). “Federal courts hold no supervisory authority over state judicial proceedings and may intervene only to correct wrongs of constitutional dimension.” Smith v. Phillips, 455 U.S. 209, 221, 102 S.Ct. 940, 948, 71 L.Ed.2d 78 (1982). Ordinarily, an evidentiary error in the state courts will not rise to the level of a constitutional violation. As this court has ex*581plained, “Because the admissibility of evidence in state court is a matter of state law, evidentiary questions are not subject to federal review under § 2254 unless there is a resultant denial of fundamental fairness or the denial of a specific constitutional right.” United States ex rel. DiGiacomo v. Franzen, 680 F.2d 515, 517 (7th Cir.1982).
Burrus contends that the trial court’s ruling excluding Dr. Jackson’s testimony denied him his federally-protected right to a fundamentally fair trial. To decide this question, we need not consider the correctness of the trial court’s ruling as a matter of Wisconsin evidence law. As the district court recognized, and as all parties to this appeal agree, we are bound by the Wisconsin Court of Appeals’ interpretation of state law. The only question we need decide is whether Burrus suffered a deprivation of any right protected by the fourteenth amendment.
It is true that an accused has a fundamental right to present witnesses in his own defense. See, e.g., Chambers v. Mississippi, 410 U.S. 284, 302, 93 S.Ct. 1038, 1049, 35 L.Ed.2d 297 (1973); Washington v. Texas, 388 U.S. 14, 19, 87 S.Ct. 1920, 1923, 18 L.Ed.2d 1019 (1967). Unlike the situation in Chambers and Washington, however, the exclusion of Dr. Jackson’s testimony did not prevent Burrus from presenting his theory of defense. To the contrary, Burrus’s counsel was permitted to argue to the jury that the killing, in effect, shocked Burrus into sobriety. Though the jurors were not persuaded, we are satisfied that they would not have reached a different verdict had they been exposed to Dr. Jackson’s testimony.
The fourteenth amendment’s guarantee of fundamental fairness in criminal proceedings does not require a trial court to permit any proposed defense expert to take the stand. In this case, the prosecution did not produce an expert, necessitating a defense rebuttal. The court thoroughly instructed the jury on the defense of intoxication. There was overwhelming evidence from which the jury could find Burrus capable of forming a specific intent at the time of the killing. Under these circumstances, we cannot say that the exclusion of Dr. Jackson’s testimony was so arbitrary or irrational as to deny Burrus due process.
For the reasons stated, the district court’s judgment denying Burrus’s petition for writ of habeas corpus is
Affirmed.
. The jury was instructed as follows:
The defense of intoxication is an issue in this case. The Criminal Code of Wisconsin provides that an intoxicated condition is a defense if such condition negatives the existence of a state of mind essential to the crime. Ordinarily, intoxication will not relieve a person from responsibility for his criminal acts. However, where a certain state of mind or intent is an essential element of the crime, an accused is not guilty if at the time of the commission of the alleged criminal act he was so intoxicated that he was unable to form the essential intent or have the essential mental state.
In this case, the defendant is charged with the crime of first degree murder, of which one of the essential elements is the intent to kill. The defendant claims that at the time of the alleged offense his condition from the use of intoxicating liquor and drugs was such that he did not form such intent. If the defendant, because of his condition, was incapable of forming and therefore did not form the intent to kill, then you must not find him guilty of first degree murder as charged in the Information. If you have any reasonable doubt as to whether or not he was so intoxicated, you must give the defendant the benefit of that doubt and find him not guilty of first degree murder. This defense does not apply to the lesser included offense of second degree murder.
. Rule 907.02 provides:
If scientific, technical, or other specialized knowledge will assist the trier of fact to understand the evidence or to determine a fact in issue, a witness qualified as an expert by knowledge, skill, experience, training, or education, may testify thereto in the form of an opinion or otherwise.
Wis.Stat. § 907.02.