This is an appeal from the denial of a petition for a writ of habeas corpus. Ralph Wallace, a Michigan prisoner serving a life sentence for first-degree murder, advances two arguments for issuance of the writ: first, that the trial court impaired his ability to present an insanity defense when it declined to order certain neurological tests, and, second, that he was denied effective assistance of counsel by sub-par performance on the part of his lawyer. The Michigan Supreme Court rejected these arguments on direct review of Mr. Wallace’s conviction. Because we conclude that the Michigan court’s decision did not represent an unreasonable application of federal law clearly established by United States Supreme Court — a prerequisite to habeas relief under 28 U.S.C. § 2254(d)(1) — we shall affirm the denial of the writ.
I
Mr. Wallace and his wife had a long history of marital difficulties. They were living separately on August 4, 1986, when they met at a tavern to discuss Wallace’s hope of taking their daughter on a fishing trip. Earlier that day Wallace had said, not for the first time, that he was going to kill his wife.
Mr. Wallace left work that afternoon feeling “rotten” about his wife and their pending divorce. Wallace — who had been treated for anxiety and depression and had a history of heavy drinking — took a prescription tranquilizer that he had obtained from a co-worker, drank “a couple” of beers at a pub, and, after going home, drank another beer or two. In his own estimation. Wallace was not intoxicated.
Mrs. Wallace telephoned him at home and asked to meet him to discuss the proposed fishing trip. Wallace agreed to meet her at the tavern. He had not carried a gun while at work or at the pub, but he took a revolver with him when he went to meet his wife.
As Mr. and Mrs. Wallace drank beer at the tavern, their conversation turned from the fishing trip to the custody battle and then to Mrs. Wallace’s sexual activity with another man. Wallace testified later that his wife began to appear larger than usual: “It looked like there was two of her real big on the wall in great big skirts moving back and forth.” He drew his revolver and shot her three times, aiming his third shot under the table after Mrs. Wallace had fallen to the floor. He then placed the gun on the bar, advised onlookers not to *91worry because “it’s only my wife,” and sat down to await the police. According to the officer who arrived on the scene first, Wallace did not appear to be intoxicated. A tavern patron who had witnessed the shooting testified to the same effect.
Mr. Wallace was charged with first-degree murder and felony use of a firearm. His defense was insanity. Pursuant to an order of the trial court, Wallace was examined on three occasions in February of 1987 by Rajendra Bhama, M.D., a psychiatrist who had treated Wallace in 1982 and 1988.
In March of 1987 Wallace moved the trial court to order certain neurological tests, arguing that they would assist Dr. Bhama in his evaluation. The court denied the motion, as it appeared that at least some of the requested tests had been performed recently by others. The court indicated that it would be willing to reconsider its ruling if Wallace could produce evidence that additional tests were still needed, but Wallace did not attempt to do so.
Dr. Bhama obtained the results of the recently performed tests, considered them in his evaluation, and discussed them in his eventual report. Just before trial the court confirmed with Wallace’s attorney that Dr. Bhama had received the neurological test results that he needed.
Dr. Bhama concluded that Wallace had suffered damage to the cortex of the brain, probably as a result of chronic alcohol abuse, and that he was psychotic. The doctor further concluded that Wallace was unable to recognize reality, to appreciate the wrongfulness of his actions, or to conform his actions to what was right. Dr. Bhama found, in other words, that Wallace was legally insane under Michigan law. See Mich. Comp. Laws § 768.21a(l).
A psychiatrist and a psychologist called by the prosecution testified that in their opinion Wallace was not mentally ill when he shot his wife. The jury found Wallace guilty on both of the charges against him, and the trial court sentenced him to life in prison without possibility of parole.
The Michigan Court of Appeals affirmed the convictions on direct review. The Michigan Supreme Court likewise affirmed. The Supreme Court held that Wallace had been prejudiced neither by the trial court’s refusal to order neurological testing nor by any errors made by Wallace’s trial attorney.
Wallace then sought a writ of habeas corpus from the United States District Court for the Eastern District of Michigan, arguing that he had been denied his due process right to present a complete defense and his right to effective assistance of counsel. The district court denied the petition, and this appeal followed.
II
Reviewing the district court’s decision de novo, see, e.g., Harpster v. Ohio, 128 F.3d 322, 326 (6th Cir.1997), cert. denied, 522 U.S. 1112, 118 S.Ct. 1044, 140 L.Ed.2d 109 (1998), we must decide whether the Michigan Supreme Court’s adjudication of Mr. Wallace’s due process and ineffective assistance claims “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). The threshold question, under § 2254(d)(1), is whether Wallace is claiming the benefit of a rule of law that had been “clearly established” before his conviction became final. See Williams v. Taylor, 529 U.S. 362, 390, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). As to Wallace’s claim that he was unconstitutionally denied neurological testing, we believe *92that the answer to this question must be “no.”
Mr. Wallace cites several U.S. Supreme Court cases standing for the broad proposition that a criminal defendant must have “a meaningful opportunity to present a complete defense.” Among these cases are California v. Trombetta, 467 U.S. 479, 485, 104 S.Ct. 2528, 81 L.Ed.2d 413 (1984), and Crane v. Kentucky, 476 U.S. 683, 690, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986). Wallace also relies on Ake v. Oklahoma, 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985), where the Supreme Court held that an indigent defendant whose sanity was legitimately at issue had to be provided with the assistance of a psychiatrist in preparing his defense. Ake, 470 U.S. at 74, 105 S.Ct. 1087. In none of these decisions, however, did the Supreme Court hold that an indigent defendant asserting an insanity defense must be furnished neurological testing in addition to the assistance of a psychiatrist.
Where warranted by the facts, we might be inclined to conclude that the right recognized in Ake extends logically to any diagnostic testing essential to the psychiatrist’s evaluation.1 But the United States Supreme Court — which, again, is the determiner of “clearly established Federal law” under § 2254(d)(1) — has not reached that conclusion. The absence of any Supreme Court decision on this point has been decried, indeed, by two justices who dissented from the denial of certiorari in Vickers v. Arizona, 497 U.S. 1033, 110 S.Ct. 3298, 111 L.Ed.2d 806 (1990). There the dissenting justices said that the Supreme Court should “decide whether the Constitution requires a State to provide an indigent defendant access to diagnostic testing necessary to prepare an effective defense based on his mental condition----” Id. at 1033. The dissenting justices surely would not have said this had the rule that Wallace seeks to apply here been “clearly established.”
Even if we believed that there is a “clearly established” rule requiring states to provide diagnostic tests when such tests are necéssary to an effective insanity defense, we could not say that the Michigan Supreme Court’s decision involved an “unreasonable application” of such a rule. 28 U.S.C. § 2254(d)(1).2 Dr. Bhama did have the benefit of neurological test results when he evaluated Wallace’s mental state, although the tests may not have been as comprehensive as he would have liked.3 Mr. Wallace did not attempt to demonstrate to the trial court that additional tests were necessary, despite the court’s invitation to do just that, and Wallace’s attorney assured the court immediately before trial that Dr. Bhama had received the test results that he needed. Most important, those results and the other available information were sufficient to allow Dr. Bhama to testify *93unequivocally that he believed Wallace to have been legally insane at the time of the shooting. In these circumstances it seems to us eminently reasonable to conclude that additional neurological tests were not necessary to an effective presentation of Wallace’s insanity defense.
Ill
In claiming that he was denied effective assistance of counsel, Mr. Wallace is plainly claiming the benefit of a rule of law that is “clearly established.” See Williams, 529 U.S. at 390, 120 S.Ct. 1495, where the Court noted that Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), governs ineffective assistance claims. The question before us. then, is whether the Michigan Supreme Court applied Strickland to the facts of Wallace’s ease in a manner that can be called “objectively unreasonable.” Williams, 529 U.S. at 409, 120 S.Ct. 1495.4 We do not think it did.
Under Strickland, Mr. Wallace’s claim could succeed only if he showed that his attorney’s performance “fell below an objective standard of reasonableness” and “that there is a reasonable probability that ... the result of the proceeding would have been different” but for his attorney’s errors. Strickland, 466 U.S. at 688, 694, 104 S.Ct. 2052. Absence of prejudice will thus defeat Wallace’s claim of ineffective assistance whether or not his attorney’s performance was deficient. See id. at 697, 104 S.Ct. 2052. It was reasonable, we believe, for the Michigan Court to conclude that any errors Wallace’s trial attorney may have committed failed to qualify as prejudicial under Strickland.
Mr. Wallace argues that his trial attorney erred by choosing not to request the following jury instruction:
“A person who is under the influence of voluntarily consumed alcohol or controlled substances at the time of the alleged offense is not for that reason alone to be judged legally insane. However, a person may be mentally ill and intoxicated with both conditions affecting his actions. It is for you to judge whether under all of the circumstances the defendant was mentally ill at the time of the events and then to apply the further test of whether or not the defendant was legally insane.”
We do not see a reasonable probability that the outcome of Wallace’s trial would have been different if this instruction had been given. Assuming that the jury understood the instruction to mean that intoxication can combine with mental illness to create legal insanity, there are at least two reasons for doubting that the jury would have found the instruction useful.
First, the evidence of intoxication was not strong. Wallace — who was accustomed to drinking heavily — testified that he had taken a tranquilizer earlier in the day and had consumed a maximum of five beers in the hours preceding the shooting. Two witnesses testified that Wallace appeared to be sober shortly after the shooting, and Wallace himself testified that he was sober just before going to meet his wife at the tavern.5
Second, the jury did not believe that Wallace was mentally ill. It was presented with the option of finding Wallace *94“guilty but mentally ill,” and it rejected that option.
Mr. Wallace argues that his attorney should have presented a defense of “diminished capacity” as an alternative to his insanity defense. At the time of Wallace’s trial, Michigan courts recognized a “diminished capacity” defense that “allow[ed] a defendant, even though legally sane, to offer evidence of some mental abnormality to negate the specific intent required to commit a particular crime.” People v. Carpenter, 464 Mich. 223, 627 N.W.2d 276, 280 (Mich.2001).6 In light of the overwhelming evidence that Wallace intended to kill his wife, we do not think it likely that such a defense would have helped him.
The jury heard testimony that Wallace had threatened in the past to kill Mrs. Wallace and that, just hours before the shooting, he had stated that “he was going to kill his wife.” Although Wallace did not ordinarily carry a gun, he brought a revolver with him to the meeting at the tavern. He shot his wife twice as they sat across from one another, and then, as Mrs. Wallace slumped to the floor, he got up, pointed his weapon under the table, and— in the words of one of the eyewitnesses— “took aim and fired again.” Wallace then assured the other patrons that they need not worry, as the victim was “only [his] wife.” Given these facts, and keeping in mind that the jury rejected a verdict of “guilty but mentally ill,” we believe there was little chance of the jury’s finding that a “mental abnormality” prevented Wallace from forming the intent to kill.
Mr. Wallace makes several additional complaints about his trial attorney’s performance, but we do not believe that the Michigan Supreme Court was required to find any of the alleged mistakes prejudicial under Strickland. For example, Wallace argues that his trial attorney erred by referring to Dr. Bhama’s diagnosis as “organic brain damage,” rather than “organic brain syndrome,” and erred as well by failing to provide Dr. Bhama with copies of police reports. We think it was well within the province of the Michigan Court to find that none of these errors (if they were errors) was so prejudicial as to “undermine confidence in the outcome” of Wallace’s trial. See Strickland, 466 U.S. at 694, 104 S.Ct. 2052.
AFFIRMED.
. See Walker v. Attorney General, 167 F.3d 1339, 1348 (10th Cir.), cert. denied, 528 U.S. 987, 120 S.Ct. 449, 145 L.Ed.2d 366 (1999), where, in a situation that did not involve § 2254(d)(1), the Tenth Circuit assumed that Ake compels a state to provide neurological testing in aid of a legitimate insanity defense.
. Wallace does not contend that the Michigan court's decision is “contrary to” clearly established law — a standard that is met only "if the state court arrives at a conclusion opposite to that reached by [the United States Supreme Court] on a question of law or if the state court decides a case differently than [the United States Supreme Court] has on a set of materially indistinguishable facts.” Williams, 529 U.S. at 405, 120 S.Ct. 1495.
. Dr. Bhama testified at trial that he "should have been allowed to have a neurological examination done in a more detailed manner” and that his diagnosis would have benefitted from further testing. In our view, this testimony does not render unreasonable a determination that Dr. Bhama was able to assist meaningfully in Wallace's defense.
. Again. Wallace has not argued that the Michigan court’s decision was "contrary to” clearly established law.
. According to Wallace’s trial attorney, Wallace “wasn't drunk that day [of the shooting]. And he said he wasn’t drunk that day. And other people said he wasn't drunk that day.” Although we dispose of Wallace's Strickland claim on the ground of lack of prejudice, we note that the attorney’s decision not to request an instruction on intoxication seems to *94have been perfectly reasonable in light of the facts.
. The Michigan Supreme Court has since determined that "diminished capacity" is not a viable defense in Michigan. See Carpenter, 627 N.W.2d at 283-84.