BOGGS, Circuit Judge.

Mario Collier was convicted by a state court jury of first-degree murder and sentenced to life imprisonment After exhausting his appeals, he filed a petition for a writ of habeas corpus. The district court denied his petition and granted a certificate of appealability on four issues: (1) whether the introduction of evidence of Collier's flight from the law was a denial of due process; (2) whether the prosecution's failure to produce a witness was a denial of due process; (3) whether Collier received ineffective assistance of counsel at the trial and appellate levels; and (4) whether the evidence was sufficient to convict him. We affirm.

I

At trial, it was established that Collier drove to a Detroit neighborhood in response to his younger brother's phone call that he and his friends were being harassed by a group of young men. Shortly after Collier's arrival, one of those young men was shot and killed. Two eyewitnesses testified that the driver of a Bonneville shot the victim, but neither got a clear enough look at the gunman to identify Collier. Collier's younger brother also testified that although he had not seen the actual shooting, he remembered that Collier had been in the driver's seat of the Bonneville immediately before the murder.

In addition to this evidence, the government also introduced graphic testimony, comprising several pages of transcript, that Collier fled from law enforcement several months after the murder. Christopher Dehn, a Detroit police officer, testified that he identified himself as an officer and then chased Collier when he did not surrender. According to this testimony, after Collier could no longer escape by running, he told Officer Dehn, "[y]ou're going to have to kill me," and then fought for control of the officer's gun. This evidence was admitted pursuant to Michigan's evidentiary rules, which allow the admission of flight evidence to show consciousness of guilt. See People v. Compeau, 244 Mich.App. 595, 625 N.W.2d 120, 123 (2001) (per curiam).

On December 7, 2000, the jury found Collier guilty of first-degree murder, and he was sentenced in January 2001 to mandatory life imprisonment. The Michigan Court of Appeals affirmed his conviction, and the Michigan Supreme Court denied his delayed application for leave to appeal. After a Michigan trial court denied his collateral motion for relief from judgment and leave to appeal was denied, Collier filed this petition under 28 U.S.C. § 2254. The district court held an evidentiary hearing, but ultimately dismissed the petition. Collier v. Lafler, No. 2:06-CV-10923, 2009 WL 909587 (E.D.Mich. Mar. 31, 2009). The court granted a certificate of appealability on four issues and Collier timely appealed.

II

Because Collier filed his petition after the effective date of the Antiterrorism and Effective Death Penalty Act (AEDPA), our review is governed by the provisions of 28 U.S.C. § 2254(d). In order to be successful, Collier must show that his claims, which were adjudicated on the merits in the Michigan courts:

(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 Supreme Court has clarified that a state court decision is "contrary to" clearly established federal law if it reaches a conclusion opposite to the Court on a question of law or decides a case differently "on a set of materially indistinguishable facts." Williams v. Taylor, 529 U.S. 362, 412-13, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). A state court's decision involves an "unreasonable application" when it "identifies the correct governing legal principle from [Supreme Court] decisions but unreasonably applies that principle to the facts of the prisoner's case." Id. at 413. In other words, the "state court's determination that a claim lacks merit precludes federal habeas relief so long as `fairminded jurists could disagree' on the correctness of the state court's decision." Harrington v. Richter, ___ U.S. ___, 131. S.Ct 770, 786, 178 L.Ed.2d 624 (2011) (quoting Yarborough v. Alvarado, 541 U.S. 652, 664, 124 S.Ct. 2140, 158 L.Ed.2d 938 (2004)). This is true even when the state court's decision is unaccompanied by any reasoning. Id. at 784.

Additionally, "[findings of fact made by a state court are presumed correct and can be contravened only where the habeas petitioner shows by clear and convincing evidence that the state court's factual findings were erroneous." Bugh v. Mitchell, 329 F.3d 496, 500 (6th Cir. 2003).

III

1. Introduction of evidence that Collier fled from the police

In his first claim, Collier argues that habeas relief is warranted because the prosecution introduced testimony of his flight and subsequent fight with an officer. Collier argues that the sensational character of the flight is so prejudicial that whatever small probative value the testimony might have is entirely outweighed. As a general matter, alleged errors in evidentiary rulings by a state court are not cognizable in federal habeas review. Coleman v. Mitchell, 244 F.3d 533, 542 (6th Cir. 2001). However, a federal court may grant relief in certain cases where the state's evidentiary ruling is so fundamentally unfair that it rises to the level of a due-process violation. Ibid.

Our cases have typically held that to show a due-process violation under AEDPA rooted in an evidentiary ruling, there must be a Supreme Court case establishing a due-process right with regard to that specific kind of evidence. See, e.g., Maldonado v. Wilson, 416 F.3d 470, 477 (6th Cir. 2005) ("The Ohio Court of Appeals' decision was not unreasonable under the AEDPA standard. The Supreme Court has never held that statements implying the results of a polygraph or similar test render the defendant's trial fundamentally unfair. . . ."). Indeed, it was for precisely this reason that we rejected an argument similar to Collier's regarding the introduction of "bad acts" evidence. See Bugh, 329 F.3d at 512 ("There is no clearly established Supreme Court precedent which holds that a state violates due process by permitting propensity evidence in the form of other bad acts evidence."). As we explained in Bugh, Estelle v. McGuire, 502 U.S. 62, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991), declined to find a due-process violation where evidence of prior bad acts was admitted. Ibid. And although the Supreme Court has questioned the probative value of "flight" evidence, see Wong Sun v. United States, 371 U.S. 471, 483 n. 10, 83 S.Ct. 407, 9 L.Ed.2d 441 (1963), it is permissible for Michigan to have evidentiary rules that allow introduction of such evidence.

However, Collier relies on our more recent decision in Ege v. Yukins, 485 F.3d 364 (6th Cir. 2007). In that case, we held that the question of whether an evidentiary ruling violated the Due Process Clause was governed by more general Supreme Court precedent:

These principles [that the admission of prejudical evidence may constitute a denial of fundamental fairness] have their roots in the Supreme Court decision of Chambers v. Mississippi 410 U.S. 284, 302-03, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973), which held that trial errors cannot "defeat the ends of justice" or otherwise deprive a defendant of her right to a fair trial. In Chambers, the Court was looking at a state trial court's improper exclusion of certain evidence that would potentially have assisted the defendant, but its tenets are equally applicable to situations involving a state trial court's improper admission of certain evidence injurious to the defendant. The ultimate question is therefore whether the state habeas court, in finding that admission of Dr. Warnick's testimony was not prejudicial to the ultimate outcome of Ege's case, unreasonably applied Chambers.

485 F.3d at 375 (emphasis omitted). Even under Chambers, however, Collier cannot show that any error in admitting the officer's testimony was so prejudicial that it fundamentally undermined his right to a fair trial.

Undoubtedly, Officer Dehn's testimony was prejudicial to some extent. However, even assuming that the evidence was improperly admitted, Collier must show that its inclusion amounted to a due-process violation. As we noted in Ege, "`[w]hether the admission of prejudicial evidence constitutes a denial of fundamental fairness turns upon whether the evidence is material in the sense of a crucial, critica[l] highly significant factor.'" Ibid., (quoting Brown v. O'Dea, 227 F.3d 642, 645 (6th Cir. 2000)). In that case, we found that the improper inclusion of bite-mark evidence amounted to a denial of due process because it was the only physical evidence linking the defendant to the crime. Id. at 376-78. In this case, by contrast, the evidence in question was peripheral to the case against Collier. Two eyewitnesses established that the driver of the Bonneville was the shooter, and Collier's own brother testified that Collier had been driving the Bonneville at the time of the murder. These witnesses were the belt and suspenders of the prosecution. Officer Dehn's testimony was only trimming. Even if the flight evidence was improper, it did not render Collier's trial fundamentally unfair.

2. The prosecution's failure to produce a witness

Alfin Thibodeaux was another eyewitness to the murder. Although the prosecution indicated its intent to call him, he disappeared and was never put on the witness stand. In a statement given to the police before trial, Thibodeaux described his recollection of events on the night of the murder: "One guy got out of one of the cars and into the first car. He was carrying the gun. The first car rode past us and pulled up to [the victim] and started shooting." When asked, "[w]hen the guy with the gun got out of the car and into the second car, where did he sit?" Thibodeaux responded, "I think the front passenger seat." Thus, Collier argues that Thibodeaux's testimony would have produced reasonable doubt as to whether the driver of the Bonneville was the murderer.

Under Michigan law, the prosecutor was obligated to produce Thibodeaux, see People v. Wolford, 189 Mich.App. 478, 473 N.W.2d 767, 770 (1991) (per curiam), unless he could not be produced in the exercise of due diligence, see People v. Canales, 243 Mich.App. 571, 624 N.W.2d 439, 442 (2000). The Michigan Court of Appeals found that the government had exercised due diligence, and accordingly denied Collier relief on this claim.

Michigan's requirement that prosecutors produce res gestae witnesses is a matter of state law, and its enforcement is outside the scope of our review. We have rejected on that basis claims raised under this very state requirement. See, e.g., Atkins v. Foltz, No. 87-1341, 1988 WL 87710, at *2 (6th Cir. Aug.24, 1988) (per curiam) ("[Although Michigan law requires the production of all res gestae witnesses, this court cannot hear state claims on petition for writ of habeas corpus. . . ." (internal citation omitted)). Wisely then, Collier does not rest on the text of the rule itself. Instead, he relies on a defendant's more general right to call witnesses on his behalf. See, e.g., Taylor v. Illinois, 484 U.S. 400, 409, 108 S.Ct. 646, 98 L.Ed.2d 798 (1988) ("The right of the defendant to present evidence stands on no lesser footing than the other Sixth Amendment rights that we have previously held applicable to the States." (internal quotation marks omitted)). However, Collier appears to have no argument that the prosecution impeded him from calling Thibodeaux or that the court excluded his testimony. Rather, Thibodeaux could not be found, despite substantial efforts on the part of the government. Thus, Collier's right to present a defense was not curtailed, and the more specific question of whether the prosecutor exercised "due diligence" is outside the scope of our AEDPA review.

3. Ineffective assistance of counsel

As an initial matter, the parties dispute what standard of review governs this issue. Collier asserts that because evidence was presented in the district court that was not presented to the Michigan courts, the panel should review this claim de novo. See Brown v. Smith, 551 F.3d 424, 429 (6th Cir. 2008) (holding that de novo is the proper standard of review "whenever new, substantial evidence supporting a habeas claim comes to light during the proceedings in federal district court"). However, we need not decide whether Collier's newly presented evidence warrants a less deferential review. His ineffective-assistance-of-counsel claims fail under any standard.

Collier first argues that his trial counsel rendered ineffective assistance by not introducing evidence that Collier was violating his parole on the night Officer Dehn chased him — claiming that this evidence would have shown a separate motive for wanting to elude the police. We disagree. Counsel is ineffective only where performance is deficient and prejudice to the defendant ensues. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). "A fair assessment of attorney performance requires that every effort be made to eliminate the distorting effects of hindsight, to reconstruct the circumstances of counsel's challenged conduct, and to evaluate the conduct from counsel's perspective at the time." Id. at 689, 104 S.Ct. 2052. Collier's trial counsel was not deficient for failing to present evidence that Collier violated his parole because that evidence would have been detrimental to his defense. It could have led the jury to speculate that Collier was a serial lawbreaker or wonder whether he broke parole to escape prosecution for the murder. Further, the jury might have questioned whether a parole violation fully explains the desperation with which Collier fought Officer Dehn. The decision not to use this evidence therefore constitutes reasonable trial strategy.

Collier also argues that his trial counsel rendered ineffective assistance in dealing with Thibodeaux's unexpected absence, specifically by failing to ensure that the trial court "take appropriate measures to ensure his presence" and by not "ask[ing] for an adjournment until Thibodeaux could be produced." Appellant's Br. at 41. Here again, however, performance was not deficient. Thibodeaux was a government witness. Nonetheless, Collier points to one line in Thibodeaux's police statement as proof that the testimony would actually have favored the defense. In this statement, Thibodeaux describes a man with a gun enter the Bonneville and when asked where the man sat, he responds, " I think the front passenger seat" (emphasis added). It would be reasonable to fear that Thibodeaux might have admitted at trial that he was not sure which side of the car the man with the gun entered. Defense counsel therefore had to make a judgment call: was the benefit of this uncertain statement outweighed by the risk of Thibodeaux's potentially inculpatory eyewitness account? In deciding not to pursue this testimony, trial counsel actually chose to capitalize on Thibodeaux's absence in his closing argument: "[I]t's interesting because the prosecutor's opening talked about the people he's going to bring in. But the one person he didn't bring in . . . is Mr. Alfih Thibodeaux." Given the uncertainty regarding Thibodeaux's testimony, this may have been the best tactical course for the defense. For this reason, we cannot say that trial counsel performed deficiently in proceeding without the testimony.

Collier also asserts that his counsel was deficient for failing to object to Officer Dehn's testimony and failing to move to suppress the testimony as the fruit of an illegal arrest. However, as we have already explained, the testimony of Officer Dehn was relatively unimportant to the prosecution's case. As such, there is no "reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." Strickland, 466 U.S. at 694, 104 S.Ct. 2052. Because Collier has failed to establish prejudice on this claim, it also fails.

Finally, Collier argues that his appellate counsel was ineffective for failing to raise an ineffective-assistance-of-counsel claim on direct review. Because we have determined that trial counsel was not ineffective, however, appellate counsel's performance was not deficient.

4. Insufficiency of the evidence

Collier's final claim is that the evidence was insufficient to convict him of first-degree murder. To determine whether the evidence is sufficient to support a guilty verdict, the reviewing court must determine whether, "after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979). Because this issue was decided on the merits by the Michigan Court of Appeals, Collier must overcome another layer of deference by showing that the state court's adjudication of the issue was an unreasonable application of Supreme Court precedent. He cannot meet this burden.

The evidence in this case is sufficient to show the elements of first-degree murder. Under Michigan law, the prosecution was required to show "(1) an intentional killing of a human being (2) with premeditation and deliberation." People v. Gayheart, 285 Mich.App. 202, 776 N.W.2d 330, 336 (2009), appeal denied, 486 Mich. 957, 782 N.W.2d 207 (2010). Collier asserts that there was not enough evidence to establish that he fired the gun or that he did so with premeditation. However, the following evidence was adduced at trial: Collier arrived on the scene in response to a phone call from his younger brother that he and his friends were being harassed, two eyewitnesses testified that the driver of the Bonneville fired the shots, and Collier's brother testified that Collier was driving the Bonneville. Even allowing for some discrepancies in the witnesses' testimony and excluding all other evidence, these submissions were enough for a rational trier of fact to find that Collier was the gunman and that the killing was premeditated.

IV

For these reasons, the district court's judgment is AFFIRMED and the petition for a writ of habeas corpus is DENIED.