BOGGS, J., delivered the opinion of the court, in which GILMAN, J., joined and CLAY, J., joined in the result. CLAY, J. (pp. 677-78), delivered a separate opinion concurring in the judgment.
OPINION
BOGGS, Circuit Judge.Angelo McMullan appeals the district court’s denial of his petition for a writ of habeas corpus. A Michigan jury convicted McMullan, inter alia, of second-degree murder. McMullan presents three grounds for habeas relief: (1) the state trial court unreasonably declined to give the jury an involuntary-manslaughter instruction; (2) trial counsel rendered ineffective assistance; and (3) the state unlawfully withheld exculpatory evidence. The district court denied McMullaris petition. For the reasons set out below, we affirm the district-court judgment.
I
A
McMullan and Jimmy “Butch” Smith were friends of thirty years and were related by marriage. The two men were drug addicts and regularly used and shared drugs.
On July 6, 2001, McMullan and his wife were attending a party at the apartment of Willie Henry Russell, Jr., a friend of McMullaris. Smith, who was not at the party, was angry because he believed that McMullan had sold him Vicodin pills that were fake. Smith sought a refund from McMullan. Smith, accompanied by his friend Gregory McDowell, drove to Russell’s apartment to find McMullan. Smith retrieved McMullan from the party, and both men returned to Smith’s car in the parking lot.
Inside the car, McMullan smoked some of his crack cocaine with Smith. McMul-lan also handed Smith some additional crack cocaine. In response to McMullaris request for payment for the crack, Smith threw McMullan the bottle of purportedly fake Vicodin pills that McMullan had sold him and refused to pay for the crack.
A fistfight ensued in the parking lot. During the fight, McMullan snatched a revolver from his wife, who was standing *665nearby. MeMullan pointed the gun one foot from Smith’s chest. The gun fired, and Smith was shot. Smith later died from the gunshot wound to the chest.
The State of Michigan charged McMul-lan with first-degree murder. Both MeMullan and McDowell testified at trial, and their testimony differed in several respects. MeMullan testified that at the time he grabbed the revolver from his wife, she was three-to-four feet from him; McDowell testified that she was fifteen-to-thirty feet away from MeMullan. McDowell also testified that, immediately before MeMullan shot Smith, MeMullan pushed Smith down into the driver’s seat of Smith’s car; MeMullan testified that he did not push Smith. MeMullan also testified that he did not recall aiming the gun, cocking the gun, and shooting Smith; MeMullan testified that he only intended to scare Smith with the gun and did not intend to shoot him. McDowell testified that immediately after Smith was shot, MeMullan grabbed cash from Smith’s pockets; MeMullan denied this.
At the time McDowell testified, he had a pending cocaine-possession charge. Because McDowell had denied ever using crack cocaine at a preliminary hearing, McMullan’s counsel sought to cross-examine him about the charge in order to impeach McDowell’s credibility. The trial court denied this request.
At the close of all evidence, the trial court instructed the jury not only on first-degree murder but also on second-degree murder and voluntary manslaughter. McMullan’s counsel requested an involuntary-manslaughter instruction, which the trial court considered and denied.
On January 25, 2002, the jury convicted MeMullan of second-degree murder, under Mich. Comp. Laws. § 750.317; possession of a firearm during the commission of a felony, under § 750.227b; and being a felon in possession of a firearm, under § 750.224f. The court found MeMullan to be a fourth-felony habitual offender, under § 769.12.
That same day, the trial court in McDowell’s case granted the government’s motion to downgrade McDowell’s cocaine charge from a felony to a misdemeanor. As part of this plea bargain, McDowell agreed to testify as needed against MeMullan.
On February 21, 2002, at McMullan’s sentencing, McMullan’s counsel sought permission to file a motion for a new trial because of McDowell’s plea deal. The prosecutor, Kennan M. DeWitt, told the court that “there was absolutely no connection between Mr. McDowell’s case [and McMullan’s case] either in facts or procedure .... There was no consideration given to McDowell connected to this case.... [McDowell’s plea] had nothing to do with this case.”
B
On appeal to the Michigan Court of Appeals, MeMullan argued that the trial court erred in declining to provide the involuntary-manslaughter instruction; that his trial counsel was ineffective for failing to cross-examine McDowell about the plea bargain; and that the government engaged in misconduct by failing to disclose the plea agreement. The Court of Appeals affirmed, with one judge dissenting from the panel’s conclusion that the trial court did not err in declining to give the involuntary-manslaughter instruction. See People v. McMullan, 284 Mich.App. 149, 771 N.W.2d 810, 813 (2009).
The Michigan Supreme Court granted leave to appeal on the sole issue of whether the involuntary-manslaughter instruction was warranted, People v. McMullan, 485 Mich. 1050, 777 N.W.2d 139, 140 *666(2010), and that court affirmed, People v. McMullan, 488 Mich. 922, 789 N.W.2d 857, 857 (2010). The Supreme Court held that, under Michigan law, a trial court should instruct a jury on involuntary manslaughter when a “rational view of the evidence” supports the instruction. Id. at 858. The court ruled 5-2 that a rational view of the evidence, “even absent [disputed] questions of fact,” did not support an involuntary-manslaughter instruction. Ibid. Specifically, the Supreme Court noted that McMullan did not “dispute that the gun was in his hand when it was cocked and fired” and that “the firearm had to be specifically cocked in order to fire.” Ibid.
Proceeding pro se, McMullan petitioned the district court for a writ of habeas corpus, seeking relief on the same three grounds as in his direct appeal. The district court denied the petition. See McMullan v. Booker, 2012 WL 603990, at *10 (E.D.Mich. Feb. 24, 2012). Because two Michigan Supreme Court justices would have reversed McMullan’s conviction for failure to provide the involuntary-manslaughter instruction, the district court granted McMullan a certificate of appeala-bility for that claim. Id. at *9. McMullan timely appealed, and we subsequently expanded the certificate of appealability to include all McMullan’s claims and appointed McMullan counsel on appeal. We now affirm.
II
Habeas relief is available to McMullan “only on the ground that [a prisoner] is in custody in violation of the Constitution or laws or treaties of the United States.” 28 U.S.C. § 2254(a). A court may not grant a habeas petition for “any claim that was adjudicated on the merits in State court proceedings” unless the state proceedings:
(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.
§ 2254(d). The “unreasonable application” clause authorizes federal courts to grant the writ when a “state-court decision unreasonably applies the law of [the Supreme Court] to the facts of a prisoner’s case.” Williams v. Taylor, 529 U.S. 362, 409, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). For a federal court to grant habeas relief, the state-court application of federal law must be “objectively unreasonable.” Ibid.
On habeas review, we examine a district court’s legal conclusions de novo. Davis v. Lafler, 658 F.3d 525, 530 (6th Cir.2011) (en banc).
Ill
Á. Involuntary-Manslaughter Instruction
McMullan contends that the state trial court erred in refusing to instruct the jury on involuntary manslaughter, and he argues that he is entitled to habeas relief under both § 2254(d)(1) and § 2254(d)(2).
1. § 2254(d)(1)
First, McMullan claims that the state court’s refusal to instruct the jury on involuntary manslaughter violated the Due Process Clause of the Fourteenth Amendment. This claim fails because McMullan cannot point to any “clearly established [fjederal law” requiring a trial court to instruct the jury on a lesser included offense in a non-capital case. § 2254(d)(1).
Instructing a jury on a lesser offense benefits the prosecution because it can afford the state a conviction when the *667evidence cannot establish the crime charged or when the jury is reluctant to convict on the harshest charge; this practice also benefits the defendant in that “it affords the jury a less drastic alternative than the choice between conviction of the offense charged and acquittal.” Beck v. Alabama, 447 U.S. 625, 633, 100 S.Ct. 2382, 65 L.Ed.2d 392 (1980). A lesser-ineluded-offense instruction provides the jury with a valuable “third option.” Id. at 634, 100 S.Ct. 2382. For this reason, Michigan, like a number of other states, requires a trial judge to instruct on a lesser included offense if a rational view of the evidence supports the instruction. People v. Cornell, 466 Mich. 335, 646 N.W.2d 127, 139 (2002); see Beck, 447 U.S. at 636 n. 12, 100 S.Ct. 2382 (collecting state eases). In homicide cases, Michigan requires an involuntary-manslaughter instruction if a rational view of the evidence supports the instruction. People v. Mendoza, 468 Mich. 527, 664 N.W.2d 685, 693 (2003). The corollary is that a trial court need not instruct on involuntary manslaughter when a rational view of the evidence does not support the instruction. See People v. Gillis, 474 Mich. 105, 712 N.W.2d 419, 439 (2006).
Federal courts may grant habeas relief only on the basis of federal law that has been clearly established by the Supreme Court. § 2254(d)(1). The Supreme Court, however, has never held that the Due Process Clause requires instructing the jury on a lesser included offense in a non-capital case. See Beck, 447 U.S. at 638 n. 14, 100 S.Ct. 2382. Simply put, “the Constitution does not require a lesser-included offense instruction in non-capital cases.” Campbell v. Coyle, 260 F.3d 531, 541 (6th Cir.2001) (citing Bagby v. Sowders, 894 F.2d 792, 795-97 (6th Cir.1990) (en banc)). What is determinative, at any rate, is that the Supreme Court has never so held.
Here, Michigan charged McMullan with first-degree murder. The trial court instructed the jury on second-degree murder and voluntary manslaughter, and it declined to instruct the jury on involuntary manslaughter. The jury convicted McMul-lan of second-degree murder. Habeas relief is available to McMullan only “on the ground that he is in custody in violation of the Constitution or laws or treaties of the United States.” § 2254(a). Because the Supreme Court has never held that due process requires lesser-included-offense instructions in a non-capital case, McMul-lan’s claim rests on no such federal ground. Therefore, his claim fails.
2. § 2254(d)(2)
a. Relevant Background
On appeal, McMullan argues that he is entitled to relief also under § 2254(d)(2), the statute’s “unreasonable determination of the facts” clause. This clause permits federal courts to grant a habeas petition when a state-court decision “was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” § 2254(d)(2). The State of Michigan asserts that McMul-lan’s § 2254(d)(2) argument constitutes an improper attempt to amend his habeas petition on appeal. McMullan responds that his petition should be read to encompass a § 2254(d)(2) claim because he filed it as a pro se litigant.1 We need not resolve whether McMullan’s petition properly raises a § 2254(d)(2) claim; McMul-lan’s claim fails under § 2254(d)(2) because the trial court’s decision to withhold an involuntary-manslaughter instruction did not rest on an unreasonable determination of fact.
*668Michigan, like other states, distinguishes between murder and involuntary manslaughter. Under Michigan law, a homicide committed with the mens rea of malice is murder. Gillis, 712 N.W.2d at 438. A homicide committed with the lesser mens rea of gross negligence or an intent only to injure is involuntary manslaughter. Ibid. The state establishes malice by showing that the accused had: an intent to kill, an intent to commit great bodily harm, or an intent to create a very high risk of death or great bodily harm with knowledge that death or great bodily harm was the probable result. Ibid.
At McMullan’s trial, the prosecutor objected to instructing the jury on both voluntary manslaughter and involuntary manslaughter. The court indicated that the voluntary-manslaughter instruction was necessary but that the court was undecided about the involuntary-manslaughter instruction. Ibid. The court asked McMullan’s counsel why it should give an involuntary-manslaughter instruction. Ibid. McMullan’s counsel replied:
[McMullan] doesn’t recall [the gun] being discharged. He doesn’t recall cocking it back. He recalls the door being pushed back and forth when the gun was discharged. Holding a gun in front of another person I think may rise to the level of [ ] gross negligence, and [ ] there was testimony from Mr. McMullan that he did not intend to kill.
Ibid. The court listened to this evidence and ultimately determined that malice existed. The court found it relevant that McMullan shot Smith during a fight. Id. at 1150. In addition, the court reasoned that “when a gun is pointed a foot or so away from a person’s chest, that sounds pretty intentional.” Ibid. There is no basis in the record to conclude that the trial court disregarded the evidence cited by McMullan’s counsel.
The Michigan Court of Appeals, reviewing the record de novo, determined that a rational view of the evidence did not support an involuntary-manslaughter instruction. McMullan, 771 N.W.2d at 813. Again reviewing all the evidence presented at trial, the Michigan Supreme Court found that “the facts inescapably show that defendant acted with malice because, at a minimum, he intended to do an act in wanton and willful disregard of the likelihood that the natural tendency of his behavior [was] to cause death or great bodily harm.” McMullan, 789 N.W.2d at 858 (internal quotation marks and alterations omitted). The court specifically found that the evidence did not show mere gross negligence or intent to injure, the two ways of establishing the mental element for involuntary manslaughter. Ibid.
b. McMullan’s Jury-Trial Argument
We owe “considerable deference” to state courts in the “application of their own law.” Bagby, 894 F.2d at 794. “That is because where, as here, the highest court of a state has reviewed a defendant’s request for a lesser included offense instruction and concluded that it is not warranted by the evidence elicited at trial, that conclusion is axiomatically correct, as a matter of state law.” Id. at 795. Even if the trial court erred as a matter of state law, we emphasize that “it is not the function of a federal habeas court to correct errors in state law.” Id. at 795. When reviewing a state-court judgment, we do not act as a super state appellate court. Payne v. Janasz, 711 F.2d 1305, 1310 (6th Cir.1983).
Both parties agree that a court may grant habeas relief “only on the ground” that a defendant’s custody violates clearly established federal law. § 2254(a); see Resp’t Br. 22; Reply Br. 9. The Supreme Court has clarified that § 2254(d)(2) func*669tions to allow “habeas petitioners to avoid the bar to habeas relief imposed with respect to federal claims adjudicated on the merits in state court by showing that the state court’s decision was based on an unreasonable determination of the facts.... ” Wilson v. Corcoran, 562 U.S. 1, 131 S.Ct. 13, 16-17, 178 L.Ed.2d 276 (2010) (internal quotation marks omitted) (emphasis added).
The federal law that McMullan invokes is the Sixth Amendment’s jury-trial right. See Pet’r Br. 13; Reply Br. 9. It is true that the Sixth Amendment affords criminal defendants the right to trial by jury. It also true that this right includes “the right to have the jury, rather than the judge, reach the requisite finding of ‘guilty.’ ” Sullivan v. Louisiana, 508 U.S. 275, 277, 113 S.Ct. 2078, 124 L.Ed.2d 182 (1993). What that means, though, is that a judge “may not direct a verdict for the State, no matter how overwhelming the evidence.” Ibid, (holding that the giving of a constitutionally deficient reasonable-doubt instruction is a structural error). The jury-trial right does not prohibit judges from declining jury instructions on lesser included offenses in non-capital cases.2
McMullan relies on Reed v. Quarterman, 504 F.3d 465 (5th Cir.2007), in support of the proposition that we should ask whether the trial court based its denial of the jury instruction on a view of the facts that a rational jury could have rejected. Reed was a capital case where the defendant sought a jury instruction on a lesser included non-capital offense. Id. at *670488-89. McMullan asserts that the distinction between a capital and non-capital case is “potentially relevant” only to a § 2254(d)(1) analysis. Reply Br. 9 n. 1. We cannot agree. The fact that the capital/non-eapital offense distinction is relevant, under Beck, to a § 2254(d)(1) analysis does not make it relevant “only” to § 2254(d)(1). In addition, the Reed standard was applied in the course of granting a certificate of appealability — not a writ of habeas corpus. We note that in Michigan, “the use of a deadly weapon” alone can establish the requisite malice for murder. People v. Bulls, 262 Mich.App. 618, 687 N.W.2d 159, 165 (2004). Here, no one disputes that McMullan used a deadly weapon.
McMullan is also correct that, as a general matter, a trial court that “dictate[s] the outcome” “has invaded the province of the jury protected by the Sixth Amendment and the Due Process Clause.” Herrington v. Edwards, No. 97-3542,1999 WL 98587, at *3 (6th Cir. Jan 26, 1999) (per curiam). But in Herrington, the trial judge literally did dictate the outcome by telling the jury, in response to a jury question, that “it would be impossible for you to find [the defendant] guilty of one count and not guilty on the other.” Ibid. That is quite a different matter from denying a requested jury instruction.
c. “Unreasonable determination of the facts”
Under what circumstances, then, can a habeas petitioner obtain relief under § 2254(d)(2)? Federal courts have struggled with this question, especially in the context of the application of deference to mixed questions of law and fact. Section 2254(d)(2), on the one hand, envisions federal review of a state court’s “unreasonable determination of the facts.” On the other hand, § 2254(e)(1) dictates that “a determination of a factual issue made by a State court shall be presumed to be correct.” The Supreme Court has declined to clarify the relationship between these two provisions, and it has “explicitly left open the question whether § 2254(e)(1) applies in every case presenting a challenge under § 2254(d)(2).” Wood v. Allen, 558 U.S. 290, 299, 130 S.Ct. 841, 175 L.Ed.2d 738 (2010); accord Rice v. Collins, 546 U.S. 333, 339, 126 S.Ct. 969, 163 L.Ed.2d 824 (2006). Other circuits have also declined to resolve the issue. See, e.g., Teti v. Bender, 507 F.3d 50, 58 (1st Cir.2007).3 As with the Supreme Court, we do not— and need not — resolve this tension here.
Even without the § 2254(e)(1) presumption in its favor, the trial court’s decision was not an unreasonable determination of facts in light of the evidence presented. First, a trial court’s decision about whether to provide a jury instruction is not the kind of fact-based determination subject to scrutiny under § 2254(d)(2). Second, the decision to withhold the jury instruction was not unreasonable.
To the extent that McMullan argues that the trial court’s decision to *671refuse the jury instruction was itself an unreasonable determination of facts, this argument fails as well. A trial court’s decision about whether to provide a jury instruction is not the kind of fact-based determination subject to scrutiny under § 2254(d)(2). Factual issues are “basic, primary, or historical facts: facts in the sense of a recital of external events and the credibility of their narrators.” Thompson v. Keohane, 516 U.S. 99, 110, 116 S.Ct. 457, 133 L.Ed.2d 383 (1995) (applying superseded § 2254) (internal quotation marks omitted). Factual issues also include a defendant’s competency to stand trial and a juror’s impartiality; these issues depend on a trial court’s appraisal of witness credibility and demeanor. Id. at 111, 116 S.Ct. 457. Some circuits have found that similar “non-historical” factual issues include whether a petitioner made a Batson prima facie showing of racial discrimination, Tolbert v. Page, 182 F.3d 677, 684 (9th Cir.1999) (en banc), and whether a petitioner waived the state-law right to appeal, Meeks v. Cabana, 845 F.2d 1319, 1323 (5th Cir.1988). Issues that are legal, not factual, include the voluntariness of a confession, the effectiveness of counsel’s assistance, and the “in custody” determination for Miranda purposes. Thompson, 516 U.S. at 111-12, 116 S.Ct. 457.
In holding that refusing a lesser-included-offense instruction does not necessarily implicate a question of fact, we observe that the decision is similar to an evidentia-ry one — the proper domain of the trial court. In federal practice, any party may request a particular jury instruction. See Fed.R.Crim.P. 30. A federal judge must decide whether a “proper evidentiary foundation” exists to give the instruction. United States v. Palma, 511 F.3d 1311, 1315 (11th Cir.2008). When deciding, the judge must view the evidence “in the light most favorable to the accused.” Ibid. For federal judges, the decision ultimately is “a matter within the trial court’s discretion.” United States v. Blood, 435 F.3d 612, 623 (6th Cir.2006).
In the specific context of a lesser-included-offense instruction, federal judges should give such an instruction “if the evidence would permit a jury rationally to find a defendant guilty of the lesser offense and acquit him of the greater.” Hopper v. Evans, 456 U.S. 605, 612, 102 S.Ct. 2049, 72 L.Ed.2d 367 (1982) (internal alterations omitted). A federal judge’s decision to deny a lesser-included-offense instruction is a way in which the “jury’s discretion is thus channelled.” Id. at 611, 102 S.Ct. 2049. Even in capital cases, “due process requires that a lesser included offense instruction be given only when the evidence warrants such an instruction.” Ibid. The decision whether to instruct is fundamentally a legal one, and it is one that belongs to the judge. This has been so for over a hundred years: “[T]he instructing or refusing to instruct ... rests upon legal principles or presumptions which it is the province of the court to declare for the guidance of the jury.” Sparj v. United States, 156 U.S. 51, 102, 15 S.Ct. 273, 39 L.Ed. 343 (1895) (Harlan, J.).
The difference between questions of law and fact can be “slippery,” Thompson, 516 U.S. at 111, 116 S.Ct. 457, but here, the trial court’s decision not to give the jury instruction was not a factual issue. It did not rest upon a subsidiary finding of historical fact or an appraisal of witness credibility. The subsidiary fact involved — that McMullan used a gun and that Smith was shot by that gun — was uncontested. It also did not involve assessing McDowell’s credibility or demeanor. We are aware of McMullan’s theory of the case: that he did not intend to kill Smith, his longtime friend. See Pet’r Br. 21-22; Reply Br. 12; R. 9-9, p. ID # 1194 (“What we have here is just a terrible situation.”). But intent to *672kill is not a necessary element of second-degree murder in Michigan. See Gillis, 712 N.W.2d at 438.
Even if the trial court’s decision were a fact-based one, we cannot say that decision was unreasonable. Section 2254(d)(2)’s unreasonableness requirement imposes “a daunting standard — one that will be satisfied in relatively few cases.” Taylor v. Maddox, 366 F.3d 992, 1000 (9th Cir.2004). We agree with the Ninth Circuit standard: “[W]e must be convinced that an appellate panel, applying the normal standards of appellate review, could not reasonably conclude that the finding is supported by the record.” Ibid. As noted above, the mere “use of a deadly weapon” can establish malice in Michigan, Bulls, 687 N.W.2d at 165, and no one disputes that McMullan used a deadly weapon. Thus, there was evidence in the record to support the trial court’s finding that malice was present and that the involuntary-manslaughter instruction was not necessary. We cannot conclude that that decision was an unreasonable one. Therefore, McMul-lan cannot prevail with his argument under § 2254(d)(2).
3. Conclusion
In short, we may not reverse the denial of McMullan’s habeas claim, whether his jury-instruction claim is construed under § 2254(d)(1) or § 2254(d)(2). First, defendants do not have a constitutional right to a lesser-included-offense instruction in non-capital cases. Campbell v. Coyle, 260 F.3d 531, 541 (6th Cir.2001); accord Calloway v. Montgomery, 512 F.3d 940, 944 (7th Cir.2008) (holding no due-process violation by refusing to instruct on involuntary manslaughter, even when petitioner was convicted of voluntary manslaughter, because “on this issue in a noncapital case, there is no clearly established Supreme Court precedent”); Dockins v. Hines, 374 F.3d 935, 938 (10th Cir.2004) (adhering to a “rule of automatic non-reviewability” on habeas “for claims based on a state court’s failure, in a non-capital case, to give a lesser included offense instruction.”). Second, McMullan has not alleged that the trial court unreasonably determined any of the underlying facts in deciding whether to give the lesser-included-offense instruction. Finally, a trial court’s decision to refuse to give a proffered jury instruction is a legal decision and not a factual determination to which § 2254(d)(2) would apply-
B. Ineffective Assistance of Counsel
McMullan also contends that his trial counsel’s failure to cross-examine McDowell about McDowell’s potential plea bargain or expectation of leniency in exchange for testifying constituted ineffective assistance of counsel. Because the Michigan Court of Appeals did not unreasonably decide that McMullan received effective assistance of counsel, we cannot grant habeas relief on this claim.
Under federal law, to establish ineffective assistance of counsel, a criminal defendant must first show that “counsel’s representation fell below an objective standard of reasonableness.” Strickland v. Washington, 466 U.S. 668, 688, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). This inquiry looks at whether trial counsel fell below the standard of a competent attorney. See id. at 688-91, 104 S.Ct. 2052. There is a “strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance.” Id. at 689, 104 S.Ct. 2052. Second, to succeed on an ineffective-assistance claim, a criminal defendant must show that counsel’s ineffectiveness prejudiced him. Id. at 692, 104 S.Ct. 2052. That is, “[t]he defendant must show that there is a reasonable probability that, but for counsel’s unprofessional errors, the *673result of the proceeding would have been different.” Id. at 694, 104 S.Ct. 2052. It is very difficult for a defendant to surmount Strickland’s high bar. See Cullen v. Pinholster, — U.S. -, 131 S.Ct. 1388, 1404-08, 179 L.Ed.2d 557 (2011) (rejecting defendant’s ineffective-assistance claim even when counsel failed to investigate at all before a penalty-phase hearing that resulted in a death sentence); see also Bobby v. Van Hook, 558 U.S. 4, 9-13, 130 S.Ct. 13, 175 L.Ed.2d 255 (2009) (rejecting defendant’s ineffective-assistance claim based on counsels’ failure to investigate more thoroughly and present more mitigating evidence), rev’g Van Hook v. Anderson, 560 F.3d 523 (6th Cir.2009).
On habeas, our review of a state court’s determination that a criminal defendant received effective assistance is particularly deferential. We do not apply Strickland directly. Rather, “[t]he pivotal question is whether the state court’s application of the Strickland standard was unreasonable.” Harrington v. Richter, 562 U.S. 86, 131 S.Ct. 770, 785, 178 L.Ed.2d 624 (2011). Were we to apply Strickland directly, “the analysis would be no different than if, for example, [this court] were adjudicating a Strickland claim on direct review of a criminal conviction in a United States district court.” Ibid. The combination of the highly deferential standards of Strickland and of § 2254(d) makes for “doubly deferential judicial review.” Knowles v. Mirzayance, 556 U.S. 111, 123, 129 S.Ct. 1411, 173 L.Ed.2d 251 (2009).
In this case, the Michigan Court of Appeals did not unreasonably apply the federal ineffective-assistance standard. Although that court identified and applied a state-law ineffective-assistance standard, Michigan has adopted the Strickland test as state law. See People v. Grant, 470 Mich. 477, 684 N.W.2d 686, 691-92 (2004). In deciding McMullan’s direct appeal, the state appellate court noted that there was no evidence that a plea bargain between McDowell and the government existed at the time McDowell testified. See McMullan, 771 N.W.2d at 815. It relied on the fact that McDowell testified on cross-examination on January 23, 2002; and the trial court in McDowell’s case did not docket the plea agreement until January 25, 2002, see Plea Agreement, People v. McDowell, No. 01-008403-FH (Genesee Cnty. Cir. Ct. Jan. 25, 2002) (no. 18), case notes (no. 17) available at http://www.co. genesee.mi.us/roaccsinq/default.aspx (enter case number, i.e., “01-008403”; then select “Case Detail”). Based on these facts, we cannot say that the Michigan court was unreasonable in concluding that McMul-lan’s counsel was not ineffective for failing to cross-examine McDowell about any purported plea agreement when there was no affirmative evidence that a plea agreement existed. Ibid.
Nor was the state appellate court unreasonable in concluding that McMullan could not show a reasonable probability that the outcome of the trial would have been different if McMullan’s counsel had cross-examined McDowell about an expectation of leniency. This is so because McMul-lan’s own testimony provided sufficient evidence of the necessary malice. Under Michigan law, second-degree murder is the unexcused causing of the death of another, with malice. People v. Smith, 478 Mich. 64, 731 N.W.2d 411, 414-15 (2007). As the state court noted, McMullan admitted that he was in an altercation with Smith; that he snatched a gun from his wife to scare Smith; that he held the gun and pointed it at Smith; that the gun fired; that Smith was shot; and that Smith died. See McMullan, 771 N.W.2d at 815-16. The state court did not unreasonably conclude that McMullan could not show a reasonable probability that the trial outcome would have differed if McMullan’s counsel *674had cross-examined McDowell about any expectation of leniency. Therefore, McMullan cannot obtain habeas relief on this ground.
C. Brady Obligation
1
McMullan also seeks habeas relief on the ground that the state appellate court unreasonably determined that the government was not obligated to disclose McDowell’s plea bargain. We deny relief because McMullan cannot establish that the Michigan Court of Appeals unreasonably concluded that no reasonable probability existed that the trial outcome would have differed if the prosecutor had disclosed a putative plea agreement.
Clearly established federal law imposes a duty on prosecutors to disclose exculpatory evidence. “[T]he suppression by the prosecution of evidence favorable to an accused upon request violates due process where the evidence is material either to guilt or to punishment, irrespective of the good faith or bad faith of the prosecution.” Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). Under current law, a prosecutor must disclose exculpatory evidence, regardless of whether the defendant requests it. See Kyles v. Whitley, 514 U.S. 419, 433, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995). “[Evidence is material only if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985). Thus, to establish a Brady violation, a defendant must show that exculpatory evidence was withheld and that there is a reasonable probability that this evidence would have affected the outcome of the trial. A prosecutor’s Brady obligation extends to disclosing the “inducements” and the “possibility of a reward” held out by the government for its witnesses, whether formalized in an agreement or not. Id. at 683, 105 S.Ct. 3375.
Here, the Michigan Court of Appeals did not unreasonably conclude that McMullan could not establish a reasonable probability that his trial outcome would have been different if the prosecutor had disclosed a plea agreement with McDowell or any possible expectation of leniency that McDowell may have had. See McMullan, 771 N.W.2d at 816-17. The state court found that there is not a reasonable probability that the withheld evidence would have undermined the jury’s conviction for second-degree murder. It relied on the fact that McMullan acknowledged that he was involved in an altercation with Smith; that he snatched a gun from his wife; that he intended to use the gun to scare Smith; and that Smith was shot. The state court concluded that McDowell’s testimony echoed McMullan’s in the crucial respects such that disclosing McDowell’s plea bargain would not have affected the outcome of McMullan’s trial. The state appellate court was not unreasonable in so concluding.
2
Although McMullan cannot succeed on his Brady claim, the prosecution in this case may not be wholly blameless. Brady establishes a floor — not a ceiling — for proper prosecutorial conduct. One criticism of Brady is that it is a weak rule. Brady creates little incentive for a prosecutor to disclose exculpatory evidence if the prosecutor believes that the evidence is not “material” within the meaning of Bag-ley. Further, defendants may never learn of undisclosed Brady material or learn of it only with great difficulty. See, e.g., Bagley v. Lumpkin, 719 F.2d 1462, 1463 (9th *675Cir.1983) (Brady evidence disclosed from defendant’s filing a request under the Freedom of Information Act), rev’d sub nom., United States v. Bagley, 473 U.S. 667, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985). A third problem with Brady — one illustrated by this case — is that prosecutors must make an ex ante decision about whether to disclose impeachment evidence, but the Brady standard of materiality is ex post— materiality is judged in light of all the evidence at trial. In this case, even though there is considerable question over whether the prosecution should have made a disclosure, any withholding would have been harmless error.
In holding that McMullan cannot show that the state court unreasonably applied Brady, we assume, without deciding, that the prosecutor should have disclosed McDowell’s plea agreement. The Supreme Court has not hesitated to reverse a state-court conviction when withheld impeachment evidence undermines confidence in the verdict. See Smith v. Cain, — U.S. -, 132 S.Ct. 627, 630-31, 181 L.Ed.2d 571 (2012); Banks v. Dretke, 540 U.S. 668, 692-703, 124 S.Ct. 1256, 157 L.Ed.2d 1166 (2004). The Michigan Court of Appeals noted that state-court rules impose on prosecutors a “duty to disclose the details of a witness’s plea agreement, immunity agreement, or other agreement.” McMullan, 771 N.W.2d at 816 (citing MCR 6. 201(B)(5)). Additionally, the Michigan Rules of Professional Conduct call for prosecutors to “make timely disclosure to the defense of all evidence or information known to the prosecutor that tends to negate the guilt of the accused or mitigates the degree of the offense.” MRPC 3.8(d); see also Model Rules of Prof 1 Conduct R. 3.8(d) (identical text). On its face, this rule contains no Bagley materiality requirement.
In this case, there is no direct evidence that McDowell had a plea bargain or an expectation of one at the time he testified on cross-examination on January 23. Two days later — the day that the jury reached a verdict in McMullan’s case — a different judge in the same court granted the government’s motion to reduce McDowell’s cocaine charge to a misdemeanor. See Plea Agreement, People v. McDowell. Under “Additional Considerations,” the plea agreement states: “Lenient Sentencing & A agrees to testify truthfully against Angelo McMullin [sic] as needed.” At the bottom of the agreement, someone also handwrote: “Criminal Case for Angelo McMullin [sic]: 01-008582.” Further, McDowell’s docket sheet indicates: “DEFT AGREES TO TESTIFY TRUTHFULLY AGAINST ANGELO MCMUL-LEN [sic] AS NEEDED (CASE #01-8582-FQ.” The use of the present verb tense on both the plea agreement and docket sheet is odd, for McDowell had already concluded his testimony in McMul-lan’s case and the jury had already begun deliberations. It might be conceivable that this note refers to McDowell’s agreement to testify against McMullan in future cases — were it not for the express inclusion of McMullan’s homicide case number. It is also plausible that a plea bargain had been in the works prior to January 25.
One month later, at McMullan’s sentencing, McMullan’s counsel informed the court that McDowell had received a plea bargain on the morning of the day that the jury convicted McMullan. McMullan’s counsel told the court: “[After learning about the plea bargain,] I was a little hot. I’ll say that.” According to McMullan’s counsel, the assistant prosecuting attorney for McMullan’s case, Kennan M. DeWitt, stated that he “had absolutely nothing to do with [McDowell’s plea deal].” McMul-lan’s counsel also asserted that, on January 25, he had spoken with McDowell’s *676defense attorney, who stated “that there was no deal that had been made for Mr. McDowell.”
DeWitt emphatically denied any connection between McMullan’s case and McDowell’s cocaine-charge downgrade. “[T]here was absolutely no connection between Mr. McDowell’s case either in facts or procedure,” DeWitt told the court. “There was no consideration given to McDowell connected to this case.” DeWitt further stated: “[McDowell] resolved a case that was pending against him, and that’s it, period. It had nothing to do with [McMullan’s] case.” If DeWitt did not know that his own prosecutor’s office had agreed to downgrade McDowell’s charge in exchange for McDowell’s truthful testimony against McMullan, he should have known. McDowell was his witness, and the Genesee County Prosecutor’s Office felony division consists of only roughly six prosecutors.4 See Genesee County, Prosecutors Office, Criminal Division-Circuit Court, http://www.gc4me.com/ departments/prosecutors_offiee/criminal_ division-circuit_court.php (last visited August 4, 2014).
The conduct of the Genesee County Prosecutor Office’s appears troubling. It is one matter to withhold impeachment evidence, albeit evidence that is not “material” within the meaning of Bagley. It is another matter to delay strategically formalizing a witness’s plea agreement until after a witness finishes testifying in order to deny plausibly that a plea agreement existed at the time the witness testified. And it is yet another matter entirely for a prosecutor to perjure himself before a judicial tribunal.
The State of Michigan has not attempted to square DeWitt’s statement with the January 25, 2002, docket entry stating that McDowell “agrees” to testify against McDowell.5 In its brief, the State of Michigan does not defend the prosecutor’s decision not to disclose McDowell’s plea; instead, it rests its Brady argument solely on the ground that disclosure would not have affected the trial outcome. See Resp’t Br. 53-56. The State of Michigan, in fact, acknowledges that “disclosure of McDowell’s anticipated plea agreement or expectation for lenience in anticipation of an agreement arguably would have allowed for more effective cross-examination.” Id. at 54. The Michigan Court of Appeals held that even if the prosecutor should have disclosed the “anticipated plea agreement,” McMullan failed to satisfy the Brady standard. McMullan, 771 N.W.2d at 816. Although we do the same, we observe:
The qualities of a good prosecutor are as elusive and as impossible to define as those which mark a gentleman. And those who need to be told would not understand it anyway. A sensitiveness to fair play and sportsmanship is perhaps the best protection against the abuse of power, and the citizen’s safety lies in the prosecutor who tempers zeal *677with human kindness, who seeks truth and not victims, who serves the law and not factional purposes, and who approaches his task with humility.
Robert H. Jackson, The Federal Prosecutor, 24 Am. Jud. Soc’y 18 (1940), available at http://www.roberthjackson.org/the-man/ speeches-artieles/speeehes/speeches-by-robert-h-jackson/the-federal-prosecutor/. It was true in 1940, and it is true today.
IV
Under 28 U.S.C. § 2254(d), McMullan’s petition for a writ of habeas corpus cannot succeed on any of the three grounds asserted. No clearly established federal law required the state court to instruct the jury on the lesser included offense of involuntary manslaughter. The state court did not unreasonably apply the standards either of Strickland or of Brady. Accordingly, we AFFIRM the district court’s judgment.
. After the district court entered its judgment, we appointed McMullan counsel on appeal.
. McMullan also argues that the jury-trial right "extends to prohibit judges from weighing evidence and making credibility determinations, as these are properly within the sphere of the jury." Reply Br. 10. He cites United States v. U.S. Gypsum Co., 438 U.S. 422, 98 S.Ct. 2864, 57 L.Ed.2d 854 (1978), as an example of a case in which a jury instruction that removed the issue of intent from the jury was found to have improperly invaded the jury's factfinding function. U.S. Gypsum Co., taken out of context, is misleading. In that case, the government charged six major gypsum manufacturers with violating section 1 of the Sherman Act. Id. at 427, 98 S.Ct. 2864. The judge instructed the jury that if it found that the manufacturers' actions had the effect of fixing prices, the jury could presume that the manufacturers intended that result. Id. at 430, 98 S.Ct. 2864. The Court held that the Sherman Act was not a strict-liability regime and that intent was an element of a criminal offense under the Sherman Act. Id. at 435-36, 98 S.Ct. 2864. Specifically, the Court found that the Sherman Act’s intent element is satisfied when a perpetrator acts with knowledge of the anticipated consequences. Id. at 446, 98 S.Ct. 2864. The Court’s ultimate conclusion that the jury instruction was improper and that "the issue of intent must be left to the trier of fact alone" rested on its interpretation of the Sherman Act — not the Sixth Amendment jury-trial right. See id. (The opinion does not even reference the Sixth Amendment.)
McMullan also relies on our decision in Barker v. Yukins, 199 F.3d 867 (6th Cir.1999), where a defendant’s sole defense was that she stabbed and killed an 81-year-old victim in order to prevent an imminent rape. Id. at 875. Although the trial court instructed the jury that a defendant may use lethal force to prevent serious bodily injury, it did not specifically instruct that a defendant is entitled to use deadly force to prevent rape. Id. at 870. The Michigan Supreme Court determined that the trial court erred but that the error was harmless because no reasonable juror would have believed the defendant’s self-defense claim. Ibid. Under these circumstances, our court concluded that the trial court's failure to instruct specifically on the issue of rape was so prejudicial that the defendant had met her burden of showing that the "improper instruction so infected the entire trial that the resulting conviction violates due process.” Id. at 876.
To the extent that Barker is germane, it does not support McMullan’s § 2254(d)(2) argument. There, the panel granted a conditional writ of habeas corpus on the ground that the Michigan Supreme Court decision involved an unreasonable application of the harmless-error test — a § 2254(d)(1) finding.
. The question whether, in order to satisfy § 2254(d)(2), a petitioner must establish only that the state-court factual determination was "unreasonable” or whether § 2254(e)(1) “additionally requires a petitioner to rebut a presumption that the determination was correct with clear and convincing evidence” has divided the courts of appeals. Wood v. Allen, 558 U.S. 290, 298, 130 S.Ct. 841, 175 L.Ed.2d 738 (2010). Our circuit has not opined on the issue, and we refrain from doing so now. In Matthews v. Ishee, 486 F.3d 883, 889 (6th Cir.2007), the panel assumed that a petitioner satisfies § 2254(d)(2) by showing that a "state court's presumptively correct factual findings are rebutted by 'clear and convincing evidence’ and do not have support in the record.” Id. at 888 (emphasis added). We do not read this as taking a clear position on the split.
. “The prosecutor’s office is an entity and as such it is the spokesman for the Government. A promise made by one attorney must be attributed, for these purposes, to the Government.” Giglio v. United States, 405 U.S. 150, 154, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972).
. In July 2008, DeWitt was fired from the Genesee County Prosecutor’s Office amid allegations of prosecutorial misconduct. Sally York, Assistant fired; Motel meeting sparked continuing probe, Flint Journal, July 30, 2008. Specifically, DeWitt was under investigation for conducting an improper personal relationship with Dana Bacon, a convicted embezzler whom DeWitt had prosecuted. Ibid. Lapeer County agreed to cease its investigation of DeWitt in exchange for DeWitt agreeing not to seek his job back. Bryan Mickle, No charges, no job for DeWitt, Flint Journal, Oct. 11, 2008.