JENNIFER WALKER ELROD, Circuit Judge:

Richard Cobb was convicted of capital murder and sentenced to death in Texas state court. He filed a habeas petition in federal district court pursuant to 28 U.S.C. § 2254. The district court denied that petition, but granted a certificate of appealability (COA) on one issue: whether the state withheld impeachment evidence from Cobb in violation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). We AFFIRM the district court's denial of habeas relief. We DENY Cobb's request for a COA on three additional issues.

I.

Cobb and Beunka Adams committed two armed robberies in August 2002. On the night of September 2, 2002, they committed a third. Armed with a shotgun, and wearing masks and gloves, they entered a convenience store known as BDJ's. Nikki Ansley (Dement)1 and Candace Driver were working as clerks that night. Also present in the store was a frequent customer, Kenneth Vandever. Ansley and Driver were made to stand together behind the cash register. Cobb and Adams demanded money. Driver opened the cash register drawer. While Cobb held the shotgun, Adams grabbed the drawer and took all of the money. Vandever, the customer, began to walk out the front door, but was ordered to join Ansley and Driver behind the register.

Cobb and Adams then decided to take Ansley, Driver, and Vandever as hostages. Driver was ordered to surrender the keys to her Cadillac, which was parked outside, and the three hostages were forced into the vehicle. Adams drove to a remote, open pasture known as the "pea patch." Everyone got out of the car, and Adams forced Driver and Vandever into the trunk while Cobb held the gun. Adams took Ansley into a wooded area and raped her. Cobb and Adams then told the three hostages that they could wait for a little while, and then leave, but soon Cobb and Adams changed their minds. After debating what to do, Cobb and Adams tied up the women hostages with their shirts and forced them to kneel by the vehicle. They began to walk away with Vandever, intending to allow him to come back later to untie Ansley and Driver. Soon they returned, however, and forced Vandever to sit by the other two victims.

After Vandever began to protest, Cobb shot him. Vandever fell forward, screaming that he had been shot. Either Cobb or Adams then shot Ansley and Driver.2 Ansley and Driver both fell forward as well, and pretended to be dead. Adams started kicking Ansley, and Cobb joined in. Cobb lifted Ansley up by her ponytail, and he and Adams put their lighters up to her face. After satisfying themselves that the three victims were dead, Adams and Cobb left the scene and went to the residence of Adams's cousin.

Vandever died, but Ansley and Driver survived. After regaining consciousness, they managed to get to safety. Ansley sustained a shotgun wound to her left shoulder, numerous broken ribs, and a collapsed lung, which required her to spend almost two weeks in the hospital. After undergoing emergency surgery, she identified Cobb and Adams from a photo lineup. Driver, who suffered a gunshot wound to her lower lip, was able to identify Adams, but not Cobb, from a photo lineup while in the hospital. Adams's cousin contacted the police and disclosed Cobb's and Adams's whereabouts. They were arrested at Adams's cousin's home on September 3, the day after Vandever's murder. Adams surrendered, but Cobb resisted arrest and had to be subdued. Under questioning, Cobb confessed to shooting Vandever and to participating in the robbery and kidnaping.

On September 23, 2002, Cobb was indicted for capital murder under Tex. Penal Code § 19.03(a)(2) (murder in the course of committing, inter alia, kidnaping and robbery). His trial began on January 5, 2004. On January 23, 2004, he was sentenced to death.

During the guilt-determination phase of the trial, Cobb admitted to participating in the robbery and kidnaping and to shooting Vandever. He testified, however, that Adams pressured him into committing the murder, threatening to kill Cobb if he refused to take part in killing the three hostages. The state cast doubt on this portion of Cobb's testimony by getting him to admit on cross-examination that he did not mention any coercion by Adams when he first confessed to the authorities. Moreover, the other surviving witnesses did not corroborate Cobb's testimony that Adams threatened him.

The state also rebutted Cobb's duress defense by calling William Elmer Thomsen to testify. Thomsen was incarcerated with Cobb at the Cherokee County Jail. Thomsen testified that, during several jailhouse conversations he had with Cobb at this time, Cobb extensively discussed Vandever's murder as well as the robberies that he and Adams committed. Thomsen testified that Cobb "thought armed robberies were the way to go. It's fast, quick, easy money." According to Thomsen's testimony, Cobb also told him that he and Adams had plans to rob a Whataburger in the near future, had they not been caught and arrested. Thomsen also testified that Cobb confided in him that he planned at his trial to blame the murder on Adams by testifying that Adams had threatened to kill him if he did not take part in shooting the hostages.

On cross-examination, the defense asked Thomsen whether he had received a deal from the state in exchange for his testimony. Thomsen avowed that he had not. He testified that when he contacted the district attorney to offer his testimony against Cobb, the charge he was facing for being a felon in possession of a firearm had already been dismissed.3 Thomsen was still in jail, however, for violating the terms of his probation for a prior offense. Although Thomsen insisted that he did not receive any benefit from the state for his testimony, he did concede that the district attorney's office contacted his parole officer on his behalf.

After the jury convicted Cobb of capital murder, the sentencing phase of Cobb's trial began. Salient here are two special issues that the jury was required to answer. First, the jury had to determine whether it was probable that Cobb would commit future criminal acts of violence that would constitute a continuing threat to society. If the jury answered this question in the affirmative, it had to determine whether mitigating circumstances made a sentence of life imprisonment without parole more appropriate than a death sentence. Tex.Code Crim. Pro. art. 37.071.

The district court summarized the evidence presented to the jury at the sentencing phase as follows:

Cobb v. Thaler, No. 2:08-CV-123, 2011 WL 672333, at *5-6 (E.D. Tex. Feb. 15, 2011) (citations omitted).

On the morning before closing arguments, the state discovered that it had not provided the defense with a letter written by the district attorney to Thomsen's parole officer. The district attorney's staff found the letter in the file of Cobb's co-defendant, Adams. The state then provided a copy of the letter to the defense. Dated January 10, 2003, the letter states:

Although it received this letter the day before closing arguments, the defense chose not to move to reopen the case to introduce the letter into evidence. In its closing, the defense argued:

The state then argued in its closing:

After hearing closing arguments, the jury returned a verdict on January 16, 2004. In response to Special Issue No. 1 — whether there was a probability that Cobb would commit criminal acts of violence that would constitute a continuing threat to society — the jury answered "yes." In response to Special Issue No. 2 — whether there were mitigating circumstances that warranted a sentence of life imprisonment instead of death — the jury answered "no." On January 23, 2004, the state court sentenced Cobb to death.

Two months later, while reviewing the file of Cobb's co-defendant, Adams, the prosecutor discovered another letter. Dated December 26, 2002, this letter was written by Thomsen and sent to the district attorney. The full text of the letter is as follows:

After receiving this letter, Cobb filed a motion for a new trial in which he claimed, inter alia, that the state committed a Brady violation by withholding the letter. The state trial court denied the motion. On direct appeal, the Texas Court of Criminal Appeals affirmed Cobb's conviction and sentence. Cobb v. State, No. AP-74875, 2007 WL 274206 (Tex.Crim.App. Jan 31, 2007) (unpublished). His subsequent state application for writ of habeas corpus was denied. Ex parte Cobb, No. WR-68192-01, 2007 WL 4306840 (Tex. Crim.App. Dec. 5, 2007) (unpublished). Cobb then filed a petition for a writ of habeas corpus in federal district court, in which he raised eleven claims. The district court denied relief on each claim. Cobb v. Thaler, 2011 WL 672333. The district court subsequently granted a COA for Cobb's Brady claim and this appeal followed.

II.

The Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA) defines "[t]he statutory authority of federal courts to issue habeas corpus relief for persons in state custody." Premo v. Moore, ___ U.S. ___, 131 S.Ct. 733, 739, 178 L.Ed.2d 649 (2011). "AEDPA prohibits federal habeas relief for any claim adjudicated on the merits in state court, unless one of the exceptions listed in § 2254(d) obtains." Id. Under § 2254(d), a federal court may not grant habeas relief on such claims unless the state court's decision (1) "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) "was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding."

A state court decision involves an unreasonable application of federal law if it "correctly identifies the governing legal rule but applies it unreasonably to the facts of a particular prisoner's case." Williams v. Taylor, 529 U.S. 362, 407-08, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). The state court's application of the law must be "objectively unreasonable," not merely "erroneous" or "incorrect." Id. 409-11, 120 S.Ct. 1495. The Supreme Court has recently emphasized that this standard is met only "in cases where there is no possibility fairminded jurists could disagree that the state court's decision conflicts with [Supreme Court] precedents." Harrington v. Richter, ___ U.S. ___, 131 S.Ct. 770, 786, 178 L.Ed.2d 624 (2011). This exception to AEDPA's relitigation bar "is difficult to meet ... because it was meant to be." Id. "[H]abeas corpus is a `guard against extreme malfunctions in the state criminal justice systems,' not a substitute for ordinary error correction through appeal." Id. (quoting Jackson v. Virginia, 443 U.S. 307, 332 n. 5, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979) (Stevens, J., concurring in the judgment)). In addition, in elaborating the "unreasonable application" exception, the Supreme Court has explained that

Yarborough v. Alvarado, 541 U.S. 652, 664, 124 S.Ct. 2140, 158 L.Ed.2d 938 (2004).

III.

Before turning to Cobb's Brady claim, we address his contention that AEDPA's standard of review is unconstitutional under Article III of the U.S. Constitution. Cobb argues that § 2254(d)(1) interferes with the decisional independence of the federal courts, and thereby violates Article III, in two ways.4 First, § 2254(d)(1) limits federal habeas relief to detentions pursuant to state court violations of "clearly established Federal law, as determined by the Supreme Court." Cobb contends that this limitation dictates how federal courts adjudicate habeas cases by restricting them to considering only certain legal authorities. In particular, Cobb argues, this restriction prevents circuit courts from giving stare decisis effect to their own precedents. Second, and relatedly, Cobb argues that § 2254(d)(1)'s "unreasonable application" standard instructs federal courts to defer to state court interpretations of federal law.

In Cobb's view, these two features of § 2254(d)(1) violate Article III by restricting the independent interpretive authority of the federal courts. Specifically, Cobb contends that these perceived restrictions violate the conception of Article III's "judicial Power" that Marbury v. Madison famously enunciated: "It is emphatically the province and duty of the judicial department to say what the law is. Those who apply the rule to particular cases, must of necessity expound and interpret that rule." 5 U.S. (1 Cranch) 137, 177, 2 L.Ed. 60 (1803). In addition, Cobb argues that § 2254(d)(1)'s asserted restrictions on independent federal adjudication offend the principle that Congress may not "prescribe rules of decision to the Judicial Department of the government in cases pending before it." United States v. Klein, 80 U.S. (13 Wall.) 128, 146, 20 L.Ed. 519 (1872); see also Plaut v. Spendthrift Farm, Inc., 514 U.S. 211, 218, 115 S.Ct. 1447, 131 L.Ed.2d 328 (1995) (identifying the quoted language from Klein as describing a type of legislation that impermissibly "require[s] federal courts to exercise the judicial power in a manner that Article III forbids").

In addressing Cobb's constitutional challenge to AEDPA, we are aided by the considered views of several of our sister circuits. Four circuits have addressed constitutional challenges to AEDPA similar to Cobb's, and each has rejected that challenge. See Evans v. Thompson, 518 F.3d 1, 6-11 (1st Cir.2008); Crater v. Galaza, 491 F.3d 1119, 1126-30 (9th Cir.2007); Green v. French, 143 F.3d 865, 874-75 (4th Cir.1998), abrogated on other grounds by Williams, 529 U.S. 362, 120 S.Ct. 1495; Lindh v. Murphy, 96 F.3d 856, 871-74 (7th Cir.1996) (en banc), rev'd on other grounds, 521 U.S. 320, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997). We are mindful, of course, that not all of our colleagues from other circuits share this view. See Evans v. Thompson, 524 F.3d 1 (1st Cir.2008) (Lipez, J., dissenting from denial of rehearing en banc) (joined by Torruella, J.); Crater v. Galaza, 508 F.3d 1261 (9th Cir. 2007) (Reinhardt, J., dissenting from denial of rehearing en banc) (joined by Pregerson, Gould, Paez, and Berzon, JJ.); Lindh, 96 F.3d at 885-90 (Ripple, J., dissenting) (joined by Rovner, J.). Indeed, Cobb relies on the dissenting opinions from the First and Ninth Circuits as support for his position.

In our judgment, Cobb's argument and the dissenting opinions on which it relies are not persuasive. As each circuit to address the question has recognized, § 2254(d)(1) does not intrude on the independent adjudicative authority of the federal courts. Rather, it limits the grounds on which federal courts may grant the habeas remedy to upset a state conviction. See Evans, 518 F.3d at 11 ("There is a world of difference between telling a court how to decide a case given a certain set of facts and limiting the availability of relief..."); Crater, 491 F.3d at 1128 ("Section 2254(d)(1) does not restrict the federal courts' power to interpret the law, but only sets standards for what state court errors of law require federal habeas relief."); Green, 143 F.3d at 874-75 ("[S]ection 2254(d)(1) does not limit any inferior federal court's independent interpretive authority to determine the meaning of federal law in any Article III case or controversy. Under the AEDPA, we are free, if we choose, to decide whether a habeas petitioner's conviction and sentence violate any constitutional rights. Section 2254(d) only places an additional restriction upon the scope of the habeas remedy in certain circumstances."); Lindh, 96 F.3d at 872 (majority opinion) ("Regulating relief is a far cry from limiting the interpretive power of the courts ... and Congress has ample power to adjust the circumstances under which the remedy of the writ of habeas corpus is deployed.").

AEDPA is hardly unique, of course, in limiting the availability of a remedy even for aggrieved individuals who may have legitimate federal constitutional claims. Plain error doctrine authorizes courts to correct forfeited errors only in rare circumstances. See United States v. Olano, 507 U.S. 725, 733-37, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993). The harmless error rule plays a similar, albeit less severe, function. See Chapman v. California, 386 U.S. 18, 22, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967). Qualified immunity can prevent meritorious constitutional plaintiffs from recovering. See Pearson v. Callahan, 555 U.S. 223, 236, 129 S.Ct. 808, 172 L.Ed.2d 565 (2009). In the habeas context, the Supreme Court's retroactivity doctrine creates a chasm between valid claims and the right to relief. See Teague v. Lane, 489 U.S. 288, 310, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989). Supreme Court precedent similarly forecloses federal habeas relief for state prisoners convicted on the basis of evidence obtained in an unconstitutional search and seizure. Stone v. Powell, 428 U.S. 465, 481-82, 96 S.Ct. 3037, 49 L.Ed.2d 1067 (1976). In short, federal courts routinely deny relief even for known constitutional violations. The "distinction between rights and remedies is fundamental." Lindh, 96 F.3d at 872.

Most fundamentally, Cobb's Article III challenge is untenable because it depends on an assumption that contradicts nearly two centuries of Supreme Court precedent. Cobb assumes that if Congress gives federal courts habeas jurisdiction to consider collateral attacks on state convictions it must give them plenary authority to consider afresh any and every error of federal law made by the state court. The Supreme Court, however, has long permitted Congress to extend habeas jurisdiction to federal courts without authorizing them to reconsider the legal determinations of criminal courts. Indeed, the common law understanding of the writ forbade reexamination of the judgments of criminal courts of competent jurisdiction. See Lindh, 96 F.3d at 867 ("The writ known in 1789 was the pre-trial contest to the executive's power to hold a person captive, the device that prevents arbitrary detention without trial. [It] did not include the ability to reexamine judgments rendered by courts possessing jurisdiction." (citing cases)). Accordingly, in 1830 the Supreme Court interpreted its habeas jurisdiction under the Judiciary Act of 1789 as prohibiting it from reevaluating a federal prisoner's conviction because "[t]he judgment of the circuit court in a criminal case is of itself evidence of its own legality." Ex parte Watkins, 28 U.S (3 Pet.) 193, 207, 7 L.Ed. 650 (1830); see also Felker v. Turpin, 518 U.S. 651, 663, 116 S.Ct. 2333, 135 L.Ed.2d 827 (1996) (discussing Watkins); Paul M. Bator, Finality in Criminal Law and Federal Habeas Corpus for State Prisoners, 76 Harv. L.Rev. 441, 465-66 (1963) (discussing Watkins's acceptance of "the black-letter principle of the common law that the writ was simply not available at all to one convicted of crime by a court of competent jurisdiction"). "[A]t common law a judgment of conviction rendered by a court of general criminal jurisdiction was conclusive proof that confinement was legal." United States v. Hayman, 342 U.S. 205, 211, 72 S.Ct. 263, 96 L.Ed. 232 (1952).

Even after Congress made the writ available to state prisoners in the latter half of the nineteenth century,5 the Supreme Court continued to adhere to the common law understanding that habeas was unavailable to test convictions by courts vested with jurisdiction. See, e.g., Ex parte Spencer, 228 U.S. 652, 660, 33 S.Ct. 709, 57 L.Ed. 1010 (1913); Harkrader v. Wadley, 172 U.S. 148, 163-64, 19 S.Ct. 119, 43 L.Ed. 399 (1898); In re Wood, 140 U.S. 278, 285-87, 11 S.Ct. 738, 35 L.Ed. 505 (1891). Over time, the Court relaxed this rule, recognizing new categories of habeas claims as challenging the convicting court's jurisdiction. See, e.g., Ex parte Siebold, 100 U.S. 371, 376-77, 25 L.Ed. 717 (1880) (unconstitutional criminal statute does not confer jurisdiction and habeas is proper to test the statute's constitutionality); Ex parte Lange, 85 U.S. (18 Wall.) 163, 175-76, 21 L.Ed. 872 (1874) (circuit court lacked jurisdiction to impose a second sentence where law only allowed imposition of one sentence). The Court also allowed habeas claims to remedy violations of federal law where the state failed to afford the prisoner "corrective process" to litigate his federal claim. See, e.g., Moore v. Dempsey, 261 U.S. 86, 90-92, 43 S.Ct. 265, 67 L.Ed. 543 (1923); Frank v. Mangum, 237 U.S. 309, 335-36, 35 S.Ct. 582, 59 L.Ed. 969 (1915). Despite these exceptions, however, the general rule remained. Not until the landmark case of Brown v. Allen, 344 U.S. 443, 73 S.Ct. 397, 97 L.Ed. 469 (1953), did the Supreme Court clearly interpret the Habeas Corpus Act of 1867 as conferring on federal courts the authority to reexamine claims fully litigated on the merits in state court. See Wright v. West, 505 U.S. 277, 285-87, 112 S.Ct. 2482, 120 L.Ed.2d 225 (1992) (plurality opinion) (recounting the history); see generally Bator, 76 Harv. L.Rev. at 463-99 (same).6 As late as 1949, Judge Learned Hand could write:

Schechtman v. Foster, 172 F.2d 339, 341 (2d Cir.1949).

In light of these centuries-old precedents, Congress may constitutionally grant federal courts habeas jurisdiction over collateral challenges to state convictions and yet limit the availability of the remedy to exceptional circumstances. As the Seventh Circuit put it in rejecting an Article III challenge identical to Cobb's: "We would have to cast history to the winds to say that [§ 2254(d)(1)], which respects fully-litigated judgments unless the state court has gone seriously wrong, transgresses constitutional limitations." Lindh, 96 F.3d at 873-74. Indeed, in rejecting a Suspension Clause challenge to a different provision of AEDPA, the Supreme Court emphasized that "judgments about the proper scope of the writ are `normally for Congress to make.'" Felker, 518 U.S. at 664, 116 S.Ct. 2333 (quoting Lonchar v. Thomas, 517 U.S. 314, 323, 116 S.Ct. 1293, 134 L.Ed.2d 440 (1996)). We reject Cobb's argument that § 2254(d)(1) is unconstitutional under Article III and proceed to his Brady claim.

IV.

Cobb argues that the state courts unreasonably applied clearly established federal law as determined by the Supreme Court in Brady. In Brady, the Court held that "the 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." 373 U.S. at 87, 83 S.Ct. 1194. Subsequent Supreme Court cases have made clear that the duty to disclose arises "even if no request is made," United States v. Agurs, 427 U.S. 97, 107, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976), and that "the individual prosecutor has a duty to learn of any favorable evidence known to the others acting on the government's behalf in the case, including the police." Kyles v. Whitley, 514 U.S. 419, 437, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995). Moreover, the duty to disclose includes impeachment evidence. United States v. Bagley, 473 U.S. 667, 676, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985).

To prevail on his Brady claim, Cobb "must show that (1) the prosecution suppressed evidence, (2) the evidence was favorable to the defense, and (3) the evidence was material to his guilt or punishment." Mahler v. Kaylo, 537 F.3d 494, 500 (5th Cir.2008). Materiality "is generally the most difficult [element] to prove." Id. "[E]vidence 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." Bagley, 473 U.S. at 682, 105 S.Ct. 3375. The Brady materiality determination is a mixed question of law and fact. LaCaze v. Warden La. Corr. Inst. for Women, 645 F.3d 728, 736 (5th Cir. 2011).

The state habeas court denied Cobb's Brady claim on the merits after entering detailed findings of fact and conclusions of law. First, it concluded that the prosecution did not suppress the evidence because Cobb "had access to the files in both his and Beunka Adams [sic] case, and failed to avail himself of the open file policy."7 Second, it concluded that Cobb "fails to show the letter was material especially in light of trial counsel insinuating a deal on cross-examination, and argument without challenge by the State." Accordingly, the state court found, "there is no reasonable probability that the outcome of the trial would have been different if trial counsel had known about the letters earlier."

The district court determined that the first of these conclusions was an unreasonable application of Brady while the second was reasonable. Cobb, 2011 WL 672333, at *9-11. It therefore denied federal habeas relief on Cobb's Brady claim. Id. at *11. In our view, both of the state court's conclusions were reasonable. We address each in turn.

A. Did the Prosecution Suppress the Evidence?

"Brady does not obligate the State to furnish a defendant with exculpatory evidence that is fully available to the defendant through the exercise of reasonable diligence." Kutzner v. Cockrell, 303 F.3d 333, 336 (5th Cir.2002) (citing Rector v. Johnson, 120 F.3d 551, 558 (5th Cir. 1997)). Relying on this quoted language, the Director argues that it was not unreasonable for the state court to conclude that "reasonable diligence" for Cobb's capital murder trial counsel would have included inspecting the file of Cobb's co-defendant Adams.8 This conclusion is buttressed by the state habeas court's factual findings, cited supra note 7, that had Cobb's attorney examined both of the open files as he requested, and as did the attorney for co-defendant Adams, he would have discovered the evidence. These factual determinations, of course, "shall be presumed to be correct" unless Cobb carries "the burden of rebutting the presumption of correctness by clear and convincing evidence." 28 U.S.C. § 2254(e)(1). Cobb has not challenged these findings of fact.

In arguing that the prosecution suppressed the evidence, Cobb relies heavily on the determination of the district court that the state court's conclusion was unreasonable. The district court concluded that Cobb's attorney exercised due diligence because "[w]hile it would have been good practice for Cobb's counsel to review the case file of his co-defendant, unless they knew that evidence the prosecution would rely on in Cobb's trial would only be found in Adams's file, they had no duty to review Adams's file." Cobb, 2011 WL 672333, at *9. Cobb also relies on the following quote from the Supreme Court to establish that his attorney exercised reasonable diligence in not inspecting Adams's file:

Strickler v. Greene, 527 U.S. 263, 284, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999).

We are persuaded that the state habeas court reasonably applied Brady in determining that the prosecution did not suppress Thomsen's letter. Neither party cites to clearly established Supreme Court case law that indicates one way or the other whether defense counsel has a duty to inspect the open file of a co-defendant. Cobb's citation to Strickler does not answer the question. Strickler merely states that defense counsel may rely on the implicit representations of the prosecution that Brady material will be available "in the open files tendered to defense counsel for their examination." Id. This statement is ambiguous as to whether "open files" includes a co-defendant's open file. Thus, the only clearly established Supreme Court determination that Cobb cites is the basic rule that the prosecution has a duty to disclose material exculpatory evidence. It was not unreasonable for the state court to conclude that the prosecution satisfied that duty by providing open access to the case files for the two co-defendants. Moreover, given that the Supreme Court has stated the Brady disclosure requirement at a high level of generality, the state court had substantial leeway in deciding whether, in this particular case, the inclusion of the evidence in Cobb's co-defendant's file satisfied the prosecution's disclosure obligation. See Yarborough, 541 U.S. at 664, 124 S.Ct. 2140 ("The more general the rule, the more leeway [state] courts have in reaching outcomes in case-by-case determinations."). Because "fairminded jurists could disagree that the state court's decision conflicts with [Supreme Court] precedents," Harrington, 131 S.Ct. at 786, we conclude that the state court's determination was reasonable.

B. Was the Evidence Material?

Cobb argues that Thomsen's letter is material because it reveals that he thought he had a deal to exchange testimony against Cobb for prosecutorial leniency. Cobb maintains that the letter contains potent impeachment evidence that was material to two jury determinations that were necessary to its imposing a sentence of death: the probability of Cobb's future dangerousness and the sufficiency of his mitigation evidence. With regard to future dangerousness, Cobb argues that each side's expert testimony cancelled the other's out, and that Thomsen's testimony that Cobb felt no remorse, wanted to escape, and would kill again, was "the tipping point." With regard to the mitigation evidence, Cobb argues that he presented a "compelling case" but that Thomsen's testimony undermined it. He argues that Thomsen's letter "would have clearly exposed Thomsen for what he was — a jailhouse snitch making up tales to get out of jail free."

The district court rejected Cobb's argument, reasoning that:

Cobb, 2011 WL 672333, at *10.

We agree with the district court that it was reasonable for the state court to determine that Thomsen's letter was immaterial. In elaborating Brady's materiality requirement, this court has held that "when the undisclosed evidence is merely cumulative of other evidence, no Brady violation occurs." Spence v. Johnson, 80 F.3d 989, 995 (5th Cir.1996) (citing Allridge v. Scott, 41 F.3d 213, 218 (5th Cir. 1994)). Although Cobb characterizes the letter as demonstrating Thomsen's belief that he had a testimony-for-leniency "deal," the letter shows nothing more than that the district attorney had agreed to clear Thomsen's felon-in-possession charge and that he was willing to cooperate with the prosecution by testifying against Cobb.9 Thus, while the defense surely could have used the letter in its cross-examination of Thomsen, it would not have significantly added to the impeachment ammunition that Cobb's counsel already had. As the state habeas court found, Cobb's counsel "aggressively cross-examined" Thomsen. Moreover, the defense emphasized during its closing argument the only facts that the letter plainly establishes: Thomsen had a strong incentive to lie and received leniency from the district attorney.

Cobb's comparison between his case and the facts in Bagley is unconvincing. The government-agent witnesses in Bagley, despite an undisclosed contract suggesting they would receive pecuniary reward for a successful outcome based on their testimony, signed affidavits attesting that they provided their testimony freely, without any promise of reward. 473 U.S. at 670-71, 105 S.Ct. 3375. Because of this affirmative misrepresentation and the prosecutor's failure to disclose the inducements, the Court concluded that "there is a significant likelihood that the prosecutor's response to respondent's discovery motion misleadingly induced defense counsel to believe that [the government witnesses] could not be impeached on the basis of bias or interest arising from inducements offered by the Government." Id. at 683, 105 S.Ct. 3375. In Cobb's case, by contrast, the defense was in no way misled about Thomsen's incentive to lie. Rather, it zealously sought to impeach Thomsen on that basis.

At the very least, "fairminded jurists could disagree that the state court's decision conflicts with [Supreme Court] precedents." Harrington, 131 S.Ct. at 786. Moreover, like Brady's disclosure requirement, the materiality standard is a general rule, meaning a wide range of reasonable applications exist. See Yarborough, 541 U.S. at 664, 124 S.Ct. 2140 ("The more general the rule, the more leeway [state] courts have in reaching outcomes in case-by-case determinations."). We therefore conclude that the state court did not unreasonably apply Brady in holding that the letter was immaterial.

V.

Finally, Cobb asks for a COA on three additional issues. He concedes, however, that each argument is foreclosed by precedent. We therefore deny his request for a COA as to each issue.

First, Cobb requests a COA on the question of whether the Texas death penalty scheme is unconstitutional under the Fifth, Sixth, Eighth, and Fourteenth Amendments to the U.S. Constitution because it requires jurors to make future dangerousness predictions beyond their skill and expertise. Cobb concedes that this argument is foreclosed by Jurek v. Texas, 428 U.S. 262, 274-76, 96 S.Ct. 2950, 49 L.Ed.2d 929 (1976).

Second, Cobb requests a COA on the question of whether the state trial court unconstitutionally relieved the state of the burden of proving the lack of mitigating circumstances beyond a reasonable doubt. Cobb concedes that this argument is precluded by Scheanette v. Quarterman, 482 F.3d 815, 828 (5th Cir.2007), and Rowell v. Dretke, 398 F.3d 370, 378-79 (5th Cir.2005).

Third, Cobb requests a COA on the question of whether the Texas death penalty scheme is unconstitutional under the Eighth and Fourteenth Amendments for failure to provide for proportionality review. He concedes that Pulley v. Harris, 465 U.S. 37, 42-44, 104 S.Ct. 871, 79 L.Ed.2d 29 (1984), forecloses this argument.

VI.

For the foregoing reasons, we AFFIRM the district court's denial of Cobb's petition for a writ of habeas corpus. We DENY Cobb's motion for an additional COA.