
568 F.3d 929 (2009)
Anthony LAMARCA, Petitioner-Appellant,
v.
SECRETARY, DEPARTMENT OF CORRECTIONS, Attorney General of the State of Florida, Respondents-Appellees.
No. 08-16775.
United States Court of Appeals, Eleventh Circuit.
May 19, 2009.
*932 Linda McDermott (Court-Appointed), McClain & McDermott, P.A., Wilton Manors, FL, for LaMarca.
Scott Andrew Browne, Tampa, FL, for Respondents-Appellees.
Before BIRCH, BLACK and WILSON, Circuit Judges.
BLACK, Circuit Judge:
Anthony Lamarca seeks a certificate of appealability (COA) to appeal three claims from his 28 U.S.C. § 2254 federal habeas corpus petition. Lamarca, a Florida prisoner under a sentence of death, was convicted of first-degree murder in 1997. In a 57-page order, the district court denied Lamarca's § 2254 petition, in which he set forth six claims for relief, and declined to issue a COA. Lamarca timely applied for a COA with this Court. We deny the application for a COA because Lamarca has failed to make a substantial showing of the denial of a constitutional right. See 28 U.S.C. § 2253(c)(2).

I. BACKGROUND
In November 1997, Lamarca was convicted of the first-degree murder of Kevin Flynn, and in February 1998, he was sentenced to death. In two opinions, the Florida Supreme Court summarized the facts adduced at trial, which we reproduce in pertinent part below. See Lamarca v. State, 785 So.2d 1209 (Fla.2001) (Lamarca I); Lamarca v. State, 931 So.2d 838 (Fla. 2006) (Lamarca II).
On the afternoon of December 2, 1995, Anthony Lamarca met his daughter and son-in-law, Tonya and Kevin Flynn, at a neighborhood bar for Tonya's birthday. Lamarca had recently been released from prison for a 1984 conviction for kidnapping and attempted sexual battery with a weapon. Lamarca asked Tonya to borrow the keys to her car, but Kevin refused and offered to drive Lamarca home instead. The two left the bar at approximately 7:45 p.m.
Later that night, at approximately 8:30 p.m., Lamarca returned to the bar alone and told Tonya that she had to pick up Kevin at Joseph Lamarca's home in Hudson County. Joseph Lamarca is Anthony Lamarca's father. When they arrived at the otherwise unoccupied house, Lamarca raped Tonya. He then appeared from a back room with a rifle in his hand and told Tonya that he was going to kill himself. He instructed her to stay put until she heard gunshots. After he left the room, Tonya fled to a nearby phone booth and reported that she heard shots being fired at a nearby residence. She gave the police Joseph Lamarca's address. When the police arrived at Joseph's house, they discovered the front door looked as though it had been kicked in, and after obtaining Joseph's *933 permission to search the residence, they found a rifle.
The police began searching for Anthony Lamarca. One detective saw Lamarca walking along a road and then observed him drop the objects he was carrying and run away. Another detective arrived at Lamarca's trailer at 2:15 a.m. on December 3. The detective looked through the bedroom window and saw the victim's body. Upon entering the trailer, he found Kevin's body on the bedroom floor, bullet casings matching the rifle recovered from Joseph's residence, and blood splattered throughout the house. Lamarca was eventually arrested in Washington state.
At trial, Stephanie Parker testified that on the night in question she heard a car drive up, she looked out her window, and she saw Lamarca and another man walking from the car to the front door of Lamarca's trailer. They appeared to be arguing because of their hand gestures. Parker stated she then fell asleep and her father subsequently awakened her at the behest of the police.
Jeremy Smith testified Lamarca arrived at Smith's home the morning after the murder, and said, "I did it. I killed him." Smith asked who he had killed, and Lamarca said, "Kevin ... it really sucked, but I had to do it." At the time Lamarca's case was being investigated, Smith was waiting to be sentenced for violating probation.
James Michael Hughes, Lamarca's former fellow inmate, testified Lamarca told him in July 1995 that Lamarca was planning to kill his son-in-law because he had raped Lamarca's daughter. Hughes had charges pending against him in Charlotte County at the time Lamarca's trial took place.
At the penalty phase, Lamarca requested to represent himself and refused to present any mitigating evidence. The trial judge appointed Lamarca's guilt phase counsel as standby counsel. At the court's request, Lamarca's counsel made a statement of the mitigation she would have presented if Lamarca had not waived his right to counsel and to present mitigation. The jury voted 11 to 1 to impose the death penalty, and the trial court agreed with this recommendation. The court found one aggravating factor, prior convictions for the violent felonies in 1984, and determined the mitigating evidence did not outweigh this factor. The trial court sentenced Lamarca to death. In 2001, the Florida Supreme Court affirmed Lamarca's conviction and sentence. Lamarca I, 785 So.2d at 1217.
In 2002, Lamarca filed a motion to vacate the judgment and sentence under Florida Rule of Criminal Procedure 3.851, raising 23 claims.[1] The trial court considered 22 claims during a five-day evidentiary hearing.[2] On September 12, 2003, the trial court denied Lamarca's motion. Lamarca appealed the trial court's order denying relief to the Florida Supreme Court. He also filed a state habeas corpus petition, raising four grounds for relief. In 2006, the Florida Supreme Court affirmed the trial court's order and denied Lamarca's habeas petition. Lamarca II, 931 So.2d at 857.
Lamarca then filed a petition for federal habeas corpus relief in the United States District Court for the Middle District of *934 Florida.[3] In his petition to the district court, Lamarca raised six claims: (1) Lamarca received ineffective assistance of counsel at the guilt phase of his capital trial, (2) the State failed to disclose exculpatory evidence to the defense and presented false and misleading testimony, (3) Lamarca was deprived of his right to present a defense by the trial court's limitation and exclusion of evidence and abridgement of Lamarca's cross-examination of Tonya Flynn, (4) Lamarca was deprived of his right to a fair trial by the trial court's allowance and admission of certain collateral acts, (5) Lamarca was deprived of his right to a fair trial by an improper remark made by the prosecution, and (6) Lamarca's sentence of death was unconstitutional because the State committed prosecutorial misconduct in the presentation of Lamarca's prior felony conviction. The district court denied relief on all claims and declined to issue a COA. The court later denied Lamarca's motion to alter or amend the judgment and again concluded Lamarca was not entitled to a COA. Lamarca has filed an application for a COA with this Court with respect to the first three claims from his federal habeas petition.

II. STANDARD FOR GRANTING A COA
This Court may issue a certificate of appealability "only if the applicant has made a substantial showing of the denial of a constitutional right." 28 U.S.C. § 2253(c)(2). Under this standard, a petitioner must show "reasonable jurists would find the district court's assessment of the constitutional claims debatable or wrong." Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 1604, 146 L.Ed.2d 542 (2000). The petitioner, however, is not required to show he will ultimately succeed on appeal, Miller-El v. Cockrell, 537 U.S. 322, 337, 123 S.Ct. 1029, 1039, 154 L.Ed.2d 931 (2003), because when we consider an application for a COA, "[t]he question is the debatability of the underlying constitutional claim, not the resolution of that debate," id. at 342, 123 S.Ct. at 1042. Accordingly, we "should not decline the application for a COA merely because [we] believe[] the applicant will not demonstrate an entitlement to relief." Id. at 337, 123 S.Ct. at 1039.
To obtain a COA when the district court has denied a habeas petition on procedural grounds without reaching the merits of the underlying constitutional claim, the petitioner must show (1) "jurists of reason would find it debatable whether the district court was correct in its procedural ruling," and (2) "jurists of reason would find it debatable whether the petition states a valid claim of the denial of a constitutional right." Slack, 529 U.S. at 484, 120 S.Ct. at 1604. "Where a plain procedural bar is present and the district court is correct to invoke it to dispose of the case, a reasonable jurist could not conclude either that the district court erred in dismissing the petition or that the petitioner should be allowed to proceed further." Id., 120 S.Ct. at 1604.

III. DISCUSSION

A. Claim One: Lamarca Received Ineffective Assistance of Counsel at the Guilt Phase of His Trial.
Lamarca maintains he received ineffective assistance of counsel because (1) his trial counsel failed to investigate and present the evidence of the benefits and motivations Jeremy Smith had to testify, (2) his *935 trial counsel failed to challenge and impeach the testimony of Tonya Flynn, (3) his trial counsel failed to call Steve Slack as a witness to rebut the testimony of Tonya Flynn, and (4) his trial counsel failed to call James Zaccagnino to rebut the testimony of James Michael Hughes.[4]
The benchmark for judging a claim of ineffective assistance of counsel is "whether counsel's conduct so undermined the proper functioning of the adversarial process that the trial cannot be relied on as having produced a just result." Strickland v. Washington, 466 U.S. 668, 686, 104 S.Ct. 2052, 2064, 80 L.Ed.2d 674 (1984). To make such a showing, the petitioner must demonstrate (1) counsel's performance was deficient, and (2) the deficient performance prejudiced the defense. Id. at 687, 104 S.Ct. at 2064.
Under the first prong of the Strickland test, the petitioner must establish "counsel made errors so serious that counsel was not functioning as the `counsel' guaranteed the defendant by the Sixth Amendment." Id., 104 S.Ct. at 2064. In other words, the petitioner "must show that counsel's representation fell below an objective standard of reasonableness." Id. at 688, 104 S.Ct. at 2064. Judicial scrutiny of counsel's performance is highly deferential, id. at 689, 104 S.Ct. at 2065, and "counsel cannot be adjudged incompetent for performing in a particular way in a case, as long as the approach taken `might be considered sound trial strategy,'" Chandler v. United States, 218 F.3d 1305, 1314 (11th Cir.2000) (en banc) (quoting Darden v. Wainwright, 477 U.S. 168, 185, 106 S.Ct. 2464, 2474, 91 L.Ed.2d 144 (1986)).
Under the prejudice prong of Strickland, the petitioner "must show that there is a 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. at 2068.

1. Jeremy Smith
Lamarca claims his trial counsel was ineffective for failing to investigate and present evidence of undisclosed consideration Smith received for his testimony. Lamarca contends his counsel's failure to discover Smith's misdemeanor retail theft conviction meant the jury was deprived of information surrounding the State's alleged assistance to Smith. He argues the district court erred when it "narrowly examined" this claim "as simply a failure to impeach Smith with a misdemeanor conviction."
The district court made two conclusions with respect to Lamarca's claim that his counsel failed to effectively impeach Smith. First, the district court concluded the state courts cited the prevailing law (Strickland) and applied that law to the facts of the case in a reasonable manner in determining Lamarca's counsel was not ineffective for failing to impeach Smith using the prior misdemeanor conviction. Second, the district court concluded the claim, to the extent it was based on the failure of Lamarca's counsel to uncover and present *936 undisclosed consideration Smith received from the State, was procedurally defaulted because the claim was not presented in state court and litigated as an ineffective assistance of counsel claim.[5] Only the second conclusion is pertinent to our resolution of Lamarca's application for a COA because, in his application, Lamarca has not argued his trial counsel was ineffective for failing to impeach Smith with the misdemeanor conviction itself.
The habeas statute requires petitioners to exhaust all available state law remedies. 28 U.S.C. § 2254(b)(1)(A). "A petitioner must alert state courts to any federal claims to allow the state courts an opportunity to review and correct the claimed violations of his federal rights." Jimenez v. Fla. Dep't of Corr., 481 F.3d 1337, 1342 (11th Cir.2007). "Thus, to exhaust state remedies fully the petitioner must make the state court aware that the claims asserted present federal constitutional issues." Snowden v. Singletary, 135 F.3d 732, 735 (11th Cir.1998).
The only ineffective assistance of counsel claim with respect to Smith that Lamarca raised in state court alleged his counsel failed to effectively cross-examine Smith with prior convictions involving crimes of dishonesty. Although Lamarca did present a claim regarding Smith's alleged undisclosed consideration from the State, this claim asserted Brady and Giglio violations by the Statenot ineffectiveness by Lamarca's counsel. In his application for a COA, Lamarca does not address the district court's conclusion that this portion of his ineffective assistance of counsel claim was procedurally barred because it was not exhausted in state court. He thus has failed to show "jurists of reason would find it debatable whether the district court was correct in its procedural ruling." See Slack, 529 U.S. at 484, 120 S.Ct. at 1604. We decline to issue a COA with respect to this issue.

2. Tonya Flynn
Lamarca argues his trial counsel was ineffective for failing to impeach Tonya Flynn with the lack of evidence supporting her allegations of sexual battery and evidence contradicting her testimony about Lamarca breaking into his father's house in Hudson. Lamarca originally presented this ground for relief as claim 3 in his 3.851 motion for post-conviction relief, in which he asserted his trial counsel failed to effectively cross-examine Tonya Flynn regarding the alleged sexual battery.
At trial, Lamarca was represented by Ron Eide and Nora McClure; Eide, a 20-year veteran of the Public Defender's Office at the time of trial, handled the guilt phase, while McClure, a 16-year veteran at the time of trial, was responsible for the penalty phase. During the five-day state evidentiary hearing, Eide provided extensive testimony regarding his trial preparation and strategy, including his decisions regarding the cross-examination of Tonya Flynn. Based on this testimony, the state trial court concluded Lamarca's claim *937 failed under Strickland. In its order denying the claim, the court first addressed Lamarca's contention that trial counsel failed to effectively cross-examine Tonya Flynn concerning her account of the sexual battery. The court noted Eide testified he deliberately limited his cross-examination of Tonya to avoid "opening a door" for the State to introduce additional incriminating evidence regarding the sexual battery, including Tonya's S.A.V.E. examination and DNA evidence reflecting Lamarca was a possible donor to saliva found on Tonya's breast,[6] and "to permit [Lamarca] a meaningful opportunity to tell his own story, a story that was credible and not completely at odds with the other testimony offered in the case." The court also reviewed the trial transcript and noted Lamarca's counsel "extensively argued the lack of DNA evidence surrounding the sexual battery during closing arguments." Finding trial counsel "was not inattentive to this issue, and was indeed fully aware of the significance of the sexual battery," the court determined the "tactical decision to limit cross-examination of Tonya ... was sound and well within the range of prevailing professional standards."
The trial court then turned to a number of alleged inconsistent statements Lamarca claimed his trial counsel should have used to impeach Tonya's testimony. It concluded none of the statements provided a basis for an ineffective assistance of counsel claim. Specifically, with respect to evidence in a police report allegedly contradicting Tonya's claim that Lamarca had kicked in the door to his father's home, the state trial court found "cross-examination would not have been proper as the alleged inconsistency would not have undermined Tonya's credibility," and "[Lamarca] failed to adduce evidence at the evidentiary hearing to develop the significance of the alleged inconsistency." Concluding its discussion of this claim, the court stated, "as [Lamarca] has failed to demonstrate deficient performance or that [he] suffered prejudice, this claim fails under Strickland and is therefore denied."
On appeal, the Florida Supreme Court affirmed the trial court's determination with respect to this claim. Lamarca II, 931 So.2d at 850. After setting out the test for demonstrating ineffective assistance of counsel under Strickland, id. at 846-47, the court noted Eide's testimony regarding his strategic decision to limit his cross-examination of Tonya Flynn "to avoid opening the door to potentially incriminating information that would not otherwise have been admissible," recognized such decisions are "virtually unchallengeable," and accordingly rejected the claim, id. at 850.
In his § 2254 petition, Lamarca challenged the state courts' conclusions that his trial counsel was not ineffective for failing to impeach Tonya Flynn and present evidence demonstrating the inconsistencies in her testimony. The district court denied this claim on the merits, concluding Lamarca had not met his burden of showing that the state courts' decisions were "contrary to" or "an unreasonable application of" Strickland, or that the state decisions' were based on "an unreasonable *938 determination of the facts." See 28 U.S.C. § 2254(d)(1)-(2).
Jurists of reason would not debate the correctness of the district court's ruling. First, Lamarca does not explain, in neither his § 2254 petition nor his application for a COA with this Court, how the state courts' decisions were "contrary to" or "an unreasonable application of" Strickland. In fact, Lamarca does not even discuss the state courts' legal conclusions in his § 2254 petition. Second, Lamarca has failed to establish the state courts made "an unreasonable determination of the facts." Lamarca has not put forth any evidence, much less clear and convincing evidence, to rebut the state courts' determinations that Eide made a strategic decision to limit his cross-examination of Tonya Flynn and that the statements from the police report "would not have undermined Tonya's credibility." See 28 U.S.C. § 2254(e)(1) ("[A] determination of a factual issue made by a State court shall be presumed to be correct. The applicant shall have the burden of rebutting the presumption of correctness by clear and convincing evidence."); Provenzano v. Singletary, 148 F.3d 1327, 1330 (11th Cir.1998) ("The question of whether an attorney's actions were actually the product of a tactical or strategic decision is an issue of fact, and a state court's decision concerning that issue is presumptively correct."). Accordingly, no jurist of reason would find the district court's denial of this claim debatable, see Slack, 529 U.S. at 484, 120 S.Ct. at 1604, and Lamarca is not entitled to a COA with respect to it.

3. Steve Slack
Lamarca alleges trial counsel was ineffective for failing to call Steve Slack as a witness to refute Tonya Flynn's version of what occurred when she returned to the bar after the alleged rape. Lamarca notes Slack told trial counsel, under oath, that Flynn did not discuss her husband's whereabouts with him or seem concerned following the alleged sexual battery. Lamarca maintains this statement contradicts Flynn's trial testimony. Lamarca originally raised this ground for relief in claim 9 of his 3.851 motion.
At the state evidentiary hearing, Lamarca's lead guilt phase counsel, Ron Eide, testified he decided not to call Slack because Slack had been drinking on the night of the murder and had provided inconsistent statements to investigators. Eide also believed Slack could have been a damaging witness for the defense; Slack testified in his deposition that Lamarca was upset when he left the bar, that Tonya Flynn was upset when she returned to the bar, and that Tonya said Lamarca had raped Tina, his other daughter.[7] After hearing both Eide's and Slack's testimony, the state trial court found Eide's explanation for not calling Slack "was well within the range of prevailing professional standards," and concluded Lamarca had failed to show, as required by Strickland, that his counsel's performance was deficient.
On appeal, the Florida Supreme Court affirmed, finding the decision not to call Slack was a reasonable strategy. Lamarca II, 931 So.2d at 849. The court articulated the test for ineffective assistance of counsel under Strickland, id. at 846-47, and then considered Eide's testimony at the state evidentiary hearing, id. at 849. Concluding the facts underlying trial counsel's assessment of Slack's credibility "were substantiated," the court determined the claim was properly denied. Id.
*939 Lamarca again raised this claim in his § 2254 petition, arguing Slack could have refuted Tonya Flynn's testimony and his trial counsel was ineffective for failing to present "this crucial contradicting impeachment information to the jury." The district court rejected this claim, concluding Lamarca had "failed to cite any clearly established federal law which establishes that the state court's resolution of this claim was improper or incorrect."
As with his ineffective assistance claim regarding the impeachment of Tonya Flynn, Lamarca does not cite any case law, including Strickland, in his discussion of this claim in his § 2254 petition. Furthermore, Lamarca does not provide, in either his § 2254 petition or his application for a COA, clear and convincing evidence to refute the state courts' determinations that Eide made a tactical decision not to call Slack and the facts underlying Eide's assessment of Slack's credibility were substantiated. See 28 U.S.C. § 2254(e)(1); Provenzano, 148 F.3d at 1330. Accordingly, reasonable jurists would not debate the district court's conclusions that the state courts' decisions were not "contrary to" or "an unreasonable application of" Strickland, or based on "an unreasonable determination of the facts." See Slack, 529 U.S. at 484, 120 S.Ct. at 1604; 28 U.S.C. § 2254(d)(1)-(2). We decline to issue a COA with respect to this claim.

4. James Zaccagnino
Lamarca argues trial counsel was ineffective for failing to present the testimony of James Zaccagnino to rebut the testimony of James Michael Hughes. Hughes testified at trial Lamarca had told him that he was going to kill his son-in-law. Hughes informed law enforcement Zaccagnino was present during the conversation. When questioned, Zaccagnino stated he never heard Lamarca make such a statement. Lamarca maintains Zaccagnino's testimony would have contradicted Hughes's testimony. This ground for relief was presented to the state courts as claim 8 in Lamarca's 3.851 motion.
The state trial court heard testimony from both Zaccagnino and Eide on this claim at the evidentiary hearing. Eide testified he chose not to call Zaccagnino as a witness because Zaccagnino had hearing difficulties, was a convicted felon serving a life sentence, and could not say unequivocally he was in the prison yard with Lamarca when the statements were made. Furthermore, Eide indicated he was concerned about any mention of "prison yard" in front of the jury.[8] The trial court found this testimony credible. It also noted Zaccagnino had trouble hearing at the evidentiary hearing, answering the first question asked of him incorrectly.[9] Based upon the testimony at the evidentiary hearing, the court concluded trial counsel's tactical decision "was well within the range of prevailing professional standards." It also determined Lamarca had failed to show the outcome would have differed if Zaccagnino had testified. Accordingly, the trial court found the claim failed under Strickland.
The Florida Supreme Court upheld the trial court's denial of this claim. Lamarca II, 931 So.2d at 849. After setting forth the standard under Strickland, id. at 846-47, the court addressed each of Lamarca's ineffective assistance of counsel claims, including *940 the failure to call Zaccagnino as a witness. With respect to this claim, the court found the facts underlying trial counsel's assessment of Zaccagnino's credibility were substantiated at the evidentiary hearing, and determined the decision not to call Zaccagnino was a reasonable strategy. Id. at 849. It thus concluded the trial court properly denied the claim. Id.
In his § 2254 petition, Lamarca maintained his trial counsel was ineffective for failing to call Zaccagnino as a witness, arguing his testimony would have cast "significant doubt about the veracity of Hughes' testimony." According to Lamarca, Zaccagnino's testimony at the state evidentiary hearing "not only rebutted Hughes [sic] testimony that Mr. Lamarca voiced the intent to kill his son-in-law, but also made it clear that Hughes had concocted his whole tale." Lamarca also noted, without citation to the record, that Zaccagnino's hearing problems did not exist in July 1995, the time of the alleged inculpatory statements. The district court rejected this claim, concluding that Lamarca had failed to cite any factual errors in the state court's resolution of the claim and that the state courts applied the correct Supreme Court precedent.
No reasonable jurist would debate the district court's assessment of this claim. See Slack, 529 U.S. at 484, 120 S.Ct. at 1604. In his § 2254 petition, Lamarca does not argue the state courts' decisions were "contrary to" or an "unreasonable application" of clearly established federal law. See 28 U.S.C. § 2254(d)(1). Nor does Lamarca point to any "unreasonable determination of the facts" on the part of the state courts. See id. § 2254(d)(2). Lamarca provides no support for his contention that Zaccagnino did not have hearing problems in 1995, and he ignores the state trial court's conclusions regarding the credibility of Eide's and Zaccagnino's testimony. Once again, Lamarca simply raises the same exact arguments he presented to the state courts, without explaining how the state courts' resolutions of this claim were erroneous. We decline to issue a COA.

B. Claim Two: Lamarca's Due Process Rights Were Violated When the State Failed to Disclose Exculpatory Evidence to the Defense and Presented False and Misleading Testimony
Lamarca claims the State violated his due process rights for not disclosing benefits James Michael Hughes and Jeremy Smith received for their testimony and for permitting false testimony from Hughes and Smith. In his COA application, Lamarca maintains the finding of the state courts and the district court that a deal is a requirement for a Brady violation is contrary to and an unreasonable application of clearly established law, citing United States v. Bagley, 473 U.S. 667, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985). He asserts "[t]he delay in sentencing Hughes [until after Lamarca's trial] in and of itself was a fact that was required to be disclosed." Lamarca also argues communications between the prosecution in his case and the prosecution in Hughes's case should have been turned over to the defense. With respect to Smith, Lamarca claims the State should have disclosed that one of its prosecutors was present at Smith's sentencing hearing. Lamarca raised this claim in two parts of his 3.851 motion claim 8 and claim 12in which he alleged Hughes and Smith received "deals," "benefits," or "agreements" from the State.
Under Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 1196-97, 10 L.Ed.2d 215 (1963), "the suppression by the prosecution of evidence favorable to an accused upon request violates due process where the evidence is material either to *941 guilt or to punishment, irrespective of the good faith or bad faith of the prosecution." A prosecutor's obligation to disclose evidence pursuant to Brady, however, is not limited to the disclosure of potentially exculpatory evidence; rather, due process also requires disclosure of impeachment evidence for cross-examination purposes. Bagley, 473 U.S. at 676, 105 S.Ct. at 3380. Thus, when the credibility of a witness is at issue, the prosecution also is required to disclose "evidence of any understanding or agreement as to a future prosecution." Giglio v. United States, 405 U.S. 150, 154-55, 92 S.Ct. 763, 766, 31 L.Ed.2d 104 (1972). Furthermore, under Giglio, the prosecution has a duty to correct false statements "[w]hen a witness conceals, through false testimony, his bias against the defendant, and the Government knows the witness has testified falsely." United States v. Meros, 866 F.2d 1304, 1309 (11th Cir.1989).
To prevail on a Brady claim, the petitioner must establish "(1) the government possessed evidence favorable to him; (2) the defendant did not possess the evidence and could not have obtained it with reasonable diligence; (3) the government suppressed the favorable evidence; and (4) the evidence was material." Davis v. Terry, 465 F.3d 1249, 1254 (11th Cir.2006). Evidence is material if there is a reasonable probability that a different result would have occurred had the evidence been disclosed. Kyles v. Whitley, 514 U.S. 419, 433, 115 S.Ct. 1555, 1565, 131 L.Ed.2d 490 (1995). In turn, a "reasonable probability" is understood to be "a probability sufficient to undermine confidence in the outcome." Bagley, 473 U.S. at 682, 105 S.Ct. at 3383.
After a five-day evidentiary hearing during which "much was made ... over whether Hughes received a benefit or promise in exchange for his testimony," the state trial court determined Lamarca had "failed to meet [his] burden of proving that Hughes received anything of benefit in exchange for his testimony," and thus denied this claim with respect to Hughes. The court similarly rejected the claim with respect to Smith, concluding the claim was based on "speculation" and Lamarca had failed to show that any promises were made to Smith, that the State withheld any evidence of a "deal," and that the State permitted false testimony by allowing Smith to testify he received no benefits in exchange for his testimony.
The Florida Supreme Court affirmed on appeal. In its discussion of this claim, the court explained the controlling law under Brady and Giglio, before analyzing, in great detail, the trial court's findings and the evidence presented by Lamarca. Lamarca II, 931 So.2d at 851-53. Based upon its review, the court concluded "the record d[id] not support Lamarca's claim that the State suppressed deals made with either Hughes or Smith in exchange for their testimony." Id. at 852. Because "the record contradict[ed] Lamarca's allegations" and the trial court's decision was "supported by competent, substantial evidence," the Florida Supreme Court denied Lamarca's Brady and Giglio claims. Id. at 853.
Lamarca raised these Brady and Giglio claims before the district court in his § 2254 petition. He asserted "the state possessed favorable information ... which would have impeached prosecution witnesses Hughes and Smiththe only witnesses who testified that Mr. Lamarca had planned and confessed to killing Kevin Flynn." He also maintained "the prosecution allowed false statements to go uncorrected as both Hughes and Smith each testified that they had not received any deal." The district court denied Lamarca relief on these grounds, noting the state *942 courts found there were no undisclosed deals or agreements with Hughes or Smith, and Lamarca failed to establish, by clear and convincing evidence, these factual findings were erroneous.
Jurists of reason would not debate the district court's assessment of Lamarca's Brady and Giglio claims. See Slack, 529 U.S. at 484, 120 S.Ct. at 1604. The state courts articulated the correct law under Brady and Giglio and then considered whether the State had offered a benefit or reward to, or made a deal or agreement with, either Hughes or Smith. Accordingly, Lamarca has failed to show the state courts' analyses were "contrary to" or "an unreasonable application of" clearly established federal law. See 28 U.S.C. § 2254(d)(1). Furthermore, the state courts made factual findings that there were no deals made or rewards offered in exchange for Hughes's or Smith's testimony, and Lamarca has not refuted these findings by clear and convincing evidence. See id. § 2254(e)(1). Thus, Lamarca has not demonstrated the state courts' decisions were "based on an unreasonable determination of the facts." See id. § 2254(d)(2). We conclude Lamarca has not made a substantial showing of the denial of a constitutional right, see id. § 2253(c)(2), and he is not entitled to a COA on this claim.

C. Claim Three: Lamarca's Due Process Rights Were Denied by the Trial Court's Limitation and Exclusion of Evidence and Abridgement of His Cross-Examination of Tonya Flynn.
Lamarca asserts the trial court denied him the right to defend against the charges by not allowing him to present evidence that Tonya and Kevin Flynn were getting a divorce, that Tonya argued with Kevin regarding his excessive drinking and sexual inadequacy, and that Tonya had engaged in an affair during a brief separation from Kevin a month and a half prior to the murder. Lamarca contends the district court's determination that the exclusion of this evidence was harmless error is debatable among jurists of reason. Furthermore, Lamarca maintains the Florida Supreme Court and the district court's conclusions were contrary to or unreasonable applications of clearly established law, citing Chapman v. California, 386 U.S. 18, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967).
Under both Florida and federal law, a trial court's decision to exclude evidence at trial is reviewed for abuse of discretion. Salazar v. State, 991 So.2d 364, 373 (Fla.2008); United States v. Tinoco, 304 F.3d 1088, 1119 (11th Cir.2002). A trial court's discretion regarding evidentiary issues, however, is subject to the requirements of the United States Constitution. See United States v. Lankford, 955 F.2d 1545, 1548 (11th Cir.1992). Among these requirements is a defendant's right to present a defense. See Chambers v. Mississippi, 410 U.S. 284, 294, 93 S.Ct. 1038, 1045, 35 L.Ed.2d 297 (1973) ("The right of an accused in a criminal trial to due process is, in essence, the right to a fair opportunity to defend against the State's accusations."). Thus, when a trial court's evidentiary rulings deprive a defendant of his right to present a defense, such rulings amount to constitutional error. Id. at 302-03, 93 S.Ct. at 1049.
A constitutional error, however, does not require an automatic reversal of a defendant's conviction and sentence. See Chapman, 386 U.S. at 21-22, 87 S.Ct. at 827. Rather, some constitutional errors may be "so unimportant and insignificant that they may, consistent with the Federal Constitution, be deemed harmless, not requiring the automatic reversal of the conviction." See id. at 22, 87 S.Ct. at 827. Under the harmless-error standard articulated *943 in Chapman and its progeny, a conviction may be affirmed only "if the reviewing court conclude[s] that, on the whole record, the error was harmless beyond a reasonable doubt." United States v. Hasting, 461 U.S. 499, 508, 103 S.Ct. 1974, 1980, 76 L.Ed.2d 96 (1983). Put differently, the reviewing court must consider "whether there is a reasonable possibility that the evidence complained of might have contributed to the conviction." See Chapman, 386 U.S. at 24, 87 S.Ct. at 828 (quoting Fahy v. Connecticut, 375 U.S. 85, 86, 84 S.Ct. 229, 230, 11 L.Ed.2d 171 (1963)). This standard is more stringent than the harmless-error standard used in habeas proceedings, under which a court must determine whether the error "had substantial and injurious effect or influence in determining the jury's verdict." See Brecht v. Abrahamson, 507 U.S. 619, 622-23, 113 S.Ct. 1710, 1713-14, 123 L.Ed.2d 353 (1993) (rejecting the Chapman standard in collateral proceedings and adopting a "less onerous" test).
Lamarca first argued the trial court's ruling limiting the evidence of Tonya Flynn's marital problems and extramarital affair violated his due process rights in his direct appeal of his conviction and sentence to the Florida Supreme Court. Lamarca's defense at trial was that Tonya Flynn murdered her husband. Prior to trial, however, the trial court granted in part the State's Motion in Limine to exclude allegations that the Flynns were getting a divorce or that Tonya had an extramarital affair. In his direct appeal, Lamarca argued the trial court's exclusion of this evidence limited his ability to establish Tonya Flynn had a motive to kill her husband, thus violating his due process rights to present evidence in support of his defense.
In its decision affirming Lamarca's conviction and sentence, the Florida Supreme Court concluded the trial court abused its discretion in excluding the evidence in question. Lamarca I, 785 So.2d at 1213. The court, however, found the abuse of discretion amounted to harmless error in light of the evidence supporting Lamarca's guilt, citing State v. DiGuilio, 491 So.2d 1129, 1135 (Fla.1986). Lamarca I, 785 So.2d at 1214. Lamarca again raised this issue in his § 2254 petition, and the district court agreed with the Florida Supreme Court's determination, concluding Lamarca had failed "to demonstrate that the Florida Supreme Court's harmless error analysis was inconsistent with any decision from the United States Supreme Court or was an unreasonable application of any such precedent. The sufficiency of the Florida Supreme Court's harmless error analysis is clearly established by a review of that Court's opinion."
No jurist of reason would conclude the decision of the district court was "debatable" or "wrong". See Slack, 529 U.S. at 484, 120 S.Ct. at 1604; 28 U.S.C. § 2254(d)(1). First, on direct review, the Florida Supreme Court used the harmless-error standard from DiGuilio, which, in turn, relies on Chapman. See DiGuilio, 491 So.2d at 1134-35 ("[W]e adopted the correct rule from Chapman and Hasting that constitutional errors, with rare exceptions, are subject to harmless error analysis. The harmless error test, as set forth in Chapman and progeny, places the burden on the state, as the beneficiary of the error, to prove beyond a reasonable doubt that the error complained of did not contribute to the verdict or, alternatively stated, that there is no reasonable possibility that the error contributed to the conviction."). Second, the district court articulated the correct harmless-error standard for habeas proceedings, citing to Brecht and noting "constitutional error will be considered harmless in a habeas proceeding *944 unless the error had substantial and injurious effect or influence on the verdict or sentence."
Finally, under either the Chapman or Brecht standard, the trial court's error was harmless in light of the other evidence supporting Lamarca's conviction. Indeed, evidence adduced at trial establishing Lamarca's guilt included his agitated state on the night of the murder; Tina Lamarca's testimony that Lamarca had told her that Kevin Flynn did not want Lamarca around Tonya Flynn or his child anymore; eyewitness accounts of Lamarca departing the bar with Kevin and in Kevin's car, and Lamarca later returning to the bar alone and with Kevin's car; the testimony of Stephanie Parker, who saw Lamarca and another man "arguing about something" outside Lamarca's trailer that night; the discovery of Kevin's body in Lamarca's trailer early the next morning; Lamarca's possession of the .22 rifle used to commit the murder in the days prior; Tonya Flynn's testimony that she saw Lamarca with the murder weapon after he raped her; the retrieval of the murder weapon from Joseph Lamarca's home; Lamarca's access to an ammunition box with .22 rounds; the discovery of a knife that Lamarca had carried prior to the murder near Kevin's body; Lamarca's statement five months before the murder that he wanted to kill Kevin; his statement to a friend the morning after the murder that he killed Kevin, that it "sucked," but that he had to do it; and his flight from law enforcement, which eventually took him to the state of Washington. Accordingly, no reasonable jurist would debate the district court's conclusion that the error did not have "substantial and injurious effect or influence in determining the jury's verdict." See Brecht, 507 U.S. at 623, 113 S.Ct. at 1714; Slack, 529 U.S. at 484, 120 S.Ct. at 1604. Lamarca is not entitled to a COA with respect to this claim.

IV. CONCLUSION
Lamarca has failed to make a "substantial showing of the denial of a constitutional right." See 28 U.S.C. § 2253(c)(2). Accordingly, we deny his application for a COA.
DENIED.
NOTES
[1]  Two of these claims were rejected at a case management conference, and one claim was added after the conference.
[2]  The evidentiary hearing took place at two separate times. On May 29, 2003, the trial court conducted a four-day evidentiary hearing. On June 27, 2003, the court heard additional testimony.
[3]  Lamarca filed his first petition for a writ of habeas corpus with the district court on June 22, 2006, and subsequently submitted three amended petitions to the court. On March 26, 2008, Lamarca filed his third and final amended petition for a writ of habeas corpus.
[4]  In his § 2254 petition to the district court, Lamarca also claimed he received ineffective assistance of counsel because (1) his trial counsel failed to call Lori Galloway as a witness to rebut the assertion that Lamarca fled the state of Florida after the murder of Kevin Flynn, (2) his trial counsel failed to call a forensic expert to testify as to the absence of physical evidence of the rape, (3) his trial counsel failed to investigate or effectively cross-examine the State's ballistics expert, and (4) his trial counsel failed to file a motion to suppress evidence seized from Joseph Lamarca's home after the murder. Lamarca has not requested a COA on claim 1 of his § 2254 petition with respect to these issues. Accordingly, we do not consider them.
[5]  In his third amended § 2254 petition before the district court, Lamarca also argued trial counsel was ineffective for failing to call Smith's best friend, John Ehrke, as a witness to testify Smith was "a known liar." This claim, however, was not presented to the state courts in Smith's direct appeal, his 3.851 motion for post-conviction relief, or his state habeas corpus motion, and, as the district court noted, Lamarca did not develop this claim during the state evidentiary hearing. Accordingly, Lamarca has not fulfilled § 2254's exhaustion requirements with respect to this claim, and, to the extent Lamarca raises this issue in his application for a COA, we conclude the district court's assessment of this claim is not debatable among jurists of reason. See Slack, 529 U.S. at 484, 120 S.Ct. at 1604; 28 U.S.C. § 2254(b)(1)(A), (b)(3).
[6]  Prior to Lamarca's trial, defense counsel filed a motion to limine to exclude evidence regarding the alleged sexual battery of Tonya Flynn, which was denied. During the State's direct examination of Tonya, the defense again objected to the introduction of any evidence related to the sexual battery, and the court noted the objection for the record. Defense counsel then attempted to impeach Tonya on the lack of physical evidence; however, the trial court, upon the State's objection, warned this line of questioning could waive defense's objection and allow the State to introduce additional evidence to corroborate and rehabilitate Tonya's testimony.
[7]  Prior to trial, defense counsel filed a motion in limine to prohibit the State from introducing evidence of the alleged sexual battery of Tina Lamarca, which the trial court granted.
[8]  Prior to trial, defense counsel filed a motion in limine to prohibit the State from introducing evidence or testimony regarding Lamarca's criminal convictions and stints in prison, which the trial court granted.
[9]  Okay. How are you employed?
A: How am I doing? Pretty good.
