On October 11, 2001, Richard Charles Duncan (“Duncan”) filed an application for federal writ of habeas corpus in the Southern District of Texas. On August 1, 2001, the district court granted the State’s motion for summary judgment and declined to issue a certificate of appealability (“COA”). Duncan now comes to this Court seeking a COA. We deny his request.
FACTS AND PROCEDURAL HISTORY
On May 25, 1995, Richard Charles Duncan (“Duncan”) was convicted of capital murder for the 1987 deaths of John and Ruth High (“the Highs”) and sentenced to death. On October 8, 1987, Ken High, one of the Highs’ two adult sons, found the Highs dead in their home. Ruth High was found in bed and John High was lying in a *743pool of blood on the kitchen floor. A gas cooker was also found connected to an open gas jet behind a washing machine. The open gas jet filled the room with a gas odor. The deaths were originally thought to be accidental, thus the house was not maintained as a crime scene. Autopsies later revealed that John High had been struck in the head with an unknown object, resulting in six lacerations, and Ruth High had been smothered to death. There was no forensic evidence put forth at trial tying Duncan to the murders.
Gary High, the Highs’ other son, had been in a homosexual relationship with Duncan for over twenty years. At some point, a third man, Robert Alexander, became involved with both Duncan and Gary High. The three were intimately involved and lived together. Duncan and Gary High were also business partners in a computer software business named Hitech Microsystems (“Hitech”).
The murder cases sat dormant until August 1993 when Robert Alexander made an anonymous call to the Houston Police Department. The police ascertained the identity of the caller as Robert Alexander, he was granted immunity, and the police arranged for him to tape phone conversations between he and Duncan who was then living in Seattle. Duncan made incriminating statements during the phone calls and a warrant was issued for Duncan’s arrest. After his arrest in Seattle, Duncan made a taped statement in which he characterized the killings as “mercy killings.” He stated that Ruth High had complained to him about John High’s deteriorating health and had asked Duncan to arrange for she and John High to be killed. He further explained that he had. arranged for a Mexican yard worker, named Oscar Rodriguez, to kill the Highs for $5,000.1 He also explained that he had originally told Robert Alexander that he killed the Highs because he wanted the Mexican yard worker to escape free and clear.
Robert Alexander testified at Duncan’s trial that Duncan had called he and Gary High in Seattle from the Hitech office in Houston on October 7 and 8, 1987 and admitted that he had killed the Highs. Robert Alexander further testified that prior to the murders Hitech had run into financial difficulties and that Duncan had speculated about ways to kill the Highs so that Gary High could come into his inheritance.2 These plans included using a propane gas cooker to create a gas leak to make the deaths appear accidental. Finally, Robert Alexander testified that he, Duncan, and Gary High met after the murders to devise a common story to tell the police.
In addition to the testimony of Robert Alexander and Duncan’s own admissions, the State also relied on the testimony of the Highs’ then-neighbor Kyle Christoffel to convict Duncan. The neighbor testified that on the morning after the murders, Duncan explained to him that John High had purchased a gas shrimp cooker, hooked it to a gas jet in the utility room, attempted to light it, then became tangled in the hose and fell.
Duncan was convicted on May 25, 1995 and sentenced to death. On October 8, 1997, Duncan’s conviction and sentence were affirmed on direct appeal to the Texas Court of Criminal Appeals. Duncan v. State, No. 72,132 (Tex.Crim.App. Oct. 8, *7441997) (en banc). The U.S. Supreme Court denied certiorari. Duncan v. State, 525 U.S. 829, 119 S.Ct. 80, 142 L.Ed.2d 62 (1998). On October 11, 2001, Duncan’s state application for post-conviction writ of habeas corpus was denied. Ex Parte Richard Charles Duncan, No. 46,927-01 (Tex.Crim.App. Oct. 11, 2000). On the same day, Duncan filed his application for federal writ of habeas corpus in the Southern District of Texas raising 16 issues. On August 1, 2002, the district court granted the State’s motion for summary judgment and declined to issue a COA. Duncan now seeks a COA from this Court.
Duncan raises four errors in his application for a COA. He contends that: (1) the district court erred in concluding that Duncan failed to establish that the testimony of Robert Alexander was false and that the prosecutor knew it was false, in violation of his due process rights; (2) the district court erred in finding that Duncan’s claim of actual innocence based on newly discovered evidence was not cognizable on federal habeas review; (3) the district court erred in finding that the state court’s determination that the facts of the offense alone were sufficient to support a finding of future dangerousness was reasonable; and (4) the district court erred in determining that the Constitution does not require appellate review of the jury’s weighing of Duncan’s mitigating evidence. For the following reasons, we deny Duncan’s request for a COA.
DISCUSSION
In order to obtain a COA, the petitioner must demonstrate “a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). “A petitioner satisfies this standard by demonstrating that jurists of reason could disagree with the district court’s resolution of his constitutional claims or that jurists could conclude the issues presented are adequate to deserve encouragement to proceed further.” Miller-El v. Cockrell, 537 U.S. 322, 123 S.Ct. 1029, 1034, 154 L.Ed.2d 931 (2003).
I. Due Process Claim — False Testimony
Duncan contends that his right to Due Process was violated because the State knowingly used the false and misleading testimony of Robert Alexander to secure his conviction. Duncan made the same contention in his state writ of habeas corpus and supported his claim with an affidavit from Gary High executed on March 26, 1998. Gary High was not presented as a witness by either party during Duncan’s trial. Duncan argues that Gary High’s affidavit constitutes newly discovered evidence “strongly contradicts the trial testimony of Mr. Alexander, and shows his true bias and motive for testifying against [Duncan].”
“A state denies a criminal defendant due process when it knowingly uses perjured testimony at trial or allows untrue testimony to go uncorrected.” Faulder v. Johnson, 81 F.3d 515, 519 (5th Cir.1996). In order to establish a due process violation Duncan must show:
(1) the evidence was false, (2) the evidence was material,3 and (3) the prosecution knew that the evidence was false. Evidence is “false” if, inter alia, it is specific misleading evidence important to the prosecution’s case in chief. False evidence is “material” only if there is any reasonable likelihood that it could have affected the jury’s verdict.
Nobles v. Johnson, 127 F.3d 409, 415 (5th Cir.1997) (citations and internal quotation marks omitted).
*745A. Falsity of Robert Alexander’s Testimony
The state habeas court found that Gary High’s affidavit was “suspect and contradicted by [Duncan’s] own statements made after his arrest and during taped telephone conversations concerning the offense.” Factual determinations made by the state court are presumed to be correct. “[T]he petitioner can rebut this presumption by clear and convincing evidence.” Dowthitt v. Johnson, 230 F.3d 733, 741 (5th Cir. 2000); see also 28 U.S.C. § 2254(e)(1). “Absent an unreasonable determination in light of the record, [federal courts] give deference to the state court’s fact findings.” Dowthitt, 230 F.3d at 741; see also § 2254(d)(2).
The district court found that Gary High’s affidavit did not establish that Robert Alexander’s testimony was false because several statements in Gary High’s affidavit are inconsistent with Duncan’s own statements. Specifically, Duncan admitted: (1) that he had spoken to Robert Alexander over the phone wherein he took responsibility for the murders; (2) that either Hitech Microsystems, or Duncan, Robert Alexander, and Gary High as individuals, borrowed money from the Highs; and (3) the loan was evidenced by a note. A review of the record indicates that the district court’s assessment was correct, Gary High’s affidavit is in fact contradicted by Duncan’s own words.4
Duncan further argues that the state court’s rejection of Gary High’s affidavit was not entitled to deference by the district court because Duncan was not afforded an evidentiary hearing. Essentially, Duncan contends that the state court could not make a credibility determination from a paper hearing. Duncan asserts that the paper hearing was inadequate because the state court did not have anything to compare Gary High’s affidavit to, for purposes of making a credibility determination, because Gary High did not testify at Duncan’s trial.
The State contends that we cannot review Duncan’s inadequate hearing argument because he did not raise the argument in the district court. See Johnson v. Puckett, 176 F.3d 809, 814 (5th Cir.1999). Duncan stated in his general statement at the beginning of his federal writ of habeas corpus that deference to the state court’s findings is required only when the state court hearing was “full and fair.” In his argument regarding the perjured testimony, Duncan merely requested an evidentiary hearing on the issue. He did not make the argument he makes on appeal, i.e. that the paper hearing was inadequate with regard to the state court’s rejection of Gary High’s affidavit. Thus, he waived this argument.
Assuming arguendo that Duncan’s inadequate hearing argument is not waived, it clearly fails to persuade us that a COA is warranted. Duncan cites to May v. Collins, 955 F.2d 299 (5th Cir.1992) for support. In May, the petitioner presented affidavits from two witnesses recanting their earlier trial testimony. The petitioner attached the affidavits to his state writ of habeas corpus. Similar to Duncan, May *746argued that the affidavits showed that the prosecutors knowingly used perjured testimony in violation of his due process rights. May, 955 F.2d at 305. The state court, without holding a hearing, found that the affidavits were “not credible and ... are unworthy of belief’ based on the fact that the affidavits were contradicted by the petitioner’s own admissions to others placing him at the scene of the murders. Id. at 305-06. During the petitioner’s federal habeas proceeding, the State argued that “the state court’s resolution of the factual issues on the basis of affidavits constituted a ‘hearing’ within the meaning of § 2254(d) sufficient to trigger the presumption [of correctness].” Id. at 306 (referencing the previous version of § 2254). This Court explained that the “presumption of correctness does not become inapplicable for the sole reasons that no five evidentiary hearing has been held.” Id. at 311. This Court held that the presumption of correctness in May was appropriate because the same judge who presided over the petitioner’s trial reviewed his writ of habeas corpus. Id. at 314. The Court reasoned that the trial judge could “compare the information presented in the various affidavits against his own firsthand knowledge of the trial” wherein both of the affiants testified. Id.
In this case, Duncan argues that the paper hearing was inadequate because the state trial judge had nothing for comparison because Gary High did not testify at trial. Although May is relevant, May is a pre-AEDPA case. As the State correctly points out, AEDPA “jettisoned all references to a ‘full and fair hearing’ from the presumption of correctness accorded state court findings of fact.” Valdez v. Cockrell, 274 F.3d 941, 949 (5th Cir.2001), cert. denied, 537 U.S. 883, 123 S.Ct. 106, 154 L.Ed.2d 141 (2002). “To reintroduce a full and fair healing requirement that would displace the application of § 2254(e)(l)’s presumption would have the untenable result of rendering the amendments enacted by Congress a nullity.” Id. at 949-50. Consistent with Valdez, Duncan can defeat the presumption of correctness only with clear and convincing evidence. Duncan failed to properly assert his inadequate state hearing argument to the district court, let alone submit clear and convincing evidence to defeat the presumption of correctness.
B. The State’s Knowledge of the Falsity
Duncan contends that the State knew that Robert Alexander’s testimony was false. Duncan claims that the State’s knowledge can be inferred from several factors: (1) Robert Alexander provided evidence only after he was granted immunity; (2) the State should have questioned the veracity of his testimony because he was able to recall details about trivial matters, but not important matters like the weapon Duncan allegedly told him he used to kill the Highs; (3) Robert Alexander’s character for untruthfulness came to light during cross-examination; and (4) the State failed to call Gary High as a witness.
The first three of these factors were squarely put before the jury. If the jury did not reject Robert Alexander’s testimony as false for these reasons, it would be absurd to impute the State with knowledge that Robert Alexander testified falsely for the very same reasons. Regarding Duncan’s fourth contention — that one can infer knowledge of falsity from the fact that Gary High was not called as a witness for the State — the district court found no evidence in the record to indicate that Gary High was ever subpoenaed by the State to be a witness. Indeed, Duncan concedes in his brief that “there is no evidence in the record indicating that the State made a last minute decision not to call Gary High as a witness.” Duncan’s assertions simply *747cannot reasonably lead to the conclusion that the State knew of any alleged false testimony by Robert Alexander.
In sum, we find that Duncan has failed to make a substantial showing that he was denied due process based on the State’s knowing use of false testimony. Reasonable jurists would not find the district court’s assessment of Duncan’s due process claim debatable or wrong. See Miller-El, 537 U.S. 322, 123 S.Ct. 1029 at 1039, 154 L.Ed.2d 931.
II. Actual Innocence
Duncan asserts that the district court erred when it found that his actual innocence claim was not cognizable on federal habeas review. “Claims of actual innocence based on newly discovered evidence have never been held to state a ground for federal habeas relief absent an independent constitutional violation occurring in the underlying state criminal proceeding.” Herrera v. Collins, 506 U.S. 390, 400, 113 S.Ct. 853, 122 L.Ed.2d 203 (1993). Duncan argues that the independent constitutional claim is the State’s knowing use of perjured testimony discussed above. As the State correctly points out, an actual innocence claim is merely a basis upon which a habeas petitioner can obtain consideration on the merits of an otherwise procedurally barred or defaulted independent constitutional claim. Duncan’s due process claim is not procedurally barred. Accordingly, we deny a COA on this issue.
III. Sufficiency of the Evidence — Affirmative Answer to the Future Dangerousness Special Issue
At the punishment phase of Duncan’s trial, the prosecution offered no additional evidence aside from the evidence it offered during the guilt phase. Under Texas law, a jury may consider, but is not limited to, several factors in determining future dangerousness: the circumstances of the offense, including the defendant’s state of mind; the calculated nature of the defendant’s acts; forethought and deliberateness; prior criminal record, and the severity of prior crimes; the defendant’s age and personal circumstances at the time of the offense; whether the defendant was acting under duress or domination of another; psychiatric evidence; and character evidence. Keeton v. State, 724 S.W.2d 58, 61 (Tex.Crim.App.1987).
The state court found that, based on the facts of the crime, there was sufficient evidence to support the jury’s finding of future dangerousness. Specifically, the state court pointed out that Duncan initially denied involvement in the murders, then later admitted his involvement in arranging the so-called “mercy killings”; the evidence revealed that the murders were brutal; Duncan devised his scheme to kill over a month or two before; Duncan did not show remorse for his crimes; and Duncan continued to shift the blame to others. The district court found that the state court’s “holding that a rational jury could find that the evidence such as that listed above demonstrated [Duncan’s] future dangerousness was not unreasonable.” We find that reasonable jurists would not find the district court’s assessment debatable or wrong.
IV. Sufficiency of the Evidence — Negative Answer to the Mitigation Special Issue
Duncan argues that the state habeas court erred by refusing to review his claim of insufficient evidence pertaining to the jury’s negative response to the mitigation special issue. The district court found that a jury may “constitutionally assign to the mitigating evidence any weight it deems appropriate.”
In Woods v. Cockrell, this Court reaffirmed its earlier decision in Moore v. Johnson, 225 F.3d 495 (5th Cir.2000), hold*748ing that “the sentencer may be given unbridled discretion in determining whether the death penalty should be imposed after it has found that the defendant is a member of the class made eligible for that penalty.” 307 F.3d 353, 359 (5th Cir.2002). This Court held that the Texas Court of Criminal Appeals can properly refrain from reviewing such a subjective determination made on the part of individual jurors. Id. Accordingly, we deny Duncan’s request for a COA on this final issue.
CONCLUSION
For the reasons outlined above, we deny Duncan’s request for a COA.
DENIED.