ORDER DENYING CERTIFICATE OF APPEALABILITY AND DISMISSING APPEAL*
Mark Jordan, a federal prisoner, seeks a certificate of appealability (COA) to challenge the district court’s denial of his motion to vacate, set aside, or correct his *773sentence under 28 U.S.C. § 2255. Exercising jurisdiction under 28 U.S.C. § 1291, we deny the COA and dismiss the appeal.
BACKGROUND
Mr. Jordan was convicted of the stabbing death of fellow inmate David Stone in the yard of the federal penitentiary in Florence, Colorado, and sentenced to 420 months’ imprisonment. We affirmed his conviction and sentence. See United States v. Jordan, 485 F.3d 1214 (10th Cir.2007). As we recounted, two eyewitnesses testified at trial that Mr. Jordan stabbed Mr. Stone then chased him across the prison yard. Id. at 1216. Other witnesses observed Mr. Jordan throwing an object, which turned out to be a knife, on the roof of a housing unit. Id. at 1217. Additional evidence linking Mr. Jordan to the attack included his DNA on the knife and a video recording of him approaching Mr. Stone immediately before the attack and then chasing Mr. Stone (the attack itself occurred outside the camera’s view). Id. Nonetheless, Mr. Jordan’s defense was that another inmate, Sean Riker, stabbed Mr. Stone and forced the knife on Mr. Jordan. Id. at 1220. Mr. Jordan then panicked, ran, and threw the knife on the roof. Id. Neither Mr. Jordan nor Mr. Riker testified at trial.
As part of his direct appeal, Mr. Jordan petitioned the United States Supreme Court for a writ of certiorari, which the Court denied on November 13, 2007. Mr. Jordan consequently had one year from that date (until November 13, 2008) to file his § 2255 motion. See 28 U.S.C. § 2255(f)(1).1
On February 5, 2008, the district court appointed counsel to assist Mr. Jordan with filing a petition for habeas corpus relief. On August 5, 2008, appointed counsel filed a motion in the criminal case for a writ of habeas corpus and for a new trial. On October 28, 2008, the district court denied the motion for a new trial as untimely under Fed.R.Crim.P. 33(b)(2) and determined that to the extent Mr. Jordan sought to challenge his conviction on constitutional grounds under 28 U.S.C. § 2255, it had to be filed in a separate, collateral proceeding. Appointed counsel then allegedly informed Mr. Jordan that counsel would not represent him in a § 2255 proceeding. Cognizant that the one-year period for filing a § 2255 motion would soon end, Mr. Jordan filed a pro se, sixty-five page § 2255 motion. On May 13, 2009, he filed an amended pro se § 2255 motion that, by the district court’s count, contained seven claims with a total of 102 subclaims.
The district court issued a detailed, 124-page order denying the § 2255 motions, finding many of the subclaims untimely or procedurally defaulted and the rest merit-less. The district court later denied Mr. Jordan’s motion for relief from judgment under Fed.R.Civ.P. 59(e), and denied his application for a COA. Mr. Jordan retained counsel and has renewed his request for a COA in this court.
DISCUSSION
A. Standard of Review
A COA is a jurisdictional prerequisite to an appeal from the denial of a § 2255 motion. See 28 U.S.C. § 2253(c)(1)(B); Miller-El v. Cockrell, 537 U.S. 322, 336, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003). A COA may be issued “only if the applicant has made a substantial showing of the *774denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). For those claims the district court denied on the merits, Mr. Jordan “must demonstrate that 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, 146 L.Ed.2d 542 (2000). For those claims the district court denied on a procedural ground, Mr. Jordan must show “that jurists of reason would find it debatable whether the petition states a valid claim of the denial of a constitutional right and ... whether the district court was correct in its procedural ruling.” Id. Because Mr. Jordan proceeded pro se in the district court, we construe his filings in that court liberally, but we do not act as his advocate. See Yang v. Archuleta, 525 F.3d 925, 927 n. 1 (10th Cir.2008).
B. Equitable Tolling
In his application for a COA, Mr. Jordan first argues the district court should have applied equitable tolling to subclaims in his amended motion that did not relate back to his original motion because appointed counsel abandoned him less than two weeks before the one-year deadline (November 13, 2008) to file his § 2255 motion. The court concluded that Mr. Jordan was not entitled to equitable tolling because he “failed to vigilantly oversee appointed counsel’s actions” and had not acted with “reasonable diligence.” Aplt.App. at 1183. The court also found that Mr. Jordan had not established an exception to § 2255(f)’s one-year limitations period by making a showing of factual innocence. See id. at 1184.
We acknowledge Mr. Jordan’s argument that the conduct of his appointed counsel satisfies the requirements for equitable tolling laid out by the Supreme Court in Holland v. Florida, — U.S. -, 130 S.Ct. 2549, 177 L.Ed.2d 130 (2010); however, Holland left equitable tolling to the discretion of district courts. Having considered the record and Mr. Jordan’s arguments, we cannot say that the district court abused its discretion by refusing to find that Mr. Jordan’s appointed counsel’s conduct was so egregious as to warrant equitable tolling. Mr. Jordan was able to file his initial § 2255 motion within the deadline followed by an amended motion in May 2009. Thus, Mr. Jordan is not entitled to a COA on this issue.2
C. Relation Back
Mr. Jordan next claims the district court erred in concluding that a number of sub-claims raised in his amended motion did not relate back to his original motion. “An amended habeas petition ... does not relate back ... when it asserts a new ground for relief supported by facts that differ in both time and type from those the original pleading set forth.” Mayle v. Felix, 545 U.S. 644, 650, 125 S.Ct. 2562, 162 L.Ed.2d 582 (2005). A district court’s findings as to whether an amended claim relates back to an original § 2255 motion are reviewed for abuse of discretion. United States v. *775Espinoza-Saenz, 235 F.3d 501, 505 (10th Cir.2000).
Mr. Jordan first argues that his amended subclaim that trial counsel was ineffective in failing to affirmatively invoke his Fifth Amendment right to present a defense and his Sixth Amendment right to compulsory process (Claim 3.a.) relates back to one of his original claims, which he characterizes in the same terms. However, Mr. Jordan initially contended only that “it was unreasonable for trial counsel to present no evidence to explain why prisoner witnesses were not cooperating with the defense,” Aplt.App. at 79,3 and later contended that, but for counsel’s failure to preserve an objection to the district court’s denial of a proffer regarding the alternate perpetrator (Mr. Riker), the standard of review on appeal would have been de novo, not an abuse of discretion, id. at 302. Clearly, the supporting facts for the amended subclaim were different in type than the original claim, and the amended subclaim therefore did not relate back. See Mayle, 545 U.S. at 650, 125 S.Ct. 2562.
Mr. Jordan next contests the district court’s finding that two amended sub-claims regarding trial counsel’s failure to interview Rudy Sabían and Frankie Quina-ta and call them as witnesses (Claims 3.bb. and 3.cc.) did not relate back to the original motion. As Mr. Jordan points out, the district court rendered a decision on the merits of a different subclaim (Claim 3.11.) that trial counsel was ineffective in failing to investigate witnesses generally. In so doing, the court referred to Mr. Sabian and Mr. Quinata specifically, notwithstanding the court’s ruling earlier in its decision that the amended subclaims specifically regarding them did not relate back. Compare Aplt.App. at 1249-50 with id. at 1267-68. Accordingly, we will instead consider whether to grant a COA on the district court’s merits decision regarding trial counsel’s failure to investigate or call Mr. Sabían and Mr. Quinata rather than Mr. Jordan’s request for a COA on the relation-back issue.
As the district court concluded, Mr. Jordan did not show that counsel’s failure to investigate Mr. Sabían or Mr. Quinata constituted ineffective assistance under the standard announced in Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). In the specific context of an uncalled witness, he must also show “that the testimony of an uncalled witness would have been favorable” and that “the witness would have testified at trial.” Snow v. Sirmons, 474 F.3d 693, 731 n. 42 (10th Cir.2007) (brackets omitted) (quotation omitted).
As to Mr. Quinata, Mr. Jordan provided only his own allegations of the proposed testimony, not an affidavit or other competent evidence regarding the content of Mr. Quinata’s proposed testimony or his willingness to testify. Accordingly, he failed to meet his burden under Snow and therefore is not entitled to a COA with regard to trial counsel’s failure to investigate or call Mr. Quinata.
In contrast, Mr. Jordan provided a declaration from Mr. Sabían stating he was willing to testify that he did not hear or see any person other than one lieutenant visit Mr. Jordan in the Special Housing Unit (SHÚ) where Mr. Jordan was placed after the attack on Stone. See ApltApp. at 459-60. Mr. Jordan contends this testimony would impeach that of a physician’s assistant, Mr. Erzouki, who testified at trial that he examined Mr. Jordan in the SHU and observed him flash a “V” sign *776with his hand to another inmate and state “Guy, I get him out of your way.” Id. at 2419:21-23. However, at best, Mr. Sablan’s proposed testimony would have impeached Mr. Erzouki as to the location of his observation (which was one subject of defense counsel’s cross-examination of Mr. Erzouki at trial), but any effect on the credibility of what Mr. Erzouki observed would have been minimal; certainly not enough for us to conclude, in light of the other evidence that Mr. Jordan stabbed Mr. Stone, that there is a reasonable probability the outcome would have been different had trial counsel investigated Mr. Sabían and called him to testify. Accordingly, Mr. Jordan is not entitled to a COA regarding trial counsel’s failure to investigate or call Mr. Sabían.
Regarding the next amended sub-claim on which he seeks a COA, Mr. Jordan originally alleged that trial counsel was ineffective in failing to allow him to testify at trial. In his amended motion, he reiterated substantially the same subclaim but added a new subclaim (Claim 4.a.) that the district court erred in refusing defense counsel’s request for an advisement of his right to testify. Mr. Jordan is not entitled to a COA on this ruling. While he mentioned the district court’s refusal to give an advisement in his original subclaim, he claimed error only in trial counsel’s actions, not those of the district court. Thus, the amended subclaim’s supporting facts were different in type. Consequently the amended subclaim did not relate back to the original motion. See Mayle, 545 U.S. at 650, 125 S.Ct. 2562.
The final relation-back issue on which Mr. Jordan seeks a COA consists of four subelaims concerning the government’s failure to disclose exculpatory or impeachment evidence, as required under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). We will consider the first two amended Brady subclaims together before turning to the other two.
In the first subclaim (Claim l.j.), Mr. Jordan alleged the government should have disclosed video recordings of the SHU entry and a lieutenant’s corridor. In the second subclaim (Claim l.k.), he contended the government should have disclosed Tyrone Davis’s agreement with the government for lenient treatment in exchange for his testimony against Mr. Jordan. Mr. Davis testified that he was selling items in the prison yard when he witnessed Mr. Jordan push or punch Mr. Stone in the back or side and run after Mr. Stone. Id. at 2369-72. Mr. Jordan alleged that Mr. Davis has since admitted his testimony was perjured. Id. at 631— 32.
Mr. Jordan does not argue that these amended subclaims relate back. Instead, he contends that he only discovered this evidence in June 2008, less than one year before he filed his amended § 2255 motion, and therefore the amended subclaims were timely under § 2255(f)(4), which triggers a one-year period for filing a § 2255 motion from “the date on which the facts supporting the claim or claims presented could have been discovered through the exercise of due diligence.” However, Mr. Jordan has not satisfied the “due diligence” portion of the § 2255(f)(4) inquiry. Concerning the video recordings, he alleged only that he did not discover them until June 2008 “through investigations of staff and other prisoners.” Aplt.App. at 630-31. Regarding Mr. Davis, he maintained that, “following the trial in this case,” which took place in August 2005, Mr. Davis contacted him to apologize for testifying falsely against him and revealed the agreement with the government. Id. at 268. Mr. Jordan added, in his reply in support of his amended § 2255 motion, that he “did not become aware of the undisclosed Davis *777agreement or of Davis’ willingness to now admit his testimony was perjured until June 2008.” Id. at 632. Because Mr. Jordan did not explain why he could not have obtained any of this information at an earlier date through diligent efforts, a COA is not warranted on these subclaims.
In the third amended Brady sub-claim that Mr. Jordan claims relates back to his original § 2255 motion (Claim II), he alleged the government should have disclosed Mr. Davis’s work record because it would show that, at the time of the attack, Mr. Davis was in the prison food service building, not in the yard, which suggests he could not have witnessed the attack. Id. at 270. Mr. Jordan contends this amended subclaim relates back to one paragraph in his original motion supporting his claim of actual innocence, that “one witness states he was in food service with Tyrone Davis at time of homicide and neither did [n]or could have witnessed assault from their location.” Id. at 109, ¶ 281. We disagree. The original subclaim centered on a different witness and did not raise a Brady issue with regard to Mr. Davis’s work record. Accordingly, the factual basis for the amended subclaim differed in type from the original claim, and the amended subclaim therefore did not relate back to the original motion. See Mayle, 545 U.S. at 650, 125 S.Ct. 2562. Thus, Mr. Jordan is not entitled to a COA on this subclaim.
The final amended Brady subclaim that Mr. Jordan claims relates back to his original § 2255 motion (Claim l.m.) concerns certain material subject to protective orders that permitted disclosure to his trial counsel but barred disclosure to him personally. He claims the government was required to disclose the material to him personally under Brady and Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972).4 He argues this subclaim relates back to a claim in his original motion that counsel was ineffective for agreeing to the protective orders without informing or consulting with him. We again disagree. The amended subclaim is based on facts that are different in type than those in the original claim. The amended subclaim therefore does not relate back to the original motion, see Mayle, 545 U.S. at 650, 125 S.Ct. 2562, and Mr. Jordan is not entitled to a COA on it.
D. Procedural Default/Z?ra% Claims
Mr. Jordan next seeks a COA regarding the district court’s conclusion that eight Brady subclaims (Claim 1., subclaims b.-i.) were procedurally defaulted under United States v. Frady, 456 U.S. 152, 102 S.Ct. 1584, 71 L.Ed.2d 816 (1982). Under Frady, the “failure to raise an issue either at trial or on direct appeal imposes a procedural bar to habeas review.” United States v. Barajas-Diaz, 313 F.3d 1242, 1245 (10th Cir.2002).5 A § 2255 movant may overcome procedural default by establishing cause and actual prejudice, Frady, 456 U.S. at 167, 102 S.Ct. 1584 (quotation omitted), or by showing that a constitutional error “has probably resulted in the conviction of one who is actually innocent,” Murray v. Carrier, 477 U.S. 478, 496, 106 *778S.Ct. 2639, 91 L.Ed.2d 397 (1986). To show cause, a petitioner must identify “some objective factor external to the defense [that] impeded ... efforts to comply with the [relevant] procedural rule.” Id. at 488, 106 S.Ct. 2639.
The district court determined that Mr. Jordan had not shown cause under the Murray standard for failing to raise these Brady claims on direct appeal. As he argued in his Rule 59(e) motion in the district court, Mr. Jordan contends that his Brady claims as a group are not subject to procedural default on collateral review because he did not discover the factual bases of these claims until after his trial (and, for some claims (he does not specify which) until after his direct appeal). He concludes it would have been inappropriate or impossible to raise these claims on direct appeal because there would have been no district court record for review. Mr. Jordan also argues that the district court erred in concluding that three specific Brady subclaims were procedurally defaulted.
We need not decide whether a Frady analysis is inapplicable in these circumstances. The district court decided these subclaims on a procedural ground, so Mr. Jordan must show “that jurists of reason would find it debatable whether the petition states a valid claim of the denial of a constitutional right and ... whether the district court was correct in its procedural ruling.” Slack, 529 U.S. at 484, 120 S.Ct. 1595 (emphasis added). Under Brady, the failure to disclose evidence favorable to a criminal defendant “violates due process where the evidence is material either to guilt or to punishment.” Brady, 373 U.S. at 87, 83 S.Ct. 1194. “For the evidence to be material, there must be ‘a reasonable probability that the result of the trial would have been different if the suppressed documents had been disclosed to the defense.’ ” United States v. Ford, 550 F.3d 975, 981 (10th Cir.2008) (quoting Stnckler v. Greene, 527 U.S. 263, 289, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999)). Having reviewed Mr. Jordan’s arguments regarding the materiality of the evidence allegedly withheld in violation of Brady in light of the other evidence at trial, we conclude he has not made a sufficient showing of Brady materiality. Thus, his petitions fail to state “a valid claim of the denial of a constitutional right.” Slack, 529 U.S. at 484, 120 S.Ct. 1595. Accordingly, we deny a COA on these subclaims.
E. Procedural Default/Intrusion on Attorney-Client Relationship
Mr. Jordan next claims the district court erred in applying procedural default to his subclaim that the government intruded on attorney-client privilege by monitoring communications in non-contact visiting booths at the prison where he was incarcerated without disclosing the monitoring (Claim 2.g.). He argues he did not discover this alleged violation until sentencing and therefore could not have raised it on direct appeal because there was no factual record to consider. He also contends the issue requires further factual development to determine whether there is constitutional error.
To the extent Mr. Jordan is renewing his contention that Frady’s procedural default rule does not apply when there is an insufficient record for consideration of an issue on direct appeal (other than ineffective assistance of counsel), we again decline to consider it because he has not shown “that jurists of reason would find it debatable whether the petition states a valid claim of the denial of a constitutional right.” Id. at 484, 120 S.Ct. 1595. Thus, we deny a COA on this subclaim.
F. Merits of one Brady Subclaim
Finally, Mr. Jordan contends the district court erred in ruling on the merits of one *779Brady subclaim relating to a lieutenant’s log book (Claim l.a.). As with his sub-claim regarding trial counsel’s failure to investigate and present Mr. Sablan’s testimony, Mr. Jordan contends that the log book would show that the physician’s assistant, Mr. Erzouki, was mistaken about the time and location of his examination of Mr. Jordan.
The district court concluded that the lieutenant’s log book was not material under Brady for two reasons. First, defense counsel used other evidence at trial to impeach Mr. Erzouki regarding the time and location of the examination, and second, nothing in the undisclosed log book suggested Mr. Jordan could not have made the “V” sign or stated to the other inmate, “Guy, I get him out of your way.” We agree with the district court’s analysis and therefore deny a COA on this subclaim.
CONCLUSION
For the foregoing reasons, we DENY Mr. Jordan’s application for a certifícate of appealability and DISMISS his appeal.