MARTIN, Circuit Judge:

John Duncan Fordham and Robin L. Williams appeal from the District Court's denial of their habeas petitions, brought pursuant to 28 U.S.C. § 2255. The District Court denied each of their petitions, holding that their claims were procedurally defaulted, but did not reach the merits. The District Court then granted a certificate of appealability on the procedural default issue. Mr. Fordham and Mr. Williams each seek to vacate their convictions and sentences, and we consolidated their appeals for consideration here.

"We review de novo a district court's grant or denial of a habeas corpus petition. The district court's factual findings are reviewed for clear error, while mixed questions of law and fact are reviewed de novo." McNair v. Campbell, 416 F.3d 1291, 1297 (11th Cir.2005) (internal citation omitted). The issue of whether a habeas petitioner's claims are subject to procedural default is a mixed question of law and fact, which we review de novo. Judd v. Haley, 250 F.3d 1308, 1313 (11th Cir.2001).

I. BACKGROUND

On May 26, 2004, a federal grand jury returned a 30-count indictment against Mr. Fordham, Mr. Williams, and several others. The indictment alleged, among other things, that these men were involved with others in a conspiracy to defraud the East Central Georgia Community Mental Health Center (CMHC), "a health care benefit program receiving federal funds, of money and property and of the intangible right to honest services, and to obtain money and property from a health care benefit program by means of false and fraudulent pretenses, representations, and promises." Specifically, the indictment described the conspiracy in the following away: Mr. Williams recommended that the CMHC hire Charles M. Brockman. Mr. Williams then arranged for Mr. Brockman to encourage the CMHC to enter into contracts with third parties of Mr. Williams' choosing and including Mr. Fordham. The contracts were very favorable to the third parties. In return, the third parties were obligated to give Mr. Williams a cut of the profit they made. Mr. Williams then bribed Mr. Brockman to do other things in furtherance of the conspiracy. The indictment also included substantive counts of bribery, theft, and money laundering for actions taken in furtherance of the charged conspiracy.

On May 5, 2005, after an eight-day jury trial, both of these defendants were convicted. Mr. Fordham was convicted of one count of health care fraud in violation of 18 U.S.C. § 1347.1 Mr. Williams was convicted of conspiracy, in violation of 18 U.S.C. § 371; four counts of health care fraud, in violation of 18 U.S.C. § 1347; one count of misapplication and theft from an organization receiving federal funds, in violation of 18 U.S.C. § 666; two counts of money laundering, in violation of 18 U.S.C. § 1956(a)(1)(B)(i); and seven counts of giving bribes to an agent of an organization receiving federal funds, in violation of 18 U.S.C. § 666(a)(2). Both Mr. Fordham and Mr. Williams appealed their convictions to this court. See United States v. Williams, 219 Fed.Appx. 963 (11th Cir. 2007). Neither challenged the legal viability of the honest services charges in the District Court or on direct appeal.

After these convictions and sentences had been affirmed on direct appeal, the Supreme Court decided Skilling v. United States, ___ U.S. ___, 130 S.Ct. 2896, 177 L.Ed.2d 619 (2010). The Skilling opinion limited, for the first time, the scope of what constitutes "honest-services" fraud under 18 U.S.C. § 1346. Id. at 2907. Jeffrey Skilling was the former chief executive officer of one of the world's biggest energy corporations, Enron, just prior to its sudden bankruptcy in 2001. After a government investigation uncovered an "elaborate conspiracy to prop up Enron's short-run stock prices by overstating the company's financial well-being." Mr. Skilling was charged with, among other things, engaging in a scheme to deceive investors about Enron's true performance by manipulating the company's publicly reported financial results. Id. at 2907-08. Most relevant here, count one of Mr. Skilling's indictment charged him with conspiracy to commit "honest-services" wire fraud, a violation of 18 U.S.C. §§ 371, 1343, and 1346, by depriving Enron and its shareholders of the intangible right of his honest services.2 See id. at 2908 & n. 1. After a four-month trial, the jury convicted Mr. Skilling on nineteen counts, including the honest-services fraud conspiracy. Id. at 2911.

The U.S. Circuit Court of Appeals for the Fifth Circuit affirmed Mr. Skilling's convictions. The Supreme Court then granted certiorari to consider two issues, including "did the jury improperly convict Skilling of conspiracy to commit `honest-services' wire fraud, 18 U.S.C. §§ 371, 1343, 1346." Id. at 2907. Mr. Skilling argued that the honest-services fraud statute was unconstitutionally vague or, in the alternative, that "his conduct [did] not fall within the statute's compass." Id. at 2925-26. Instead of invalidating the statute because it is impermissibly vague, the Supreme Court adopted a limiting interpretation. The Court held, contrary to the decisions of many lower courts, that the statute did not criminalize undisclosed self-dealing or conflicts of interest. See id. at 2933 & n. 44. However, the Court was clear that § 1346 continues to be viable insofar as it criminalizes bribery and kickback schemes. Id. at 2931.

Significantly, because the government never alleged that Mr. Skilling's conspiracy involved bribery or kickbacks, the Court determined he did not commit honest-services fraud. Id. at 2934. Having reached this conclusion, the Court reasoned that Mr. Skilling's conspiracy conviction — based on an indictment that had alleged three objects of the conspiracy, including honest-services wire fraud, money-or-property wire fraud, and securities fraud — was flawed under Yates v. United States, 354 U.S. 298, 77 S.Ct. 1064, 1 L.Ed.2d 1356 (1957) (holding that constitutional error occurs when a jury is instructed on alternative theories of guilt and returns a general verdict that may rest on an invalid theory). Id. But the Court was clear that this determination did not necessarily require reversal because Yates error is subject to harmless error analysis. Id. (citing Hedgpeth v. Pulido, 555 U.S. 57, 129 S.Ct. 530, 172 L.Ed.2d 388 (2008) (per curiam)). Thus the Court remanded the case for harmless error analysis. Id. On remand, the Fifth Circuit examined the record and "conclude[d] beyond a reasonable doubt that the verdict would have been the same absent the alternative-theory error" because "the jury was presented with overwhelming evidence that Skilling conspired to commit securities fraud [an alternative object of the conspiracy]."3 United States v. Skilling, 638 F.3d 480, 483-84 (5th Cir.2011), cert. denied, ___ U.S. ___, 132 S.Ct. 1905, 182 L.Ed.2d 807 (2012).

In light of Skilling, Mr. Fordham and Mr. Williams filed separate § 2255 motions challenging their convictions and sentences. They each argued that the rule announced by the Supreme Court in Skilling, limiting the scope of the honest-services fraud statute, rendered their convictions invalid. The scope of honest-services fraud was only directly relevant to the conspiracy and health care fraud charges, but Mr. Williams argued that the errors infected his whole trial.4 The District Court dismissed each of the § 2255 motions holding that they presented claims that were procedurally defaulted.

II. DISCUSSION

Under the procedural default rule, a defendant generally must advance an available challenge to a criminal conviction on direct appeal or else the defendant is barred from raising that claim in a habeas proceeding. McKay v. United States, 657 F.3d 1190, 1196 (11th Cir.2011). Neither Mr. Fordham nor Mr. Williams dispute here that they failed to challenge the legal viability of their honest-services fraud charges in the District Court or on direct appeal.

A default like the one presented here may be excused, however, if one of two exceptions applies. The exceptions are: (1) cause and actual prejudice, and (2) actual innocence. Bousley v. United States, 523 U.S. 614, 622, 118 S.Ct. 1604, 1611, 140 L.Ed.2d 828 (1998) (explaining that if a defendant fails to raise a claim on direct review, "the claim may be raised in habeas only if the defendant can first demonstrate either `cause' and actual `prejudice,' or that he is `actually innocent'" (internal citations omitted)). Mr. Fordham and Mr. Williams argue that their defaults are excusable under both exceptions to the procedural default rule. We will address each argument in turn.

A. CAUSE AND PREJUDICE

For a default to be excused under the first exception, "a convicted defendant must show both (1) `cause' excusing his... procedural default, and (2) `actual prejudice' resulting from the errors of which he complains." United States v. Frady, 456 U.S. 152, 168, 102 S.Ct. 1584, 1594, 71 L.Ed.2d 816 (1982). Both Mr. Fordham and Mr. Williams argue that they suffered actual prejudice because the jury returned a verdict that may have rested on an invalid theory of honest-services fraud. In support of this argument, they point to references throughout the trial to "honest services" and a single reference in the jury instructions to a theory of honest-services fraud invalidated by the Skilling Court.

However, a conviction will not be overturned on collateral review because of the mere mention of an invalid theory for conviction unless the petitioners "can demonstrate that the jury could have relied on that theory to convict him." Lomelo v. United States, 891 F.2d 1512, 1516 (11th Cir.1990). Considering the language in the indictment, the trial transcript, and the jury charge in its entirety, see id. at 1516-19, we conclude that the only theory of honest-services fraud that could have been a basis for conviction was bribery, which is a valid basis for an honest-services fraud conviction even after Skilling. The charges were clearly directed toward defendants' scheme to defraud the CMHC of money and of Mr. Brockman's honest services. In turn, Mr. Brockman's honest services were only jeopardized through bribes. The government did not allege that Mr. Brockman had any independent interest in the third-party contracts which could have implicated undisclosed self-dealing and conflicts of interest, the now invalid theories of honest-services fraud.

We agree with the District Court that Mr. Williams' convictions on the substantive counts charging him with "giv[ing] things of value to defendant Brockman" in furtherance of the scheme to defraud health care benefit programs of money were convictions for bribery, which do not implicate the theories of honest-services fraud which have been invalidated. This point is equally true for count eight, the fraud count underlying Mr. Fordham's conviction. The jury convicted Mr. Fordham of participating in a scheme in which Mr. Brockman was bribed to enter into generous contracts with Mr. Fordham and others, thereby depriving CMHC of Mr. Brockman's honest services. The jury was simply not presented with any theory that rested on Mr. Brockman's undisclosed self-interest.

To prevail on a cause and prejudice theory, a petitioner must show "actual prejudice." "Actual prejudice means more than just the possibility of prejudice; it requires that the error worked to [the petitioner's] actual and substantial disadvantage, infecting his entire trial with error of constitutional dimensions." Ward v. Hall, 592 F.3d 1144, 1179 (11th Cir.2010) (alteration and quotation marks omitted). Mr. Fordham and Mr. Williams have identified as prejudice only things that do not meet this standard. At the same time, the record demonstrates that their jury was presented with evidence that they participated in a scheme involving the payment of bribes. The Skilling decision did nothing to remove bribery as a method for committing honest-services fraud. The sporadic references to "honest services" and the single jury instruction on the now invalid theory of honest services are not sufficient to show that Mr. Fordham and Mr. Williams were prejudiced in light of the evidence of their participation in an actual bribery scheme.

Because Mr. Fordham and Mr. Williams have failed to show that they suffered actual prejudice that worked to their substantial disadvantage, the cause and prejudice exception cannot be used to excuse them of their procedural default.

B. ACTUAL INNOCENCE

Alternatively, procedural default can be overcome if the petitioner establishes that he is actually innocent. See Bousley, 523 U.S. at 622, 118 S.Ct. at 1611. This is a narrow exception. See e.g., McKay, 657 F.3d at 1198. "To establish actual innocence, the petitioner must demonstrate that, in light of all the evidence, it is more likely than not that no reasonable juror would have convicted him." Bousley, 523 U.S. at 623, 118 S.Ct. at 1611 (quotation marks omitted).

Mr. Fordham and Mr. Williams both argue conclusively that they are actually innocent because the honest-services fraud statute cannot be used as a basis for their convictions. However, as set out above, these men have failed to show that their convictions were more likely than not based on an invalid theory of honest-services fraud. Rather, the record of their trial demonstrates that their convictions were based on traditional fraud and the deprivation of honest services through bribery. Also, although Mr. Fordham argues the contrary, the fact that he was acquitted of being part of the specific conspiracy charged in the indictment, does not negate the jury's finding of his guilt in participating in a scheme to defraud that involved Mr. Williams bribing Mr. Brockman to get the CMHC to enter into contracts with Mr. Fordham and Mr. Fordham paying substantial portions of the profits earned under those contracts to Mr. Williams.

Because Mr. Fordham and Mr. Williams have failed to show actual innocence as to the theories supporting their convictions that remain intact following Skilling, the actual innocence exception does not apply to overcome their procedural default.

III. CONCLUSION

For these reasons, we affirm the District Court's denial of both Mr. Fordham's and Mr. Williams' § 2255 motions.

AFFIRMED.