This matter is before us on remand from the Supreme Court for reconsideration in light of its recent opinion in United States v. Booker.1 At our request, the parties have commented on the impact of Booker. For the following reasons, we conclude that Booker does not affect Defendant-Appellant Saul Navarro-Molina’s sentence.

I. BACKGROUND

Navarro-Molina, a citizen of Mexico, pleaded guilty to and was convicted of being in the United States illegally after removal, in violation of 8 U.S.C. § 1326(a). Standing alone, a § 1326(a) offense carries a maximum penalty of two years’ imprisonment and one year of supervised release. Navarro-Molina’s § 1326(a) offense, however, did not stand alone: Prior to his removal from the United States, Navarro-Molina was convicted of an aggravated felony, which, under 8 U.S.C. § 1326(b)(2), increased the maximum penalty for his § 1326(a) offense to 20 years’ imprisonment and three years’ supervised release. Navarro-Molina’s presentencing report (“PSR”) recommended that he receive a total offense level under the U.S. Sentencing Guidelines of 21, which included a 16-level upward adjustment for his prior aggravated felony conviction, and a 3-level downward adjustment for acceptance of responsibility for his § 1326(a) offense. Combined with Navarro-Molina’s Criminal History Category of III, his offense level of 21 resulted in a Guidelines sentencing range of 46-57 months’ imprisonment. The district court accepted the PSR’s recommendation and sentenced Navarro-Molina at the bottom-end of the Guidelines sentencing range, imposing a sentence of 46 months’ imprisonment. Navarro-Molina objected to the sentence on the ground that it exceeded the maximum authorized by § 1326(a), but the district court overruled his objection.

Navarro-Molina then appealed his sentence to this court, arguing that it exceeded the statutory maximum in violation of his rights under the Fifth Amendment’s Due Process Clause because the indictment charging him with a § 1326(a) violation did not separately state a § 1326(b) offense. In his brief on appeal, Navarro-Molina acknowledged that precedent foreclosed his argument, but he raised it anyway to preserve possible Supreme Court review. We affirmed the district court’s judgment in an unpublished opinion.2 Navarro-Molina then petitioned the Supreme Court for a writ of certiorari. After the Court handed down Booker, Navarro-Molina filed a supplemental petition for certiorari with the Court in which, for the first time, he raised a Booker challenge to his mandatory Guidelines sentence. In response, the Supreme Court granted Navarro-Molina’s petition, vacated our judgment affirming his sentence, and remanded to us for reconsideration in light of Booker.3 We again affirm Navarro-Molina’s sentence.

*888II. DISCUSSION

A. Standard of Review

Navarro-Molina raised his Booker claim for the first time in his supplemental petition for certiorari. We will therefore review his Booker claim only in the presence of “extraordinary circumstances.”4 Although we have yet to flesh out the contours of precisely what constitutes “extraordinary circumstances,” we know that the extraordinary circumstances standard is more onerous than the plain error standard.5 If, therefore, Navarro-Molina cannot meet the requirements of plain error review, he certainly cannot satisfy the requirements of extraordinary circumstances review.6 And Navarro-Molina cannot: He has failed to show, as is required by plain error review, that the error in his case affected his substantial rights. We therefore need not address whether extraordinary circumstances exist.

Under plain error review, we will not remand for resentencing unless there is “(1) error, (2) that is plain, and (3) that affects substantial rights.”7 If the circumstances in a case meet all three criteria, we may exercise our discretion to notice the error only if it “seriously affects the fairness, integrity, or public reputation of judicial proceedings.”8 Under Booker, a district court’s sentencing of a defendant under the formerly-mandatory Sentencing Guidelines (1) constitutes error (2) that is plain.9 Whether the error affects substantial rights is a more complex inquiry in which the defendant bears the burden of proof. He will carry this burden only if he can “show[] that the error ‘must have affected the outcome of the district court proceedings.’ ”10 That may be shown, in turn, by the defendant’s “demonstration of] a probability ‘sufficient to undermine confidence in the outcome.’ ” 11 To demonstrate such a probability, the defendant must identify in the record an indication that the “sentencing judge-sentencing under an advisory [Guidelines] scheme rather than a mandatory one-would have reached a significantly different result.” 12 By all accounts, this burden is “difficult”13-but not impossible14-to meet.

B. Merits

In measuring a defendant’s attempt to show that a plain error affected his substantial rights, our decisions have considered “two issues: first, whether the judge made any statements during sentencing indicating that he would have imposed a lesser sentence had he not considered the Guidelines mandatory; [and] second, the *889relationship between the actual sentence imposed and the range of sentences provided by the Guidelines.”15 Navarro-Molina does not contend that the district court made any statements expressing a preference for a lower sentence: In his brief on appeal he concedes that “the district court made no particular remarks disagreeing with the requirements of the mandatory guidelines,” or otherwise indicating that it would have sentenced him differently under an advisory Guidelines scheme. Instead, Navarro-Molina calls to our attention “mitigating circumstances”-namely, the facts that he returned to the United States to seek work, and that he requested that the district court order him to undergo alcohol and drug treatment-“that support a finding of a reasonable likelihood of a lower sentence.” In addition, Navarro-Molina argues that the district court’s decision to impose the lowest term of imprisonment permitted by his Guidelines sentencing range-which Navarro-Molina contends was “[apparently” based on “the[] mitigating circumstances” surrounding his case-indicates that the district court would likely have imposed a different sentence under an advisory set of Guidelines.

We hold that Navarro-Molina has not carried his burden of showing that Booker error “ ‘affected the outcome of [his] district court proceedings.’ ”16 First, under our decision in United States v. Bringier, Navarro-Molina’s invocation of the district court’s imposition of a sentence at the bottom of the Guidelines range is not enough to carry his burden.17 And, contrary to Navarro-Molina’s argument, Bringier is not distinguishable from this case. Navarro-Molina contends that unlike the Bringier defendant, he presents sufficient mitigating circumstances to raise a reasonable likelihood that the district court would have imposed a lower sentence under an advisory Guidelines scheme. But the differences between this case and Bringier-for example, that Bringier was a “large-scale drug trafficker” while Navarro-Molina is “an illegal alien who merely crossed the border to find work”-have no bearing whatsoever on the question whether we may infer from a Guideline-minimum sentence that Navarro-Molina would have been sentenced differently under an advisory scheme. The significance of any factual differences is, of course, borne out in the sentences imposed: Bringier was sentenced to a Guideline-minimum 30 years’ imprisonment, compared to Navarro-Molina’s 46 months. Yet, in neither case may we conclude that the district court would have imposed a lesser sentence under an advisory scheme. Navarro-Molina’s attempt to distinguish Bringier is simply unconvincing.

Second, Navarro-Molina contends that his mitigating circumstances themselves raise a reasonable likelihood that the district court would have imposed a lower sentence under an advisory Guidelines scheme. “Despite the [district] court’s demonstrated willingness to impose the lowest available sentence,” contends Navarro-Molina, “it could not reduce [his sentence] below 46 months based on the most sympathetic circumstances of his case [because, under the then-mandatory Guidelines,] Navarro’s drug and alcohol problems were not grounds for departure.” *890This argument misses the mark. All Navarro-Molina has done is raise the mere possibility that, post-Booker, the district court would have considered Navarro-Molina’s drug and alcohol problems as a reason to impose a lower sentence. But he has not pointed us to any indication in the record that the district court actually would have done so had it been so empowered. Under Mares, a defendant must do more than raise a mere possibility to carry his burden; he must “ ‘show that the error actually did make a difference: if it is equally plausible that the error worked in favor of the defense, the defendant loses; if the effect of the error is uncertain so that we do not know which, if either, side it helped the defendant loses.’ ”18 Navarro-Molina therefore fails to carry his burden, and thus fails to satisfy plain error review. We need not reach his argument that the error in his sentencing seriously affected the fairness, integrity and public reputation of the proceedings.

Finally, in a last-ditch effort, Navarro-Molina expresses disagreement with the mechanics of Mares ’s plain error standard. He recognizes that Mares forecloses this argument, but he nonetheless raises the point to preserve a challenge to Mares’s articulation of the plain error standard of review, arguing that in Mares we got it wrong, while the plain error standard employed by other courts (the Sixth Circuit, for example19) gets it right. Mares is the settled law of this circuit, however, and we may revisit it only en banc or following a Supreme Court decision that actually or effectively overturns it.20

Because Navarro-Molina cannot satisfy plain error review, he does not present extraordinary circumstances entitling him to resentencing. We affirm his sentence.

III. CONCLUSION

As there exist no extraordinary circumstances or other grounds for relief, Navarro-Molina’s sentence is AFFIRMED. The Government’s pending motions to reinstate our prior affirmance and, in the alternative, to extend time to file its supplemental brief are DENIED as moot.