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 Alfredo Gonzalez-Trejo’s sentence.
I. BACKGROUND
Gonzalez-Trejo, a citizen of Mexico, pleaded guilty to and was convicted of reentering the United States illegally following 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. Gonzalez-Trejo’s § 1326(a) offense, however, did not stand alone: Prior to his removal from the United States, Gonzalez-Trejo 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. At his sentencing— which occurred prior to Booker — Gonzalez-Trejo’s prior conviction also led to a 16-level increase in his offense level under the U.S. Sentencing Guidelines. Following the Guidelines, the court sentenced Gonzalez-Trejo to 46 months’ imprisonment. Gonzalez-Trejo objected to the sentence on the ground that it exceeded the maximum authorized by § 1326(a), but the district court overruled his objection.
Gonzalez-Trejo then appealed his sentence to this court, arguing that it exceeded the statutory maximum in violation of his rights under the Fifth Amendment because the indictment charging him with a § 1326(a) offense did not separately state a § 1326(b) offense. After we affirmed his sentence in an unpublished opinion,2 Gonzalez-Trejo petitioned the Supreme Court for a writ of certiorari, asserting his Booker claim for the first time. The Supreme Court granted Gonzalez-Trejo’s petition, vacated our judgment affirming his sentence, and remanded to us for reconsideration in light of Booker.3 We again affirm Gonzalez-Trejo’s sentence.
II. DISCUSSION
A. Standard of Review
Gonzalez-Trejo raised his Booker claim for the first time in his petition for a writ *860of 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, Gonzalez-Trejo cannot meet the requirements of plain error review, he certainly cannot satisfy the requirements of extraordinary circumstances review. And Gonzalez-Trejo cannot; as he concedes, his claim does not survive plain error review. We therefore need not address his argument that, for a variety of reasons, the extraordinary circumstances standard is inapplicable in this case.
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.”6 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.”7 Under Booker, a district court’s sentencing of a defendant under the formerly-mandatory Sentencing Guidelines (1) constitutes error that (2) is plain.8 Whether the error affects substantial rights is a more complex inquiry for 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.’ ”9 That may be shown, in turn, by the defendant’s “demonstration of] a probability ‘sufficient to undermine confidence in the outcome.’ ”10 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.”11 By all accounts, this burden is “difficult”12 —but not impossible13 — to meet.
B. Merits
In his supplemental letter brief, Gonzalez-Trejo concedes that “Mares appears to foreclose [his] plain-error claim in this circuit.” Specifically, Gonzalez-Trejo is unable to point to any indication in the record that there is a probability that the sentencing judge would have sentenced him differently under an advisory Guidelines scheme. Instead, he preserves a challenge to the standard of review we adopted in Mares, arguing that in Mares we got it wrong and the plain error standard employed by other courts (the Sixth Circuit, for example14) gets it right. *861Mares 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.15 Accordingly, we affirm the sentence imposed by the district court below.
III. CONCLUSION
As there exist no extraordinary circumstances or other grounds for relief, Gonzalezr-Trejo’s sentence is AFFIRMED.
Pursuant to 5th Cir. R. 47.5, the court has determined that this opinion should not be published and is not precedent except under the limited circumstances set forth in 5th Cir. R. 47.5.4.
. 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005).
. United. States v. Gonzalez-Trejo, 110 Fed. Appx. 460 (5th Cir.2004).
. Alfaro v. United States, 543 U.S. 1183, 125 S.Ct. 1422, 161 L.Ed.2d 182 (2005).
. United States v. Taylor, 409 F.3d 675, 676 (5th Cir.2005).
. Id.
. United States v. Cotton, 535 U.S. 625, 631, 122 S.Ct. 1781, 152 L.Ed.2d 860 (2002).
. Id.
. United States v. Mares, 402 F.3d 511, 521 (5th Cir.2005).
. Id. (quoting United States v. Olano, 507 U.S. 725, 734, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993)).
. Id. (quoting United States v. Dominguez Benitez, 542 U.S. 74, 124 S.Ct. 2333, 159 L.Ed.2d 157 (2004)).
. Id.
. United States v. Pennell, 409 F.3d 240, 245 (5th Cir.2005); see also United States v. Rodriguez-Gutierrez, 428 F.3d 201, 203 (5th Cir. 2005) ("[T]he Supreme Court mandates that establishing [plain] error ‘should not be too easy.’ ”) (quoting United States v. Dominguez Benitez, 542 U.S. 74, 124 S.Ct. 2333, 159 L.Ed.2d 157 (2004)).
. See Pennell, 409 F.3d at 245.
. See, e.g., United States v. Barnett, 398 F.3d 516 (6th Cir.2005).
. See Hogue v. Johnson, 131 F.3d 466, 491 (5th Cir. 1997).