This matter is before us on remand from the United States Supreme Court in light of its recent opinion in United States v. Booker. 1 At our request, the parties have submitted supplemental letter briefs addressing the impact of Booker. For the following reasons, we find that Booker does not affect Defendant-Appellant Ernesto Alvarado’s sentence.

I. BACKGROUND

In March 2003, a grand jury indicted Alvarado and his co-defendant, Efrain Mendez, for knowingly possessing with the intent to distribute more than five kilograms of cocaine, in violation of 21 U.S.C. §§ 841(a)(1) and (b)(1)(A). In April 2003, Alvarado agreed to plead guilty to the indictment and, in exchange, the government agreed to (1) recommend that Alvarado receive a three-level downward adjustment of his offense level for acceptance of responsibility, and (2) recommend a sentence at the low end of the applicable United States Sentencing Guidelines range.

At the re-arraignment hearing, the government submitted the factual basis for the plea. Specifically, the government stated that on February 11, 2003, Alvarado and Mendez drove a van into a Border Patrol checkpoint at Falfurrias, Texas. When a drug dog alerted to their van, the Border Patrol agent directed the vehicle to a secondary inspection area. The agent found four cardboard boxes containing 50 bundles of a material that the agent suspected to be a controlled substance. The defendants confessed to the agent that they knew they were transporting contraband, but stated that they thought it was marijuana. The substance retrieved from the van was subjected to laboratory analysis, which revealed that it was cocaine. The analysis also confirmed that the defendants possessed more than five kilograms of cocaine. The defendants declared at the re-arraignment hearing that the government had accurately summarized the facts underlying their pleas of guilty. The district court found that there was a factual basis to support a finding of guilt, and accepted the defendants’ guilty pleas.

At sentencing, the district court questioned whether Alvarado qualified for the safety-valve provision of the Guidelines, which would have entitled him to a two-level downward adjustment of his offense *215 level. 2 The criteria for the safety-valve provision include, inter alia, that “the defendant has truthfully provided to the Government all information and evidence the defendant has concerning the offense.” 3 As the parties disputed the applicability of the safety-valve provision, the court held a hearing to determine whether it applied. The government’s case agent testified that it was her opinion that the defendants knew they were transporting cocaine, not marijuana, and that the defendants were not forthcoming with the government regarding the facts and evidence regarding them offense. The district court then questioned the defendants. At the conclusion of the hearing, the district court (1) credited the government case agent’s testimony, (2) found the defendants not credible, and (3) determined that Alvarado did not qualify for a sentence reduction under the safety-valve provision. Accordingly, the district court imposed a 168-month term of imprisonment and five years of supervised release. Alvarado appealed his sentence, objecting on the ground that the district court erred when it held that he failed to meet the criteria of the safety-valve provision. We rejected Alvarado’s argument and affirmed the sentence in an unpublished opinion. 4

II. DISCUSSION

A. Standard of Review

The parties dispute whether Alvarado raised his Booker claim for the first time on appeal or in his petition for certiorari. If Alvarado raised his Booker claim for the first time in his petition for certiorari, we will not review it absent “extraordinary circumstances.” 5 The extraordinary circumstances standard is more demanding than the plain error review that we employ when a defendant has raised his Booker claim for the first time on appeal. 6 Therefore, if a defendant cannot satisfy plain error review, he certainly cannot satisfy extraordinary circumstances review. 7

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.” 8 If the circumstances meet all three criteria, we may exercise our discretion to notice the error, but only if it “seriously affects the fairness, integrity, or public reputation of judicial proceedings.” 9 Since Booker, sentencing under mandatory Guidelines constitutes error, and that error is plain. 10 Whether the error affects substantial rights is a more complex inquiry in which the defendant bears the burden of proof. He carries his burden only if he can “demonstrate a probability ‘sufficient to undermine confidence in the outcome.’ ” 11 The defendant demonstrates such a probability when he identifies from the record an indication that the sentencing judge would have reached a significantly different result un *216 der an advisory Guidelines scheme. 12 We need not resolve the parties’ dispute as to when Alvarado raised his Booker claim because his claim does not pass the plain error standard.

B. Analysis

First, Alvarado contends that we should remand for resentencing because he presents special circumstances. Specifically, “he was sentenced for Possession with Intent to Distribute cocaine although at both his plea and sentencing, he specifically disputed any knowledge of cocaine and consistently asserted that he believed that he was transporting marijuana.” At the outset, we note that Alvarado pleaded guilty to knowingly possessing cocaine with the intent to distribute it. In light of Alvarado’s voluntary admission of guilt, it is unlikely that an advisory Guidelines scheme would have affected the sentencing judge. Furthermore, as noted supra, the district court did not find Alvarado credible. Thus, Alvarado’s assertion that the court would have sentenced him differently because he thought he was transporting marijuana instead of cocaine is unpersuasive.

Second, Alvarado insists that the district court misapprehended its authority to depart below the Guidelines, and it would have done so “on the grounds that [Alvarado] was not aware that he was transporting cocaine and thought, instead, that he was transporting marijuana.” In support of his argument, Alvarado observes that the district court stated that no grounds for departure existed except a downward departure for substantial assistance. This, however, hardly serves as an indication that the district court would have been inclined to depart downwardly but for the then-mandatory nature of the Guidelines. Furthermore, it is improbable that the sentencing judge would have acted differently on the ground that Alvarado advances because, as we have already observed, the record establishes that the sentencing judge did not find Alvarado credible. Accordingly, Alvarado fails to carry his burden.

III. CONCLUSION

As the district court did not commit plain error, Alvarado’s sentence is

AFFIRMED.