Damon Amedeo appeals Ms 120-month sentence following a guilty plea to one count of cocaine distribution on the grounds that (1) the district court should have recused itself from his resentencing; (2) the sentence violated the mandate rule; (3) the sentence violated 18 U.S.C. § 3742(g); (4) his due process rights were violated by the retroactive application of Booker, and (5) the sentence was unreasonable. For the reasons that follow, we affirm.

I. Background

On February 7, 2002, Amedeo was arrested in connection with the death of Douglas Rozelle III.^[1] He was later charged in a nine-count superceding indictment with one count each of unlawful drug use while in possession of a firearm, 18 U.S.C. § 922(g)(3); distribution of cocaine to a minor, 21 U.S.C. § 859; cocaine distribution, 21 U.S.C. § 841; possession with intent to distribute marijuana, 21 U.S.C. § 841; and five counts of distribution of marijuana to a minor, 21 U.S.C. § 859. Pursuant to a plea agreement, Amedeo pleaded guilty to the count of distributing cocaine to a minor, 21 U.S.C. § 859(a), and the Government dropped the remaining charges.

After the sentencing hearing on February 13, 2003, the district court sentenced Amedeo to 216 months’ imprisonment and eight years of supervised release, based on an offense level of 37; a criminal history category of I; and enhancements for vulnerable victim, U.S.S.G. § 3A1.1, abuse of trust, § 3B1.3, and obstruction of justice, § 3C1.1. The sentence also included upward departures on the grounds that: (1) Amedeo committed the offense to facilitate a sexual assault on Rozelle, § 5K2.9; (2) Amedeo’s offense resulted in Rozelle’s death, § 5K2.1; (3) Amedeo engaged in extreme conduct by failing to seek medical help for Rozelle and by having unprotected sex with Rozelle despite being infected with hepatitis C, § 5K2.8; and (4) Amedeo distributed drugs to multiple minors, § 5K2.0. The district court denied Ame-deo’s request for a reduction based on acceptance of responsibility pursuant to § 3El.l(a).

Amedeo appealed the sentence to this court, and on May 28, 2004, this court affirmed in part, vacated in part, and remanded for further proceedings. United States v. Amedeo, 370 F.3d 1305, 1325 (11th Cir.2004) (“Amedeo I”). Specifically, this court affirmed all of the enhancements and the denial of the acceptance-of-responsibility reduction. Id. at 1316-21. This court vacated the upward departures under §§ 5K2.0, 5K2.1, 5K2.8,^[2] and 5K2.9, on the grounds that: Amedeo’s November 2001 sexual assault on Rozelle, his drug use with minors other than Rozelle, his January 2002 sexual encounters with Rozelle, and Rozelle’s death were beyond the scope of “relevant conduct” for purposes of § 1B1.3, as these incidents did not constitute a “common scheme or plan” in connection with Amedeo’s offense of conviction. Amedeo I, 370 F.3d at 1313-24.

On August 2, 2004, the district court[*828] issued a Bums^[3] notice indicating its intention to consider on remand a departure under U.S.S.G. § 4A1.3 (underrepresentation of criminal history). Anticipating a forthcoming decision by the Supreme Court addressing the applicability of Blakely^[4] to the Sentencing Guidelines, Am-edeo filed a motion for a continuance, which the district court granted.

On January 12, 2005, the Supreme Court issued its opinion in United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), which held, inter alia, that the Sentencing Guidelines could not be imposed in a mandatory manner, but that sentencing courts were required to consider the Guidelines along with other statutorily relevant factors. Id. at 258-67, 125 S.Ct. at 764-69. The Booker Court also held that this remedial holding was to be applied to cases pending on direct review. Id. at 268, 125 S.Ct. at 769. On February 1, 2005, the district court issued an amended notice of its intent to consider a departure under § 4A1.3 based on Ame-deo’s sexual contact with Rozelle. Prior to the resentencing hearing, Amedeo filed a motion requesting that the district judge recuse himself, which the court denied.

At the resentencing hearing on March 11, 2005, the district court calculated the Guidelines range at 37-46 months, decided not to impose an upward departure, and found that the Guidelines range did not reflect the seriousness of the crime in light of 18 U.S.C. § 3553(a). The court held that Booker constituted an exception to the mandate rule, as it was an intervening “radical change in the law governing sentencing guideline applications” that required the court to apply the Guidelines in an advisory manner by imposing a reasonable sentence in light of § 3553(a). The court then imposed a sentence of 120 months’ imprisonment.

II. Discussion

A. Recusal from Resentencing

On appeal, Amedeo argues that the district court erred in failing to recuse itself for his resentencing. We review a judge’s decision not to recuse for an abuse of discretion. United States v. Berger, 375 F.3d 1223, 1227 (11th Cir.2004).

Section 455 of Title 28 of the U.S. Code creates two conditions for recu-sal. United States v. Patti, 337 F.3d 1317, 1321 (11th Cir.2003). First, § 455(a) provides that a judge shall disqualify himself in any proceeding in which his impartiality might reasonably be questioned. 28 U.S.C. § 455(a). Under § 455(a), recusal is appropriate only if “an objective, disinterested, lay observer fully informed of the facts underlying the grounds on which re-cusal was sought would entertain a significant doubt about the judge’s impartiality.” Patti 337 F.3d at 1321 (citation omitted). And “judicial rulings alone almost never constitute a valid basis for a bias or partiality motion.” Liteky v. United States, 510 U.S. 540, 555, 114 S.Ct. 1147, 1157, 127 L.Ed.2d 474 (1994) (citation omitted).

Second, § 455(b) provides that a judge also shall disqualify himself where, inter alia, he actually “has a personal bias or prejudice concerning a party, or personal knowledge of disputed evidentiary facts concerning the proceeding.” 28 U.S.C. § 455(b)(1) (emphasis added). The bias or prejudice “must be personal and extrajudicial; it must derive from something other than that which the judge learned by participating in the case.” McWhorter v. City of Birmingham, 906 F.2d 674, 678 (11th[*829] Cir.1990) (citation omitted). “[Ojpinions held by judges as a result of what they learned in earlier proceedings” do not constitute bias or prejudice. Liteky, 510 U.S. at 551, 114 S.Ct. at 1155. Thus, “[i]t has long been regarded as normal and proper for a judge to sit in the same case upon remand, and to sit in successive trials involving the same defendant.” Id.

Here, Amedeo asserts both that there was an appearance of impartiality and that there was actual bias on the part of the district court. He argues that a fully-informed lay observer might reasonably conclude that the district court intended to sentence him above his Guidelines range without regard to what was authorized by law, as evidenced by, inter alia, (1) the public nature of the initial sentencing, (2) this court’s rejection of two of the district court’s upward departures, (3) the district court’s consideration on remand of new upward departures, and (4) the district court’s use of § 3553(a) to impose an upward variance on the same factual bases it had used to support the upward departures this court had rejected in Amedeo I. He also contends that the district court’s use of § 3553(a) at resentenc-ing was a pretextual means of sentencing him above the Guidelines range, thereby demonstrating the district court’s bias. We disagree.

First, regarding Amedeo’s initial sentencing, this court observed that “[i]t is clear the district court conducted the [original] sentencing proceedings with the utmost care and sensitivity to the parties, and grappled rigorously and conscientiously with the challenging issues presented.” Amedeo I, 370 F.3d at 1325. And although both Amedeo’s initial sentence and this court’s overturning of that sentence were “public events,” nearly all federal judicial proceedings are public and most district courts have some of their rulings overturned on appeal. The fact that the district court on remand continued to view Amedeo’s conduct as sufficiently serious to warrant a sentence above the Guidelines range was not improper. Indeed, “[i]f the judge did not form judgments of the actors in those court-house dramas called trials, he could never render decisions.” Liteky, 510 U.S. at 551, 114 S.Ct. at 1155. Again, “opinions held by judges as a result of what they learned in earlier proceedings” do not constitute bias or prejudice. Id. Nothing in the record demonstrates that the district court had developed a personal or extrajudicial bias against Amedeo (pursuant to § 455(b)(1)), see McWhorter, 906 F.2d at 678, or that a fully-informed lay observer would entertain a significant doubt about the district judge’s impartiality (pursuant to § 455(a)), see Patti, 337 F.3d at 1321. Accordingly, we conclude that the district judge’s decision not to recuse himself was not an abuse of discretion.

B. The Mandate Rule

Amedeo next argues that the district court’s imposition of a sentence above the Guidelines range violated this court’s mandate in Amedeo I because the district court considered conduct beyond the offense of conviction, namely Amedeo’s November 2001 sexual assault on Rozelle, his drug use with minors other than Rozelle, his January 2002 sexual encounters with Rozelle, and Rozelle’s death. Whether the district court violated our mandate in Am-edeo I is a question of law that we review de novo. United States v. Tamayo, 80 F.3d 1514, 1518 (11th Cir.1996).

“The law of the case doctrine, self-imposed by the courts, operates to create efficiency, finality[,] and obedience within the judicial system” so that “[a]n appellate decision binds all subsequent proceedings in the same case.” Id. at 1520[*830] (citation omitted). “The mandate rule is simply an application of the law of the case doctrine to a specific set of facts.” Id. (citation omitted). Accordingly, when acting under an appellate court’s mandate, a district court “cannot vary it, or examine it for any other purpose than execution; or give any other or further relief; or review it, even for apparent error, upon a matter decided on appeal; or intermeddle with it, further than to settle so much as has been remanded.” Id. (quoting Litman v. Mass. Mut. Life Ins. Co., 825 F.2d 1506, 1510-11 (11th Cir.1987)) (internal quotation marks omitted). The law of the case doctrine (and, by implication, the mandate rule) applies to findings made under the Sentencing Guidelines. See, e.g., United States v. Bordon, 421 F.3d 1202, 1207-08 (11th Cir.2005) (declining to consider a challenge to a Guidelines calculation that was previously reviewed and affirmed by this court).

This court has recognized three exceptions to the mandate rule: “(1) a subsequent trial produces substantially different evidence, (2) controlling authority has since made a contrary decision of law applicable to that issue, or (3) the prior [appellate] decision was clearly erroneous and would work manifest injustice.” United States v. Stinson, 97 F.3d 466, 469 (11th Cir.1996).

On appeal, Amedeo contends that this court’s Amedeo I mandate not only struck the upward departures, but also prohibited the district court from considering the factual bases for these departures, namely, Amedeo’s drug use with Rozelle and other minors, his sexual contact with Rozelle, and Rozelle’s death. He also argues that the intervening decision in Booker does not qualify as a change in controlling authority sufficient to allow this court’s mandate in Amedeo I to be exceeded on remand because Booker “was not a change in controlling law which made a contrary result applicable,” and this court’s original decision in Amedeo I was not clearly erroneous.

We conclude that the second exception to the mandate rule applies in this case, as Booker constituted an intervening change in the law of sentencing that made a contrary decision of law applicable. We agree that imposing a Guidelines departure based on acts that this court deemed beyond the scope of relevant conduct under § IB 1.3 would have violated the Amedeo I mandate, as, indeed, the official title of § 1B1.3 is “Relevant Conduct (Factors that Determine the Guideline Range)." U.S.S.G. § 1B1.3 (emphasis added). But after Booker, which was decided after Am-edeo I, the district court on remand had the discretion to impose a variance—a sentence outside the Guidelines range— based on the factors set forth in § 3553(a), including the defendant’s history and characteristics, the Guidelines range, affording adequate deterrence, and protecting the public from further crimes of the defendant. United States v. McVay, 447 F.3d 1348, 1353 (11th Cir.2006). On remand, the district court did not impose an upward departure, rather, the district court applied Booker, an intervening change in the law that made the Guidelines advisory, and imposed a sentence based on its consideration of the factors set forth in § 3553(a). Thus, we conclude that our “relevant conduct” mandate in Amedeo I did not apply to the district court’s imposition of a variance based on § 3553(a), and therefore, the district court did not violate our mandate.

C. 18 U.S.C. § 874.2(g)

Amedeo also argues that the district court violated 18 U.S.C. § 3742(g)(2) by imposing an above-the-Guidelines sentence on bases not considered in his origi[*831] nal sentence. We review de novo the district court’s interpretation and application of the Sentencing Guidelines. United States v. Barakat, 130 F.3d 1448, 1452 (11th Cir.1997).

Section 3742(g)(2) provides that, at re-sentencing,

[a district court] shall not impose a sentence outside the applicable guidelines range except upon a ground that—(A) was specifically and affirmatively included in the written statement of reasons required by section 3553(c) in connection with the previous sentencing of the defendant prior to the appeal; and (B) was held by the court of appeals, in remanding the case, to be a permissible ground of departure.

18 U.S.C. § 3742(g)(2). Amedeo’s original sentencing hearing was held on February 13, 2003, and judgment was entered on March 5, 2003. Sections 3742(g)(2) and 3553(c) were enacted on April 30, 2003. See Prosecutorial Remedies and Other Tools to End the Exploitation of Children Today Act of 2000, (PROTECT Act), Pub.L. No. 108-21, Title IV, § 401, 117 Stat. 650, 669-71.

This court has not addressed whether and how § 3742(g)(2) applies to cases where the original sentence was imposed before the current version of § 3742(g)(2) was enacted. But circuits that have addressed this issue have held that § 3742(g)(2)(A)’s requirement regarding a written statement of reasons is inapplicable in these circumstances. See United States v. Cole, 357 F.3d 780, 786 (8th Cir.2004); United States v. Derbes, 369 F.3d 579, 583-84 (1st Cir.2004); United States v. Kostakis, 364 F.3d 45, 53 (2d Cir.2004). For instance, in Kostakis, the Second Circuit reasoned that “because such statutory limitations did not exist at the time of’ the defendant’s initial sentencing, “neither [the defendant] nor the sentencing court were aware that these grounds could be precluded on remand.” Kostakis, 364 F.3d at 53.

Regarding the applicability of § 3742(g)(2), we join our sister circuits and hold that this provision does not apply to sentences imposed before § 3742(g)(2) was enacted. We therefore conclude that Am-edeo’s sentence on remand did not violate § 3742(g)(2).

D. Ex Post Facto Application of Booker at Resentencing

Amedeo also argues that the district court’s ex post facto application of Booker to his detriment at resentencing violated his due process rights. “We review de novo a defendant’s claim that his sentence violated ex post facto principles.” United States v. Thomas, 446 F.3d 1348, 1350 (11th Cir.2006).

As stated above, in Booker, the Supreme Court held that its remedial holding, making the Guidelines advisory, was to be applied to cases pending on direct review. Booker, 543 U.S. at 268, 125 S.Ct. at 769. In United States v. Duncan, 400 F.Sd 1297, 1306 (11th Cir.), cert. denied, — U.S. -, 126 S.Ct. 432, 163 L.Ed.2d 329 (2005), this court rejected the defendant’s argument that the retroactive application of Booker to his case would increase his sentence beyond that authorized by the jury’s verdict, thereby operating as an ex post facto law in violation of his due process rights. Id. at 1307. We reasoned that although mandatory Guidelines were in place at the time of the defendant’s criminal conduct, “the law of this Circuit then recognized the U.S. Code as the source of the maximum sentence.” Id. at 1308 (citations omitted). As such, this court held that the defendant “had sufficient warning to satisfy” due process concerns. Id.

[*832] Here, Amedeo contends that Duncan is not controlling because he preserved his objection below, entitling him to de novo review, whereas in Duncan, the issue was considered on plain error review. He also argues that this court’s Amedeo I mandate left the district court with an exact Guidelines calculation that it should have imposed and that Booker was applied to his detriment. He further argues that because he pleaded guilty, he did not have any realistic notice or expectation that he could be sentenced to 10 years. We are unpersuaded.

First, Amedeo’s attempt to distinguish Duncan as a “plain error ease” is misplaced, as it relies on a portion of the Duncan opinion regarding the sentencing court’s constitutional error of applying the Guidelines in a mandatory fashion based on judicial factfinding. See Duncan, 400 F.3d at 1299, 1304. The portion of the opinion rejecting the defendant’s ex post facto claim held that there was no ex post facto/due process violation, and thus, no error in this regard. Id. at 1307-08. Moreover, we have applied both the reasoning and holding of Duncan in cases where the fair warning/due process issue was not before us on plain error review. See, e.g., Thomas, 446 F.3d at 1354-55. Next, as discussed above, Booker was an intervening change in the law making mandatory application of the Guidelines unlawful. Finally, the terms of Amedeo’s plea deal made clear that the district court had the authority to impose a sentence up to the statutory maximum of 40 years. Thus, Amedeo had sufficient warning to satisfy ex post facto and due process concerns. See Duncan, 400 F.3d at 1308. We therefore conclude that the retroactive application of Booker to Amedeo’s case did not violate his rights.

E. Reasonableness of the Sentence

Finally, Amedeo argues that his sentence of 120 months’ imprisonment was unreasonable. We review the sentence imposed for reasonableness. United States v. Castro, 455 F.3d 1249, 1251 (11th Cir.2006).

After correctly calculating the advisory Guidelines range, “[a] district court may impose a sentence that is either more severe or lenient than the sentence [this court] would have imposed, but that sentence must still be reasonable.” United States v. Talley, 431 F.3d 784, 788 (11th Cir.2005). Our “[r]eview for reasonableness is deferential,” and “the party who challenges the sentence bears the burden of establishing that the sentence is unreasonable in the light of both [the] record and the factors in section 3553(a).” Id. “The weight to be accorded any given § 3553(a) factor is a matter committed to the sound discretion of the district court[,]” and “[w]e will not substitute our judgment in weighing the relevant factors.” United States v. Williams, 456 F.3d 1353, 1363 (11th Cir.2006) (citations omitted). “Although sentencing courts must be guided by these factors, nothing in Booker or elsewhere requires the district court to state on the record that it has explicitly considered each of the § 3553(a) factors or to discuss each of the § 3553(a) factors.” Thomas, 446 F.3d at 1357 (citations omitted) (emphasis in original). “Rather, an acknowledgment by the district judge that he or she has considered the § 3553(a) factors will suffice.” United States v. Turner, 474 F.3d 1265, 1281 (11th Cir.2007). Nonetheless, “[t]he reasons given by the district court for its selection of a sentence are important to assessing reasonableness.” Williams, 456 F.3d at 1361. “A sentence based on an improper factor fails to achieve the purposes of § 3553(a) and may be unreasonable, regardless of length.” Id.

[*833] Regarding the factors that may be considered in fashioning a reasonable sentence, 18 U.S.C. § 3661 provides that “[n]o limitation shall be placed on the information concerning the background, character, and conduct of a person convicted of an offense which a court of the United States may receive and consider for the purpose of imposing an appropriate sentence.” 18 U.S.C. § 3661. And after Booker, “courts may still consider relevant facts concerning a defendant’s background, character, and conduct” when imposing a reasonable sentence. United States v. Faust, 456 F.3d 1342, 1348 (11th Cir.2006) (internal quotation omitted).

Amedeo contends that his sentence is unreasonable because (1) it was substantially greater than necessary to meet the goals of punishment set forth in § 3553(a); (2) the district court improperly ignored mitigating factors such as his first-offender status, his voluntary surrender of his law license, his incident-free incarceration history, and his history of public service; and (3) the district court improperly relied on factual findings that had either been “built into” the enhancements sustained on appeal, or reversed as inappropriate sentencing considerations. We disagree.

Here, the district court correctly calculated the Guidelines range, and the court’s statements during the resentencing hearing and in its resentencing order show that it considered the factors set forth in § 3553(a). For example, during the hearing, the court emphasized its “responsibility to impose no greater sentence than is required by the factors set forth in the guidelines and in Title 18, Section 3553(a).” And in the sentencing order, the court stated that it had considered “the particular historical circumstances and characteristics of the defendant!, § 3553(a)(1),]” that it imposed a sentence to “satisfy the dictates of 18 U.S.C. § 3553(a)[,]” and that it found “[Amedeo’s] sentence to be reasonable and necessary to protect the public from further crimes of the defendant!, § 3553(a)(2)(C)], to reflect the seriousness of the offense[, § 3553(a)(2)(A)], to afford an adequate level of deterrence to criminal conduct[, § 3553(a)(2)(B)], and to promote respect for the law[, § 3553(a)(2)(A)].” As stated above, in imposing a reasonable sentence, the district court need only “acknowledge” that it “considered the § 3553(a) factors[,]” Turner, 474 F.3d at 1281, and need not discuss each of these factors in either the sentencing hearing or in the sentencing order, see Thomas, 446 F.3d at 1357. Thus, although the district court’s sentencing order made no mention of evidence that arguably mitigated in Am-edeo’s favor under § 3553(a), we cannot say that the court’s failure to discuss this “mitigating” evidence means that the court erroneously “ignored” or failed to consider this evidence in determining Amedeo’s sentence. More important, Amedeo has not persuaded us that the resulting sentence was unreasonable in light of the particularly egregious circumstances of this case and the limited mitigating value of the evidence he presented. Additionally, as discussed above, we conclude that this court’s mandate in Amedeo I did not prohibit the district court from considering conduct such as Amedeo’s drug use with other minors, his sexual contact with Rozelle, and Rozelle’s death in imposing a variance based on the § 3553(a) factors. And- as for Amedeo’s argument that certain aspects of his conduct (such as the abuse of the attorney-client relationship) had already been considered in imposing an enhancement under U.S.S.G. § 3B1.3, Amedeo points to no authority that deems it impermissible for the district court to also have considered this conduct in imposing a variance in light of the factors set forth in § 3553(a). In our view, based on the extraordinary circumstances of this[*834] case, it was reasonable for the district court to rely on certain aspects of Ame-deo’s conduct, particularly his abuse of the attorney-client relationship, that it had already considered in imposing an enhancement. We therefore conclude that Ame-deo’s sentence was reasonable.

III. Conclusion

For the foregoing reasons, we AFFIRM.