OPINION

IKUTA, Circuit Judge:

Jose Maria Vasquez-Cruz appeals from the 24-month prison sentence imposed following his conviction for illegal reentry in violation of 8 U.S.C. § 1326(a). He argues that the district court procedurally erred by failing to analyze whether he was entitled to a downward departure from the applicable sentencing range under the U.S. Sentencing Guidelines and by failing to adequately explain the chosen sentence. He also argues that the district court imposed a substantively unreasonable sentence. We have jurisdiction pursuant to 28 U.S.C. § 1291, and we affirm.

I

On December 15, 2010, the Bureau of Immigration and Customs Enforcement ("ICE") investigated a report that a previously deported alien was residing unlawfully in Reno, Nevada. The investigation led ICE agents to Vasquez-Cruz, a citizen of Mexico who had previously been removed from the United States on four occasions. On June 3, 2011, Vasquez-Cruz pleaded guilty to unlawful reentry by a deported, removed, or excluded alien in violation of 8 U.S.C. § 1326(a) without a plea agreement.

Taking into account Vasquez-Cruz's five prior criminal convictions for burglary, battery, and battery on a police officer, the presentence report calculated Vasquez-Cruz's total offense level as 13 and Criminal History Category as IV, which translated to a Guidelines range of 24 to 30 months imprisonment. The presentence report noted that Vasquez-Cruz might be culturally assimilated to the United States because he entered the country for the first time at age 8, but recommended against a downward departure from the Guidelines range on that basis. The report also noted that Vasquez-Cruz had learning disorders and mild retardation, but recommended that the district court not apply a downward variance under 18 U.S.C. § 3553(a) because of Vasquez-Cruz's criminal history which included four battery convictions. The presentence report then recommended a low-end guideline sentence of 24 months.

In response to the presentence report, Vasquez-Cruz filed a sentencing memorandum requesting a sentence of twelve months and one day. Vasquez-Cruz first argued that the district court should grant him a downward variance under 18 U.S.C. § 3553 on account of his cultural assimilation and mental disability. Vasquez-Cruz then argued that he was entitled to a downward departure under U.S.S.G. § 2L1.2 cmt. n.81 on account of his cultural assimilation. To support his request for a downward variance or departure, Vasquez-Cruz attached the expert reports of Dr. Martha B. Mahaffey, Ph.D., who diagnosed Vasquez-Cruz with mild mental retardation and other disabilities, and Dr. Amado M. Padilla, Ph.D., who concluded that Vasquez-Cruz "meets the necessary criteria for cultural assimilation."

At the sentencing hearing, the district court listened to the parties' arguments, including discussion of Vasquez-Cruz's cultural assimilation and mental disability. Before imposing a sentence, the court stated that it had "carefully considered" the presentence report, defendant's sentencing memorandum, and the expert reports, and "also considered the factors which the Court is required to consider under 18 United States Code, Section 3553(a)." The court held that the appropriate Guidelines range was 24 to 30 months and remarked that Vasquez-Cruz "doesn't fall outside the heartland of that, nor do I see any basis for a variance [or] departure in this case." The court then imposed a sentence of 24 months, at the low end of the Guidelines range. It reasoned that, although "inclined to impose a sentence at the highest end of the guideline range, or even consider a departure upward" because of Vasquez-Cruz's "fairly extensive" and "troubling" criminal history, a low end sentence was nevertheless warranted "because of the defendant's mental capacity."

Vasquez-Cruz timely appealed his sentence. On appeal, Vasquez-Cruz argues that the district court procedurally erred by failing to determine whether he was entitled to a departure under the Sentencing Guidelines before considering whether he was entitled to a variance under 18 U.S.C. § 3553(a). This failure, Vasquez-Cruz argues, violates the sequencing required by U.S.S.G. § 1B1.1, as amended in 2010, which directs district courts to first determine the Guidelines range, then consider departures from the Guidelines, and finally consider "the applicable factors in 18 U.S.C. § 3553(a) taken as a whole." Vasquez-Cruz also asserts that the district court procedurally erred by failing to give an adequate explanation of the chosen sentence, and that the district court abused its discretion by imposing a substantively unreasonable sentence.

II

In reviewing a sentence determination, a court "must first ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the § 3553(a) factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentence — including an explanation for any deviation from the Guidelines range." Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007). If the district court's sentence is procedurally sound, "the appellate court should then consider the substantive reasonableness of the sentence imposed under an abuse-of-discretion standard." Id.

A

We turn first to Vasquez-Cruz's argument that the district court procedurally erred by failing to address whether he was entitled to a departure for cultural assimilation under U.S.S.G. § 2L1.2 cmt. n.8 before applying the sentencing factors set forth in 18 U.S.C. § 3553(a).

We have long held that we do not review the procedural correctness of a district court's discretionary decision to depart from the Guidelines range. Rather, we "treat the scheme of downward and upward `departures' as essentially replaced by the requirement that judges impose a `reasonable' sentence." United States v. Mohamed, 459 F.3d 979, 986 (9th Cir. 2006); see also United States v. Ellis, 641 F.3d 411, 421 (9th Cir.2011). In Mohamed we explained that, even if the district court erred in applying a departure, there would be no point in reversing for such an error because "the sentencing judge still would be free on remand to impose exactly the same sentence by exercising his discretion under the now-advisory guidelines" and "[s]uch a sentence would then be reviewed for reasonableness." 459 F.3d at 987. For this reason, any erroneous application of the departure would be harmless so long as the sentence actually imposed was substantively reasonable. Therefore, "our review of the so-called departure would have little or no independent value" and "would result in wasted time and resources in the courts of appeal, with little or no effect on sentencing decisions." Id.2 We made clear that these rules governed the appellate review of post-Booker sentences, id. at 985-86 (citing United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005)), and did not prevent "consultation of the system of departures that existed under the mandatory regime, either by the district court or by this court," id. at 987. In declining to review departures, we acknowledged that we were parting ways with several of our sister circuits, and instead following the Seventh Circuit, which had declared that "`the concept of "departures" has been rendered obsolete in the post-Booker world.'" Id. at 986 (quoting United States v. Arnaout, 431 F.3d 994, 1003 (7th Cir.2005)).

Vasquez-Cruz argues that Mohamed was abrogated by the Sentencing Commission's 2010 amendment to § 1B1.1 of the Guidelines, referred to as Amendment 741. See U.S.S.G. app. C, vol. III, at 352-54 (2011). As explained by the Sentencing Commission, Amendment 741 reorganized the text of § 1B1.1 to divide the existing sentencing procedure into three steps.3 The specific language changes to § 1B1.1 made by Amendment 741 were relatively minor. First, the amendment made non-material adjustments to the instructions to district courts for determining the correct Guidelines range.4 Second, the amendment grouped the instructions into three subsections (subsections (a) to (c) with nested paragraphs (1) to (8)), rather than listing all instructions in order as subsections (a) to (i). Finally, the amendment added subsection (c), which, per Booker, requires the district court to determine the substantive reasonableness of the sentence by considering "the applicable factors in 18 U.S.C. § 3553(a) taken as a whole." U.S.S.G. § 1B1.1(c). The Sentencing Commission also amended the Commentary to § 1B1.1 to note that "[s]ubsections (a), (b), and (c) are structured to reflect the three-step process used in determining the particular sentence to be imposed." U.S.S.G. app. C, vol. III, at 353 (2011). In its statement of reasons for Amendment 741, the Sentencing Commission explained that while most circuits "agree on a three-step approach" to determining a sentence, "including the consideration of departure provisions," the Seventh Circuit had stated "that departures are `obsolete.'" Id. at 353-54. According to the Sentencing Commission, Amendment 741 "resolves the circuit conflict and adopts the three-step approach followed by a majority of circuits in determining the sentence to be imposed." Id. at 354. Although not mentioned by the Sentencing Commission, our decision in Mohamed also followed the Seventh Circuit approach.

We now face the question whether Amendment 741 abrogates our decision in Mohamed to review a district court's imposition of a sentence outside the Guidelines range only for substantive reasonableness. Under our "law of the circuit" doctrine, we generally hold that "a published decision of this court constitutes binding authority which `must be followed unless and until overruled by a body competent to do so.'" Gonzalez v. Arizona, 677 F.3d 383, 389 n. 4 (9th Cir.2012) (en banc) (quoting Hart v. Massanari, 266 F.3d 1155, 1170 (9th Cir.2001)). Of course, a change in the language of an applicable Guidelines provision, including a change in application notes or commentary, supersedes prior decisions applying earlier versions of that provision, just as we would be bound to apply the updated version of an agency rule or regulation. See Stinson v. United States, 508 U.S. 36, 44-45, 113 S.Ct. 1913, 123 L.Ed.2d 598 (1993) (holding that "the guidelines are the equivalent of legislative rules adopted by federal agencies," and the "commentary ... assist[s] in the interpretation and application of those rules"). For example, in United States v. Van Alstyne, 584 F.3d 803 (9th Cir.2009), we considered Guidelines Amendment 617, which amended § 2B1.1 (relating to various fraud offenses) to establish the method for calculating losses incurred because of fraud when determining a defendant's offense level. We held that the amended provision superseded a prior decision that had applied a different methodology. Id. at 817. Similarly, in United States v. McEnry, 659 F.3d 893 (9th Cir.2011), we held that Guidelines Amendment 591, which removed a sentence in the introduction to the Statutory Appendix and § 1B1.2(a) in order to clarify that offense conduct should not be considered in selecting the applicable offense guideline section, superseded prior decisions that had relied on the excised language. Id. at 899 & n. 8.

Amendment 741, however, does not make the sorts of changes to the language or application of a Guidelines provision that would overrule our prior case law.

First, unlike the amendments at issue in Van Alstyne and McEnry, the amendment to § 1B1.1 did not make any material changes to that provision. Rather, the language of the amended § 1B1.1 used substantially identical language to the language interpreted in Mohamed. Compare § 1B1.1(i) (2006) ("Refer to Parts H and K of Chapter Five, Specific Offender Characteristics and Departures, and to any other policy statements or commentary in the guidelines that might warrant consideration in imposing sentence"), with § 1B1.1(b) ("The court shall then consider Parts H and K of Chapter Five, Specific Offender Characteristics and Departures, and any other policy statements or commentary in the guidelines that might warrant consideration in imposing sentence. See 18 U.S.C. § 3553(a)(5)."). These immaterial changes give us no basis for abrogating Mohamed. Nor does the background commentary amount to a change in the law in place at the time we decided Mohamed because the commentary merely advises district courts to follow the three-step process in imposing a sentence.

Second, Amendment 741 is not inconsistent with our reasoning in Mohamed. Amendment 741 gives procedural direction to the district courts regarding the sequence of sentencing determinations, and does not purport to require the appellate courts to review the district courts' departures determinations. Mohamed, on the other hand, did not interpret the Guidelines's sequencing provisions; rather, it set forth "our approach to reviewing post-Booker sentences," 459 F.3d at 984, as appellate courts, and did "not preclude consultation of the system of departures that existed under the mandatory regime, either by the district court or by this court," id. at 987. Furthermore, nothing in Amendment 741 undercuts our reasoning in Mohamed that reviewing post-Booker departures "would result in wasted time and resources" because any error in applying departure provisions would ultimately be harmless. Id. Although we have held that procedural errors in determining the correct sentencing range are generally prejudicial and require reversal, United States v. Munoz-Camarena, 631 F.3d 1028, 1031 (9th Cir.2011), Amendment 741 does not even address Mohamed's opposite conclusion that an error in making a discretionary departure determination is not such a procedural error requiring reversal, see Gall, 552 U.S. at 51, 128 S.Ct. 586 (listing procedural errors, not including errors in applying departure provisions), and that our review of a departure error is subsumed in the review of the ultimate sentence for substantive reasonableness. Because Mohamed's determinations on these points relate to appellate procedure, an area outside the purview of the Sentencing Commission, we cannot say that Amendment 741 requires us to alter the approach established in Mohamed.

We conclude that in this case, the law of the circuit is controlling. Because Amendment 741 addresses the district courts' procedures, rather than the courts of appeals' procedures, and in light of our law of the circuit doctrine, we cannot say that Amendment 741 so changed the legal landscape that we are free to reconsider and overrule Mohamed. See Hart, 266 F.3d at 1172.

We note that our reading of Mohamed accords with the Seventh Circuit's decision in United States v. Guyton, 636 F.3d 316, 319 n. 2 (7th Cir.), cert. denied ___ U.S. ___, 132 S.Ct. 132, 181 L.Ed.2d 53 (2011). As discussed above, Mohamed followed the Seventh Circuit's approach in declining to review departures for procedural correctness. See Mohamed, 459 F.3d at 987. The Seventh Circuit, when presented with the same argument made here, held that the amendment to U.S.S.G. § 1B1.1 did not affect its holdings in Johnson and Arnaout (the cases followed by this court in Mohamed) because this line of cases "should not discourage district courts from taking genuine guidance from all the Guidelines, including their departure provisions, as required under the amended section 1B1.1." Guyton, 636 F.3d at 319 n. 2. We agree.

In sum, we adhere to our precedent that requires us to decline to review whether the district court procedurally erred by failing to grant Vasquez-Cruz a departure or by failing to consider departures before applying the § 3553(a) factors. Accordingly, we decline Vasquez's invitation to review the district court's denial of a departure (as well as the court's consideration of Vasquez's departure and variance arguments together, rather than as separate steps). Instead, we review the district court's exercise of discretion only for substantive reasonableness. Mohamed, 459 F.3d at 986-87.

B

We next consider Vasquez-Cruz's argument that the district court procedurally erred by failing to adequately explain the chosen sentence. See Gall, 552 U.S. at 51, 128 S.Ct. 586. This argument likewise fails.

A district court may commit a procedural error if it fails to adequately explain the sentence selected, including any deviation from the Guidelines range. United States v. Fitch, 659 F.3d 788, 796-98 (9th Cir.2011); United States v. Carty, 520 F.3d 984, 992 (9th Cir.2008) (en banc). The district court must "set forth enough to satisfy the appellate court that [it] has considered the parties' arguments and has a reasoned basis for exercising his own legal decisionmaking authority." Rita v. United States, 551 U.S. 338, 356, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007). While a within-Guidelines sentences does "not necessarily require lengthy explanation," id., "[w]here the defendant or prosecutor presents nonfrivolous reasons for imposing a different sentence ... the judge will normally go further and explain why he has rejected those arguments," id. at 357, 127 S.Ct. 2456. In United States v. Carter, 560 F.3d 1107 (9th Cir.2009), we held that the district court need not give explicit reasons for rejecting a defendant's argument for a Guidelines departure where the record reflects that the court considered defendant's evidence and arguments. Id. at 1118-19.

Here, the district court's explanation for the sentence it imposed was legally sufficient. The district court explained that Vasquez-Cruz's case was within the "heartland" of the Guidelines range, and that it did not "see any basis for a variance [or] departure in this case." The court then expressly considered the § 3553(a) factors, concluding that, notwithstanding Vasquez-Cruz's "fairly extensive" criminal history, a low-end sentence was warranted because of Vasquez-Cruz's mental disability. Because the record makes clear that the sentencing judge considered the relevant evidence and argument, Vasquez-Cruz's claims of procedural error fail. See Carter, 560 F.3d at 1118-19.

C

Because Vasquez-Cruz has not identified any "significant procedural error," we review the sentence for substantive reasonableness. Gall, 552 U.S. at 51, 128 S.Ct. 586. We conclude the district court's within-Guidelines sentence was reasonable in light of the totality of circumstances, taking into account Vasquez-Cruz's four prior deportations and five other criminal convictions as well as the evidence of his cultural assimilation and mental capacity. The record establishes that the district court carefully weighed the § 3553(a) factors before coming to the conclusion that it did not "see any basis for a variance [or] departure in this case." The district court expressly considered Vasquez-Cruz's mental disability. Specifically, the court observed that, although inclined to impose a high-end sentence or depart upward, a low-end sentence was nevertheless appropriate "because of the defendant's mental capacity" which "probably diminishes his ability to totally function as a person who did not have that type of disability would function" and "warrants some consideration in the guideline range." Although the district court did not mention cultural assimilation, its decision to order a low-Guidelines sentence notwithstanding Vasquez-Cruz's "fairly extensive" criminal history is certainly reasonable. When, as here, "`the judge's discretionary decision accords with the Commission's view of the appropriate application of § 3553(a) in the mine run of cases, it is probable that the sentence is reasonable.'" Carty, 520 F.3d at 994 (quoting Rita, 551 U.S. at 351, 127 S.Ct. 2456).

For the reasons given, we affirm the judgment of the district court.

AFFIRMED.