
641 F.3d 1189 (2011)
UNITED STATES of America, Plaintiff-Appellee,
v.
Juan Felipe RODRIGUEZ-CASTRO, Defendant-Appellant.
No. 10-50273.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted May 4, 2011.
Filed June 2, 2011.
*1190 Kurt D. Hermansen, San Diego, CA, for the appellant.
Emily J. Keifer, Assistant United States Attorney, San Diego, CA, for the appellee.
Before: BARRY G. SILVERMAN, RICHARD C. TALLMAN, and RICHARD R. CLIFTON, Circuit Judges.
Opinion by Judge CLIFTON; Concurrence by Judge SILVERMAN.

OPINION
CLIFTON, Circuit Judge:
Juan Felipe Rodriguez-Castro ("Rodriguez") pled guilty to importing 33.46 kilograms of cocaine in violation of 21 U.S.C. §§ 952 and 960. Rodriguez was sentenced to 57 months imprisonment. Rodriguez appeals this sentence, contending that the district court erred in declining to decrease the base offense level, as recommended by the plea agreement he had entered into with the government. The district court found that Rodriguez failed to demonstrate he was a "minor participant" in the offense. Accordingly, the court determined that Rodriguez was not entitled to a minor-role adjustment to the offense level. We conclude that the district court did not clearly err in its factual determination or abuse its discretion in declining to award the minor-role adjustment. We also conclude that the sentence imposed was substantively reasonable. We thus affirm the sentence imposed upon Rodriguez by the district court.

I. Background
Rodriguez was arrested for entering the United States from Mexico with a large amount of cocaine, 33.46 kilograms, hidden within the gas tank of his vehicle. Rodriguez later admitted that he knew an unlawful drug was concealed in the vehicle but claimed that he did not know that it *1191 was cocaine. He said that several weeks prior to his arrest, he was asked by a coworker to accept a vehicle, register the vehicle in his name, and cross the border with drugs hidden inside, in exchange for between $3,500 and $4,000. Rodriguez agreed to the offer. In order to develop a record at the Port of Entry, Rodriguez crossed into the United States with the vehicle at least two or three times prior to the crossing during which he was arrested.
After his arrest, Rodriguez entered into a plea agreement with the government. The agreement noted that the sentence was within the sole discretion of the sentencing judge, but also provided that the parties would jointly make recommendations as to the calculations to be made under the now-advisory United States Sentencing Guidelines. In particular, the parties recommended that Rodriguez be granted a two-level downward adjustment in the offense level, pursuant to U.S.S.G. § 3B1.2(b), on the ground that Rodriguez played a minor role in the offense, as he was merely a courier.[1] The agreement stated that "Defendant must adequately set forth a factual basis to support a minor role." Had Rodriguez received this minor-role adjustment, Rodriguez's base offense level would have also been decreased three levels pursuant to U.S.S.G. § 2D1.1(a)(5)(ii).[2] Assuming a minor-role adjustment, the plea agreement recommended a sentence of between 41 and 51 months.
The Presentencing Report recommended that Rodriguez not be given a minor-role adjustment, and in calculating the Guidelines sentencing range, the district court declined to award such a minor-role adjustment to Rodriguez. Judge Burns determined that Rodriguez failed to prove he had played only a minor role in the offense, emphasizing Rodriguez's role in preparing for the offense. Judge Burns also expressed doubt that such a substantial quantity of cocaine would have been entrusted to a minor participant.
The expressed dissatisfaction of Judge Burns with the government's practice in his district of offering a minor-role adjustment recommendation at an early stage of plea negotiations became a matter of contention during Rodriguez's sentencing, and it is raised by Rodriguez as part of his appeal. The government explained to the district court that its practice was to offer the minor-role adjustment as part of a plea agreement, even though relatively little might be known at that point about the particular defendant's actual role. The government contended that it would later require the defendant to factually support his qualification for the minor role, as the agreement provided, and that it would withdraw the recommendation if it concluded that the defendant did not provide a sufficient basis. Judge Burns questioned this practice, expressing his view that the government's approach was backwards and that a minor-role recommendation *1192 should not be offered until there was a factual basis established for it.
In sentencing Rodriguez, the district court calculated the adjusted offense level under the Sentencing Guidelines to be 27. The court also considered the factors under 18 U.S.C. § 3553(a), and in the course of doing that, exercised its discretion to vary downward from the Guidelines calculation by two additional levels, to avoid unwarranted disparities when compared to similarly situated defendants. That effectively reduced Rodriguez's adjusted offense level to 25. Because Rodriguez was in criminal history category I, that variation suggested a Guidelines sentencing range of 57 to 71 months. The court imposed a sentence of 57 months.
Because the court imposed a sentence greater than the Guidelines range proposed in the plea agreement, the waiver of appeal contained in the plea agreement did not apply. Rodriguez timely appealed.

II. Discussion
Rodriguez raises several arguments on appeal. First, he contends that judicial estoppel and the plea agreement preclude the government from arguing on appeal in support of the imposed sentence. Second, he asserts that Judge Burns abused his discretion by declining to award a minor-role downward adjustment in the offense level decrease on the basis of his personal disagreement with the government's plea policy. Third, Rodriguez contends that the sentence imposed was substantively unreasonable.
We review de novo the district court's interpretation of the Sentencing Guidelines. United States v. Rodriguez-Cruz, 255 F.3d 1054, 1058 (9th Cir.2001). The district court's application of the Guidelines to the facts of a particular case is reviewed for an abuse of discretion. Id. Similarly, we review the substantive reasonableness of a sentence for abuse of discretion. United States v. Carty, 520 F.3d 984, 993 (9th Cir.2008) (en banc). A district court's finding that a defendant is not a minor participant in criminal activity is a factual determination reviewed for clear error. United States v. Hursh, 217 F.3d 761, 770 (9th Cir.2000).

A. Judicial Estoppel and the Plea Agreement
We first address whether the government is judicially estopped from arguing in support of the sentence imposed by the district court, and whether in so arguing the government is in breach of the plea agreement. Clearly, it is not.
Under the plain terms of the plea agreement, the government is "free to support on appeal the sentence actually imposed." The government has not violated the plea agreement by taking the position on appeal that the sentence should be affirmed. See United States v. Schuman, 127 F.3d 815, 817-18 (9th Cir.1997) (per curiam).
The government's position on appeal is not that Rodriguez was not entitled to a minor-role adjustment, but that the district court did not err in declining to award the adjustment. This argument is not inconsistent with its argument to the district court, so estoppel cannot apply here. See Russell v. Rolfs, 893 F.2d 1033, 1037 (9th Cir.1990) (noting that estoppel applies where a party makes an assertion in a legal proceeding that directly contradicts an earlier assertion).

B. Minor-Role Adjustment
We next turn to the issue of whether Rodriguez was entitled to a minor-role adjustment and, more broadly, whether the court properly calculated the appropriate Sentencing Guidelines range. We conclude that the district court did not clearly err in finding that Rodriguez failed to establish *1193 that he played a minor role in the offense and did not abuse its discretion in applying the Guidelines.
A decrease of two offense levels is warranted under U.S.S.G. § 3B1.2(b) if the "defendant was a minor participant in any criminal activity." The comments to the Guidelines clarify that a minor participant is one who "plays a part in committing the offense that makes him substantially less culpable than the average participant." Id. § 3B1.2 cmt. n. 3(A) (emphasis added); see United States v. Cantrell, 433 F.3d 1269, 1283 (9th Cir.2006). The determination of a "minor role" is "heavily dependent upon the facts of the particular case." U.S.S.G. § 3B1.2 cmt. n. 3(C).
Rodriguez's appeal is largely premised upon his assertion that Judge Burns denied the minor-role adjustment solely because he disagreed with the government's plea agreement policy. That premise is incorrect.
Judge Burns's critique of the government's policy did not reflect a practice on his part to automatically reject all minor-role pleas. To the contrary, Judge Burns noted during the sentencing hearing that he had given minor-role reductions to some other couriers in the past. Judge Burns acted within his authority to determine whether the particular facts regarding this particular defendant supported a minor-role adjustment. He found that they did not. The court was not bound by the parties' recommendation, and Rodriguez does not contend that it was.
We begin our review of the challenged finding with the understanding that a defendant "may be a courier without being either a minimal or a minor participant." United States v. Lui, 941 F.2d 844, 849 (9th Cir.1991). We have "denied downward adjustments to defendants who were couriers where some additional factor showing that they were not a[sic] minor or minimal participants existed." United States v. Davis, 36 F.3d 1424, 1436 (9th Cir.1994). Such instances include when the defendant imported a substantial amount of drugs. Id. at 1436-37 (citing Lui, 941 F.2d at 849). In addition, it is well established that "[t]he defendant bears the burden of proving that he is entitled to a downward adjustment based on his role in the offense." Cantrell, 433 F.3d at 1282 (citations and alterations omitted).
In support of its finding, the district court cited both Rodriguez's role in preparing for the offense and the substantial quantity of drugs involved. As to the first, the court noted that Rodriguez accepted the car, registered it in his name in advance, and made several crossings across the border to create a crossing record. With respect to the quantity of drugs, the parties do not dispute that 33.46 kilograms of cocaine was a substantial amount. We have "recognized that possession of a substantial amount of narcotics is grounds for refusing to grant a sentence reduction," even in amounts smaller than 1 kilogram. Lui, 941 F.2d at 849 (citations omitted). The court was justifiably skeptical that this amount of drugs would be entrusted to a minor player.
The district court did not clearly err in finding that Rodriguez did not meet his burden to prove he had a minor role in the offense, and it did not abuse its discretion in declining to award Rodriguez the minor-role reduction under § 3B1.2(b). Because the § 3B1.2(b) adjustment was not warranted, Rodriguez was not entitled to the additional reduction under § 2D1.1(a)(5). A reduction under § 2D1.1(a)(5) is applied only "if ... the defendant receives an adjustment under § 3B1.2" (emphasis added). There is no support in the record for Rodriguez's claim that Judge Burns purposefully circumvented § 2D1.1(a)(5), and therefore no procedural error occurred.


*1194 C. Substantive Reasonableness of the Imposed Sentence

Finally, Rodriguez contends that his 57-month sentence was substantively unreasonable under the 18 U.S.C. § 3553(a) factors. We disagree.
With respect to Rodriguez's primary objection, the fact that Judge Burns stated the sentence was an "appropriate sentence" instead of a sentence "not greater than necessary" does not indicate the court applied an incorrect standard. This Court has itself stated that a district court should arrive at an "appropriate sentence." Carty, 520 F.3d at 991. Moreover, the district court is not required to articulate each specific § 3553 factor or use specific phrases during the sentencing process. See United States v. Diaz-Argueta, 564 F.3d 1047, 1051-52 (9th Cir.2009). Rodriguez's reliance on this particular phrase is therefore unavailing.
The district court did not abuse its discretion when weighing the totality of the circumstances and the § 3553 factors. See Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007). Judge Burns considered Rodriguez's work history, the lack of a criminal record in Mexico, his role as a "conscientious father," and the need to avoid unwarranted sentence disparities. The court was also cognizant, however, of the need to deter Rodriguez and other individuals from bringing in "huge amounts of cocaine."

III. Conclusion
The sentence imposed upon Rodriguez by the district court is affirmed.
AFFIRMED.
SILVERMAN, Circuit Judge, with whom Judge TALLMAN joins, concurring:
George Gobel once said that he sometimes feels like the whole world is a tuxedo and he, a pair of brown shoes. That must be how Judge Burns feels when the AUSA and defense counsel jointly and routinely present for his approval plea agreements containing fact-based sentencing inducements before the facts are even known. When Judge Burns refuses to rubber-stamp these agreements, counsel balk. Who does he think he is? Doesn't he understand that he's messing up the plea bargaining process? As the appellant's opening brief puts it, "The district court abused its discretion by failing to apply the minor-role adjustment when both parties recommended the adjustment." A.O.B. at 16. Never mind that the district judge is obligated  not just encouraged but obligated  to accurately calculate the sentencing guidelines no matter what the parties would like it to be. Once the guidelines have been calculated correctly, a district judge is then free to deviate from them for good cause, which is exactly what Judge Burns did here, in the defendant's favor, no less.
I completely agree with my colleagues that no matter how eagerly both counsel sought to get rid of this case by way of plea agreement, Judge Burns was well within his discretion in ruling that this defendant was not shown to be entitled to a minor-role adjustment. Other reductions, yes, but not that one. The majority opinion, which I fully join, explains why.
Sentencing is solely the responsibility of the judge. Like the little boy who tells the emperor he's not wearing any clothes, Judge Burns can hardly be faulted for telling the parties that their boilerplate factual findings lack a basis in fact.
NOTES
[1]  The relevant portion of section 3B1.2 provides: "Based on the defendant's role in the offense, decrease the offense level as follows:... (b) If the defendant was a minor participant in any criminal activity, decrease by 2 levels." U.S.S.G. § 3B1.2(b).
[2]  U.S.S.G. § 2D1.1(a)(5) provides that the base offense level will be the greatest of:

The offense level specified in the Drug Quantity Table set forth in subsection (c), except that if (A) the defendant receives an adjustment under § 3B1.2 (Mitigating Role); and (B) the base offense level under subsection (c) is (i) level 32, decrease by 2 levels; (ii) level 34 or level 36, decrease by 3 levels; or (iii) level 38, decrease by 4 levels. If the resulting offense level is greater than level 32 and the defendant receives the 4-level ("minimal participant") reduction in § 3B1.2(a), decrease to level 32.
