ORDER AND JUDGMENT **
WADE BRORBY, Circuit Judge.Appellant challenges his sentence for possessing with intent to distribute 500 grams or more of methamphetamine. He argues that the district court erred in not granting a downward departure from the sentencing guidelines for providing substantial assistance to the government. While we lack jurisdiction to consider the district court’s refusal to depart downward, we have jurisdiction to review Appellant’s sentence for reasonableness. Conducting a reasonableness review, we determine that Appellant must be resentenced.
*662 Background
During a traffic stop in Kansas, a Highway Patrol Trooper discovered over 1,700 grams of methamphetamine in a vehicle occupied by Appellant and an associate. Both men were later indicted for unlawfully entering the United States and for possessing with intent to distribute 500 grams or more of methamphetamine. Appellant pleaded guilty to the possession count and the Government agreed to move to dismiss the unlawful-entry count.
The Presentence Investigation Report (PSR) calculated Appellant’s offense level as thirty-five and his criminal history as category two. Accordingly, Appellant fell in the guideline sentencing range of 188 to 235 months. The PSR also stated that there was no information to warrant a departure.
The Government later moved for “a 24 month reduction from the low end of the guideline range, resulting in a sentence of 164 months.” ROA, Vol. 2, Doc. 25 at 1. The Government stated only that “[t]he defendant has provided substantial assistance, as that term is used in [U.S.S.G.] § 5K1.1 and 18 U.S.C. [§ ] 3553(e), to the Government.” ROA, Vol. 2, Doc. 25 at 1. At the sentencing hearing, the district court reviewed the motion and commented, “This doesn’t tell me anything.” Id., Vol. 4, at 4. The Government then offered more substance:
The hang-up in the case was with the co-defendant. [Appellant], through proffering with his attorney, provided a proffer to the United States stating what he would say if he was to testify. He also was willing to testify against the co-defendant. Once the co-defendant’s counsel was notified of that, then the co-defendant did plead. So the Government believed that it was instrumental by [Appellant] for his cooperation and willingness to cooperate, so [the] Government filed the [motion] for a 24 month deviation from the advisory guidelines....
Id. The district court denied the motion, stating: “Rolling over on a co-defendant isn’t substantial assistance in my judgment.” Id. at 5.
The district court then heard the parties’ sentencing recommendations. While the Government recommended 188 months without elaborating, Appellant’s counsel recommended that “[Appellant] receive the low end of the sentencing guideline range” based, in part, on Appellant’s willingness to testify against his co-defendant. Id. at 5-6. The district court sentenced Appellant to the high end of the guideline range, 235 months, stating only that “the presentence report is accurate.” Id. at 7.
This appeal followed.
Discussion
I. Appellate Jurisdiction
“Upon motion of the government stating that the defendant has provided substantial assistance in the investigation or prosecution of another person who has committed an offense, the court may depart from the guidelines.” U.S.S.G. § 5K1.1; accord 18 U.S.C. § 3553(e). But “a district court’s discretionary refusal to grant a downward departure, including a refusal after a government motion pursuant to § 5K1.1,” is beyond our jurisdiction. United States v. Fitzherbert, 13 F.3d 340, 344 (10th Cir.1993). We have jurisdiction only in “the very rare circumstance that the district court states that it does not have any authority to depart from the sentencing guideline range for the entire class of circumstances proffered by the defendant.” United States v. Miranda-Ramirez, 309 F.3d 1255, 1258 (10th Cir. 2002) (quotation omitted).
Appellant and the Government both contend that we have jurisdiction. *663They argue that the district court failed to consider the particular circumstances of this case and instead announced that the entire class of defendants who cooperate against co-defendants is ineligible for § 5K1.1 relief. We disagree. Upon reviewing the Government’s motion, the district court observed that the motion revealed nothing about the circumstances of Appellant’s assistance to the Government. This prompted the Government to reveal those circumstances. The district court then characterized the extent of Appellant’s assistance as “[r]olling over,” and it denied the motion. At no time did the district court suggest that it lacked the authority to depart downward for cooperation against a co-defendant. See United States v. Rodriguez, 30 F.3d 1318, 1319 (10th Cir.1994) (“[U]nless the judge’s language unambiguously states that the judge does not believe he has authority to downward depart, we will not review his decision.”). Rather, the district court considered whether Appellant’s willingness to testify against his co-defendant constituted “substantial assistance,” and concluded that it did not. We lack jurisdiction to review that exercise of discretion.1 Accordingly, we DISMISS that portion of this appeal.
II. Reasonableness
Nevertheless, in light of United States v. Booker, 543 U.S. 220, 264, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), we do have jurisdiction to review Appellant’s sentence for reasonableness. See United States v. Chavez-Diaz, 444 F.3d 1223, 1229 (10th Cir. 2006). A sentence that falls within a properly calculated advisory range receives a presumption of reasonableness that may be rebutted by “demonstrating that the sentence is unreasonable when viewed against the other factors delineated in [18 U.S.C.] § 3553(a).”2 United States v. Kristl, 437 F.3d 1050, 1054 (10th Cir.2006).
Neither Appellant nor the Government discuss reasonableness in light of the prescribed factors. Instead, they assert that the sentence is unreasonable because the district court “refused to even consider the [Government’s] motion for a ‘substantial assistance’ reduction.” Aplt. Br. at 21; see also Aplee. Br. at 8. But as we indicated above in Part I, the district court considered whether Appellant’s cooperation with the Government was substantial assistance and found that it was not.
To the extent Appellant maintains that his sentence is unreasonable because the district court failed to consider his cooperation when it selected 235 months from the 188-to-235-month guideline range, we agree with the Second Circuit that in formulating a reasonable sentence under § 3553(a), a sentencing judge “should take under advisement ... the *664contention that a defendant made efforts to cooperate.” United States v. Fernandez, 443 F.3d 19, 33 (2d Cir.), cert. denied, — U.S. -, 127 S.Ct. 192, 166 L.Ed.2d 143 (2006). Appellant’s counsel argued for a low-end sentence based on Appellant’s cooperation, but the district court did not address it. Indeed, the district court did not reference any of the § 3553(a) factors in sentencing Appellant.3 “There is no question that, in addition to guiding our reasonableness review on appeal, the sentencing factors set forth in 18 U.S.C. § 3553(a) must be considered by the district court itself when imposing a sentence.” United States v. Sanchez-Juarez, 446 F.3d 1109, 1115 (10th Cir.2006). While “we will not demand that the district court recite any magic words to show us that it fulfilled its responsibility to be mindful of the factors that Congress has instructed it to consider,” we may not “simply presume [that] the district court weighed a party’s arguments in light of the § 3553(a) factors.” Id. at 1115-16 (quotations omitted). Consequently, when a defendant raises “substantial contentions concerning non-Guidelines § 3553(a) factors and the district court imposes a sentence within the Guidelines range,” the district court should “explain on the record how the § 3553(a) factors justify the sentence.” See United States v. Lopez-Flores, 444 F.3d 1218, 1222 (10th Cir.2006), petition for cert, filed, No. 06-5217 (U.S. July 7, 2006); see also Sanchez-Juarez, 446 F.3d at 1117 (requiring the district court to make a sufficient § 3553(a) record when presented with a “nonfrivolous argument”).
Because we cannot discern from the record whether the district court relied on the guidelines alone or whether it considered Appellant’s cooperation in light of the § 3553(a) factors, we REMAND to the district court with instructions to vacate Appellant’s sentence and to resentence him after expressly considering his request for a sentence reflecting his cooperation with the Government.4
After examining the briefs and appellate record, this panel has determined unanimously that oral argument would not materially assist the determination of this appeal. See Fed. R.App. P. 34(a)(2); 10th Cir. R. 34.1(G). The case is therefore ordered submitted without oral argument. This order and judgment is not binding precedent, except under the doctrines of law of the case, res judicata, and collateral estoppel. It may be cited, however, for its persuasive value consistent with Fed. R.App. P. 32.1 and 10th Cir. R. 32.1.
. Other circuits have likewise recognized a jurisdictional bar to reviewing whether a defendant’s willingness to testify against or to inculpate a co-defendant is “substantial assistance.” See, e.g., United States v. Foster, 988 F.2d 206, 208, 210 (D.C.Cir.1993); United States v. Dellinger, 986 F.2d 1042, 1043 (6th Cir. 1993).
. The § 3553(a) factors include: (1) the nature and circumstances of the offense and the history and characteristics of the defendant; (2) the need to reflect the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense; (3) the need for deterrence; (4) the need to protect the public; (5) the need to provide the defendant with needed educational or vocational training or medical care; (6) the kinds of sentences available; (7) the Sentencing Guidelines range; (8) pertinent policy statements of the Sentencing Commission; (9) the need to avoid unwanted sentencing disparities; and (10) the need to provide restitution to victims.
. The PSR was likewise silent as to § 3553(a).
. In remanding for resentencing, we in no way express an opinion regarding what the ultimate sentence should or should not be.