
532 F.3d 625 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Darryl W. CHAPMAN and John Frank, also known as Jack Frank, Defendants-Appellants.
Nos. 07-3637, 07-3639.
United States Court of Appeals, Seventh Circuit.
Argued May 28, 2008.
Decided July 10, 2008.
Paul W. Connell (argued), Jeffrey M. Anderson, Office of the United States Attorney, Madison, WI, for Plaintiff-Appellee.
Thomas G. Wilmouth (argued), Federal Defender Services of Eastern Wisconsin, Inc., Milwaukee, WI, Michele A. Tjader, Tjader & Chirafisi, Madison, WI, for Defendants-Appellants.
*627 Before EASTERBROOK, Chief Judge, and RIPPLE and WOOD, Circuit Judges.
*626 RIPPLE, Circuit Judge.
Darryl Chapman and John Frank each were convicted and sentenced for unrelated drug crimes. While serving their sentences, both men independently provided substantial assistance to the Government. Accordingly, the Government filed motions to reduce their otherwise final sentences under Federal Rule of Criminal Procedure 35(b). The district court granted the Government's motions, reducing Mr. Chapman's sentence from 120 to 102 months and Mr. Frank's sentence from 84 to 72 months. On appeal, the defendants contend that the district court failed to consider properly their arguments for greater sentence reductions. For the reasons set forth in this opinion, we affirm the judgment of the district court.

I

BACKGROUND
Darryl Chapman and John Frank each pleaded guilty to unrelated charges of knowingly and intentionally distributing cocaine in violation of 21 U.S.C. § 841(a)(1). On April 19, 2006, the district court sentenced Mr. Chapman to 120 months' imprisonment. On September 13, 2006, the district court sentenced Mr. Frank to 84 months' imprisonment. Both of these sentences were within the applicable sentencing guidelines range, but both were at the higher end of their respective ranges.
After they were sentenced, both defendants independently gave substantial assistance to the Government. At great risk to the safety of his family and himself, Mr. Chapman gave law enforcement officers the name of his former cocaine source. His cooperation resulted in the apprehension and conviction of a major source of marijuana and cocaine distribution in the area. Mr. Frank also named his drug source, and that information assisted in the conviction of three other individuals. In return for this assistance, the Government filed a motion to request a reduction in their sentences under Rule 35(b).
At Mr. Chapman's hearing before the district court, both the Government and Mr. Chapman's counsel noted the timeliness, truthfulness, completeness and reliability of his assistance, as well as the fact that Mr. Chapman had been threatened in prison because of his cooperation. In light of these circumstances, the Government requested that the court reduce Mr. Chapman's offense level by two levels and then impose a sentence at the bottom of the resulting guidelines rangespecifically, 84 months. Mr. Chapman agreed with this recommendation.
The district court granted the Government's motion and reduced Mr. Chapman's offense level by two levels; however, it imposed a sentence of 102 months, a sentence at the high end of the guidelines range. The court remarked that Mr. Chapman's significant criminal history counseled against imposing a lower sentence, and it stated that a sentence of 102 months "will still hold this defendant accountable for his criminal conduct while factoring in his substantial assistance." Chapman Tr. at 7-8.
Similarly, at Mr. Frank's hearing, the Government and the defense counsel requested that the court reduce Mr. Frank's sentence based upon his significant assistance. The Government did not propose a particular reduction, but Mr. Frank suggested a five-level reduction. The court granted the Government's motion and decided to reduce Mr. Frank's offense level by one level. It sentenced Mr. Chapman to 72 months' imprisonment, a sentence at *628 the high end of the new guidelines range. Much like it did in Mr. Chapman's case, the court emphasized Mr. Frank's significant prior criminal history as well as the substantial quantity of drugs that had been involved in his crime. The court stated that 72 months' imprisonment will "hold this defendant accountable for his criminal conduct while factoring in his substantial assistance." Frank Tr. at 8.

II

DISCUSSION

A.
An appeal from a Rule 35(b) order is an appeal from an "otherwise final sentence," over which we have jurisdiction only in limited circumstances. United States v. McGee, 508 F.3d 442, 444 (7th Cir.2007); see also 18 U.S.C. § 3742(a). Section 3742 does not grant appellate courts jurisdiction to review a district court's exercise of its discretion under Rule 35(b). See McGee, 508 F.3d at 444-45 ("[O]ur jurisdictional mandate is limited and does not extend to a district court's discretionary decisions regarding sentencing.").[1] Accordingly, our review of a sentence reduction here is more limited than our review of an original sentence. We ask only whether the reduction was imposed in violation of the law, not whether the new sentence imposed was reasonable. See id. at 445.
The Government characterizes the defendants' claims as mere complaints that the district court did not exercise its discretion to reduce their sentences to the extent they had hoped. In the Government's view, the defendants' arguments do not amount to an allegation that they were sentenced "in violation of law"; therefore, in its view, we do not have jurisdiction to consider their claims under section 3742.
If the defendants' arguments could be reduced to the simple claim that the district court, after considering the appropriate factors, should have granted a greater reduction, then appellate review indeed would be impermissible here. We cannot accept, however, the Government's characterization of the defendants' arguments. As we understand their arguments, Mr. Chapman and Mr. Frank do not simply contend that the district court should have reduced further their sentences. Instead, they submit that the district court, in determining the proper sentence, considered factors that it should not have considered (i.e., factors already considered at the original sentencing), and failed to consider factors that it should have considered (i.e., the disparity between the defendants' reduction and reductions granted to other defendants who had given similar levels of assistance to the Government, and, in Mr. Chapman's case, the fact that both the Government and the defendant agreed on a suggested sentence of 84 months). We suggested in McDowell that an assertion of this type of methodological error "alleges an error of law subject to our jurisdiction under section 3742(a)." 117 F.3d at 978; see also United States v. Doe, 351 F.3d 929, 932 (9th Cir.2003) (holding that the appellate court did have jurisdiction under section 3742 to review whether the district court's consideration of factors other than substantial assistance in denying *629 the Government's Rule 35(b) motion was improper); United States v. Manella, 86 F.3d 201, 203 (11th Cir.1996) (same). Consequently, we have jurisdiction to consider the defendants' legal claims.

B.
The defendants submit that the district court imposed their sentences "in violation of law," 18 U.S.C. § 3742(a), for three reasons. First, they contend that the district court focused improperly upon their criminal histories and the nature of their crimes, factors already considered at their original sentencing. Second, they contend that the district court improperly failed to consider their arguments regarding the potential for unwarranted sentencing disparities. Third, Mr. Chapman suggests that the district court's dismissal of the Government's request for a sentence of 84 months, without explanation, was unwarranted. We shall consider each of these arguments in turn.

1.
To the extent that the defendants contend that the district court's consideration of their criminal histories and the nature of their crimes was improper because those factors already had been considered at the initial sentencing hearing, we have jurisdiction to consider their claim. The substantive argument made here was made in the Ninth Circuit case of Doe, 351 F.3d at 932, and in an Eleventh Circuit case relied upon by the defendants, Manella, 86 F.3d at 203-05, although it ultimately was rejected by both courts. The Ninth Circuit in Doe held that a court may look to the section 3553 factors in imposing a new sentence under Rule 35(b), even though those factors already had been considered at the original sentencing hearing. Doe, 351 F.3d at 932. Similarly, the Eleventh Circuit held that Rule 35(b) does not prohibit consideration of the section 3553 factors, including the seriousness of a defendant's offense, in deciding the extent to which a defendant's sentence should be reduced for substantial assistance. Manella, 86 F.3d at 204-05.
The reasoning of these decisions is persuasive. Nothing in the text of Rule 35(b) limits the factors that may militate against granting a sentence reduction or for granting a smaller reduction than requested. The defendants do not provide any persuasive reasons for restricting the court's consideration to factors not considered at the original sentencing hearing. On the other hand, a faithful and pragmatic adherence to the mandate of 18 U.S.C. § 3553(a) counsels that the nature and extent of any reduction be determined in light of all the sentencing factors set forth in the statute. Post-arrest cooperation cannot be assessed in a vacuum. Whether such cooperation represents an opportunistic attempt to obtain a sentence reduction or a genuine alteration in the defendant's life perspective can best be determined by assessing that cooperation in light of earlier criminal history and the nature of the crime for which the defendant is presently being sentenced. Accordingly, we conclude that the district court did not act in violation of the law when it considered the defendants' prior criminal histories and the seriousness of their offenses in determining the extent of the reductions granted under Rule 35(b).
At oral argument, defense counsel appeared to concede that the district court was permitted to consider the defendants' prior criminal histories and the nature of their offenses; instead, he objected only to the excessive weight that was given to these factors. To the extent that the defendants object to the manner in which the district court chose to exercise its discretion, however, we do not have jurisdiction *630 to review their claims. See McGee, 508 F.3d at 444-45; McDowell, 117 F.3d at 978.

2.
The defendants next object to the district court's alleged refusal to consider their non-frivolous arguments in favor of greater sentence reductions. At their hearings before the district court, both Mr. Chapman and Mr. Frank emphasized that the amount of assistance that they had provided to the Government was greater than the typical case of assistance, which often results in a one or two-level reduction. The defendants also referenced other cases in which courts had reduced a defendant's sentence by more than thirty percent for providing substantial assistance, and they suggested that a greater reduction would prevent unwarranted sentencing disparity among like defendants  a factor to be considered under 18 U.S.C. § 3553.
In its explanation of the sentences it imposed, the district court did not address explicitly the defendants' contention that their assistance to the Government had been exceptional; nor did it mention the concern of potential sentencing disparities. The court simply noted that a specific reduction in the defendants' offense level (two levels for Mr. Chapman, one level for Mr. Frank) was appropriate because they had provided the Government with substantial assistance; however, it emphasized that this assistance did not wash away the defendants' criminal histories and conduct. Chapman Tr. at 6-7; Frank Tr. at 8. The court concluded that a sentence at the higher end of the resulting guidelines range was necessary to account properly for these important factors. Chapman Tr. at 6-7; Frank Tr. at 8. In both cases, it stated that the sentence it imposed was "reasonable, responsible, relevant, and necessary to accomplish these purposes as set forth in 18 United States Code Section 3553(a). Such a sentence will still hold this defendant accountable for his criminal conduct while factoring in his substantial assistance." Chapman Tr. at 7-8; Frank Tr. at 8 (identical statements).

a.
We first address the defendants' contention that the district court committed legal error by failing to consider the potential for sentencing disparities among similarly situated defendants. Relying on Rita v. United States, ___ U.S. ___, 127 S.Ct. 2456, 2468, 168 L.Ed.2d 203 (2007), and United States v. Cunningham, 429 F.3d 673, 676 (7th Cir.2005),[2] they submit that the sentencing court, if asked by either party, must consider the various sentencing factors set forth in 18 U.S.C. § 3553(a). These factors include the need to avoid unwarranted sentencing disparities in like cases. See 18 U.S.C. § 3553(a)(6).
We certainly have jurisdiction to consider whether a district court is required to reevaluate the section 3553 sentencing factors and, more particularly, to consider the potential for sentencing disparities when granting a sentence reduction under Rule 35(b). However, we need not decide the issue at this time. Whether or not the district court was required to consider the section 3553 factors when granting a sentence reduction under Rule 35(b), the records reveal that the court in fact did so here. Although the court did not mention the phrase "sentencing disparity" in either of its opinions, it did emphasize other relevant *631 section 3553(a) factorsnamely, the nature of the defendants' criminal conduct and their prior criminal histories. It further noted that the imposed sentences were "reasonable, responsible, relevant and necessary to accomplish these purposes as set forth in 18 United States Code Section 3553(a)." Chapman Tr. at 7; Frank Tr. at 8. In other words, the court chose to exercise its discretion in a manner that emphasized the defendants' prior criminal acts and other section 3553 factors. As we noted earlier, the weight that the district court assigns to permissible factors when exercising its discretion under Rule 35(b) generally is not subject to our review.
Here, the court did not evidence a misapprehension about its authority to consider the section 3553 factors on a Rule 35(b) motion; nor did it suggest that it refused to consider those factors. Indeed, the court stated that it did consider the relevant section 3553(a) factors, and it believed that the sentences that it imposed were necessary to account for the defendants' criminal history and conduct. We have little reason to doubt that the district court considered the factors that it said it did.[3] Accordingly, we need not determine whether the court otherwise would have been required to consider the section 3553(a) factors in ruling on a Rule 35(b) motion.

b.
We next consider the defendants' contention that the district court committed legal error when it failed to consider their argument that they had provided greater assistance to the Government than the usual case of substantial assistance. We have noted repeatedly our reluctance to require sentencing judges to address explicitly every argument that a defendant makes at a sentencing hearing. Cunningham, 429 F.3d at 679. The Supreme Court recently expressed a similar reluctance, although it cautioned that a district court should explain its decision in a way that assures reviewing courts that it considered the parties' arguments. See Rita, 127 S.Ct. at 2468-69 ("Sometimes a judicial opinion responds to every argument; sometimes it does not. . . . The sentencing judge should set forth enough to satisfy the appellate court that he has considered the parties' arguments and has a reasoned basis for exercising his own legal decision-making authority."). We noted in United States v. Miranda, 505 F.3d 785 (7th Cir. 2007), that "[a] judge need not comment on every argument the defendant raises," particularly if the argument is so weak that it does not merit discussion. Id. at 792.
In this case, we have no reason to doubt that the district court considered the defendants' arguments. The court here concluded that the defendants had provided substantial assistance; however, it also concluded that the defendants' significant criminal histories and criminal conduct required a sentence of 102 or 72 months, respectively. This is not a refusal to consider the extent of the assistance provided by the defendants: It is a determination that the extent of the assistance provided did not outweigh other relevant considerations. In the district court's view, the sentences that it imposed were necessary to account for the defendants' substantial criminal histories and conduct. As explained above, we do not have jurisdiction to review this discretionary sentencing determination. *632 See McGee, 508 F.3d at 444-45; McDowell, 117 F.3d at 977-78.

3.
Finally, we turn to Mr. Chapman's objection that the district court's method of calculating his sentence reduction was legal error. At Mr. Chapman's hearing, the Government suggested that the court impose a sentence of 84 months, and Mr. Chapman agreed to that proposed sentence.[4] Nevertheless, in its decision to sentence Mr. Chapman to 102 months' imprisonment, the district court did not reference explicitly the Government's 84-month proposal. Instead, it applied a two-level reduction to Mr. Chapman's previous offense level and selected a sentence at the higher end of the resulting guidelines range. Relying on United States v. Thomas, 930 F.2d 526, 531 (7th Cir.1991), Mr. Chapman submits that "[t]he government's recommendation should be the starting point for the district court's analysis." In his view, the district court failed to begin its analysis with the Government's proposed sentence of 84 months, as required by law, and therefore it committed legal error.
At Mr. Chapman's hearing, the district court did not mention explicitly that the Government had proposed a sentence of 84 months' imprisonment. It did, however, begin its analysis by granting a two-level reduction in Mr. Chapman's offense level, which was the mechanism by which the Government had arrived at its 84-month proposed sentence. The court noted that the reduced offense level, when paired with the defendant's criminal history category, resulted in an advisory guidelines range of 84-105 months. It then explained that a sentence in the upper half of the reduced range was necessary and appropriate for Mr. Chapman, considering his significant criminal history and serious criminal conduct. Although the opinion did not explicitly invoke the Government's proposed 84-month sentence, the record indicates that the judge was aware of the Government's proposed sentence and that he proceeded from that starting point. Accordingly, the district court's method of calculation was not error. Its conclusion that a 102-month sentence was necessary to account for other important sentencing considerations is not reviewable on appeal.

Conclusion
For the reasons set forth above, we affirm the judgment of the district court.
AFFIRMED
NOTES
[1]  See also United States v. McDowell, 117 F.3d 974, 978 (7th Cir.1997) ("We thus lack jurisdiction to hear McDowell's claim that the district court abused its discretion by granting a reduction too paltry to reflect the value of his post-sentencing assistance to the government."); United States v. Haskins, 479 F.3d 955, 957 (8th Cir.2007); United States v. McKnight, 448 F.3d 237, 238 (3d Cir.2006); United States v. Sykes, 356 F.3d 863, 865 (8th Cir.2004).
[2]  See also United States v. Miranda, 505 F.3d 785, 792 (7th Cir.2007); United States v. Acosta, 474 F.3d 999, 1003-04 (7th Cir.2007).
[3]  Cf. United States v. Cunningham, 429 F.3d 673, 676 (7th Cir.2005) ("[A]re we left in serious doubt whether the judge connected the facts relating to the statutory factors to the sentence he imposed?").
[4]  The Government calculated the proposed sentence of 84 months by applying a two-level reduction in his offense level. It reduced his offense level from 27 to 25, and it applied his criminal history category of IV. This yielded a guidelines range of 84-105 months. The Government suggested that the court should impose the lowest sentence within this range, or 84 months, even though it had originally imposed a sentence at the high end of the original guidelines range.

Mr. Chapman arrived at the 84 months sentence using a different method of calculation. He suggested that the court apply a four-level reduction and choose a sentence at the high end of the resulting guidelines range. Pairing an offense level of 23 and a criminal history category of IV yields a sentence range of 70-87 months. A sentence of 84 months is near the high end of that range.
The district court did not address specifically either of these methods of calculation.
