We confront at the outset of this case a jurisdictional question: whether a defendant may appeal the computation of his sentencing range, when he already has a sentence below the lower bound of the range he thinks is right. Surprisingly, none of the courts of appeals has addressed this question, although dictum from the Supreme Court implies an answer.

Details of this case matter little to the jurisdictional inquiry, but the pattern is familiar. Timothy Burnett was caught peddling cocaine and marijuana. Hoping to reduce his punishment, he agreed to help the prosecutor convict his confederates. According to calculations the district court accepted, the presumptive range for Burnett’s crimes is 121 to 151 months. The prosecutor recommended a 25% discount for Burnett’s assistance, see U.S.S.G. § 5K1.1, and the district judge imposed a sentence of 91 months’ imprisonment. Burnett believes that the starting point for this departure was too high. He thinks that he was a “minor” participant in the drug ring, which if so would have led the judge to subtract two offense levels under U.S.S.G. § 3B1.2(b). Take away two levels, and the resulting range becomes 100 to 125 months in prison. Deduct another 25% for assistance and the range is 75 to 94 months. The rub, however, is that the 25% deduction is a downward departure, and a defendant cannot appeal the district court’s refusal to exercise discretion to depart from the lower bound of the range. United States v. Franz, 886 F.2d 973 (7th Cir.1989). The[*139] range Burnett believes correct is 100 to 125 months. His current sentence is 91 months, lawful under his own calculations. If the district judge had given the two level decrease Burnett sought, and then imposed a sentence of 91 months’ imprisonment, Burnett could not have appealed. He thinks that the same sentence becomes appealable because of the judge’s adverse resolution of the range issue. Yet only judgments are appeal-able; litigants may not contest remarks judges make along the way. Warner/Elektra/Atlantic Corp. v. County of DuPage, 991 F.2d 1280 (7th Cir.1993). Is the dispute about the application of § 3B1.2(b) more than academic? Would an opinion of this court be more than advisory?

To these rhetorical questions, the answers are affirmative. Correction of a legal error often leads to a revision in the judgment, and the possibility that the district judge will impose the same sentence does not preclude review. Consider some common cases under the Guidelines, (a) The judge gives two reasons for a sentence, one legally correct and the other legally erroneous. Either reason could support the sentence, but it is unclear whether the judge would have imposed the same sentence had he known that only one of the two reasons was proper. We will vacate the sentence and remand for resentencing under the correct view. United States v. Croom, 50 F.3d 433 (7th Cir.1995). See also United States v. Ferro, 948 F.2d 352 (7th Cir.1991) (affirming a sentence identical to one that had earlier been vacated because of legal errors), (b) The judge makes a legal error in determining the Guideline range, but upward departure would be allowable on the ground to which the judge referred. We will vacate the sentence and remand for resentencing under the correct legal view. United States v. Ruffin, 997 F.2d 343 (7th Cir.1993). (c) The judge imposes a sentence that is included in two overlapping ranges. As a result of a legal mistake, the judge believes the higher range to be correct; but even with the mistake rectified, the same sentence could be imposed from the lower range. Unless the judge expressly states that he would impose the same sentence whichever range is correct, we will vacate the sentence and remand for the exercise of discretion under the correct legal view. United States v. Mount, 966 F.2d 262 (7th Cir.1992). Just so in a case such as this one: the defendant has the potential for gain on a remand, because the district judge may have meant to grant a substantial discount from the properly calculated range.

Many opinions say that the court of appeals cannot review the district court’s decision not to make a discretionary downward departure, and cannot review the amount of any departure the judge chooses to make. E.g., Bischel v. United States, 32 F.3d 259, 265 n. 6 (7th Cir.1994). This is so not because of a prohibition in the statute but because of a lack of authorization to review discretionary decisions about departures. The statute supplying the authority to review sentences, 18 U.S.C. § 3742, creates only two categories that could be relevant. The defendant may argue that the sentence was “imposed in violation of law” or was “imposed as a result of an incorrect application of the sentencing guidelines”. Ordinarily a judge’s refusal to depart downward cannot be characterized as a “violation of law” or “an incorrect application of the sentencing guidelines,” but it is not hard to see instances where one or both of these criteria would be met. A judge who refuses to depart because he believes that he is legally forbidden to do so sets up a claim that the sentence rests on “an incorrect application of the sentencing guidelines”. See United States v. Poff, 926 F.2d 588, 590-91 (7th Cir.1991) (en banc); United States v. Johnson, 997 F.2d 248, 252 (7th Cir.1993). Similarly, a judge who refuses to depart (or selects an amount of departure) for reasons related to race, sex, religion or several other criteria has imposed a sentence “in violation of law”. We lack jurisdiction to review the sentence only when none of these arguments is available to the defendant.

Burnett’s contentions on this appeal boil down to a claim that his sentence of 91 months’ imprisonment is “a result of an incorrect application of the sentencing guidelines.” 18 U.S.C. § 3742(a)(2). Failure to subtract two levels for his “minor” role is the “incorrect application,” and the sentence of 91 months is the “result” in the sense that it likely would have been lower had the judge[*140] known that the correct range is 100 to 125 months. Cf. United States v. Yahne, 64 F.3d 1091, 1094-95 (7th Cir.1995). Of course we cannot know that it would have been lower. Perhaps the judge is fixed in his opinion that 91 months is the right sentence for someone who committed Burnett’s crimes and offered the assistance he did. Perhaps not. He has not told us. The treatment of overlapping guideline ranges (example c above) offers a close parallel — with the difference that instead of two overlapping guideline ranges we have one range plus a zone of reasonable departures. If the district judge had said that he would impose a 91-month sentence whether or not he thought Burnett a “minor” participant, then there would be no point to this appeal. As things stand, however, the actual sentence may be a “result” of the decision about minor-participant status. How much the decision affected the sentence does not matter to our jurisdiction.

It is in the interest of the legal system and defendants alike to ensure that even “discounted” sentences rest on a legally correct foundation. We therefore conclude that § 3742(a)(2) provides jurisdiction to entertain a claim that an error in the calculation of the guideline range influenced the sentence, whether or not that sentence ultimately falls below the properly calculated range. Accord, Williams v. United States, 503 U.S. 193, 203, 112 S.Ct. 1112, 1120, 117 L.Ed.2d 341 (1992) (“When a district court has intended to depart from the guideline range, a sentence is imposed ‘as a result of a misapplication of the Guidelines if the sentence would have been different but for the district court’s error.”) (dictum); cf. United States v. Gomez, 24 F.3d 924, 927 (7th Cir.1994); United States v. Harris, 994 F.2d 412, 414 (7th Cir.1993).

Thus we arrive at the merits, but we do not tarry. Whether to treat a defendant as a “minor participant” is “heavily dependent upon the facts of the particular case”, U.S.S.G. § 3B1.2 Background Note, which implies a correspondingly limited appellate role. United States v. Stephenson, 53 F.3d 836, 850 (7th Cir.1995). The “minor participant” reduction permits a court to take account of the fact that the relevant-conduct provisions of the Guidelines often hold a defendant responsible for other persons’ acts. A bit player in a large scheme can be deemed accountable for much that he did not do. Yet giving chauffeurs the same punishment as bigwigs simultaneously overpunishes the small fry and reduces the marginal penalty for being a bigwig (although the chiefs do get separate enhancements). Burnett was a driver, and sometimes a courier, in a larger organization. He participated for 18 months of the conspiracy’s 30-month duration, and he was a peripheral figure in negotiations for the purchase and sale of the drugs he transported. He was paid $350 per trip and did not share in the venture’s profits. Only twice did he drive by himself to pick up, pay for, and deliver drugs; even then someone else had arranged for the transactions. In this sense he was a small cog in the scheme. But § 3B1.2 does not ask whether the defendant was minor in relation to the organization, or how easily he could have been replaced; it asks the judge to determine whether he was minor in relation to the crime of which he was convicted, id. at Application Note 4, and in relation to the conduct for which he has been held accountable. See United States v. Willis, 49 F.3d 1271, 1275 (7th Cir.1995). When a courier is held accountable for only the amounts he carries, he plays a significant rather than a minor role in that offense. Henchmen and factotums therefore do not receive automatic reductions. United States v. Cea, 963 F.2d 1027, 1032 (7th Cir.1992); United States v. Osborne, 981 F.2d 1139, 1157-59 (7th Cir.1991). Couriers are integral to the success of drug rings, and long-term couriers properly may be treated as “average” participants, and therefore ineligible for the minor-participant reduction. United States v. Corral-Ibarra, 25 F.3d 430, 439 (7th Cir.1994).

For 18 months Burnett made almost weekly trips to Chicago to drive drugs back to Taylorville. He observes that the conspiracy lasted a year longer, but the district court took this into account by holding him accountable only for drugs actually transported during his 18 months of participation. Burnett emphasizes that he was[*141] paid $350 per trip, but the record does not reveal what portion of the conspiracy’s net proceeds his fee represented. He did not offer evidence of the difference between retail and wholesale price of the drugs and did not attempt to estimate the conspiracy’s other expenses. As he bears the burden of establishing “minor participant” status, United States v. Soto, 48 F.3d 1415, 1423 (7th Cir.1995), this omission is difficult to overcome. Only one element of the district court’s treatment of the subject gives us pause: the judge deemed it significant that Burnett sometimes was paid in drugs. How this made his role any more significant the judge did not explain, and it is not immediately apparent. The quantities involved were small in relation to the venture’s inventory. Burnett might have sold the drugs he received, making a profit on the turn; but this would be equally true if he bought drugs for cash from his confederates. Whatever easy profit there was to be had would be reflected in the exchange rate between drugs and cash on payday. But we do not think that the district judge placed much weight on the form of payment. Although the subject came up at sentencing, the judge’s written explanation for his sentence omits mention of the payment terms.

Section 3B1.2(b) does not define “minor participant” but does emphasize the judge’s discretion. This means that its principal office is to give the district judge a means to mitigate unduly harsh punishment that mechanical application of the relevant-conduct rules might yield. The district judge did not pile on the offense levels through the relevant-conduct rules in this case and therefore saw no pressing need to mitigate the sentence by applying § 3B1.2(b). That was a reasoned and reasonable judgment, which we therefore do not disturb. Had the judge decided the other way, we would not have disturbed that decision either. United States v. Johnson, 997 F.2d 248, 250, 253 (7th Cir. 1993). This is what it means to say that a judge has discretion.

AFFIRMED.