
660 F.3d 471 (2011)
United States of America, Appellee
v.
Patrick C. DAVID, Appellant.
No. 10-3024.
United States Court of Appeals, District of Columbia Circuit.
Argued October 6, 2011.
Decided November 4, 2011.
Lisa B. Wright, Assistant Federal Public Defender, argued the cause for appellant. With her on the briefs was A.J. Kramer, Federal Public Defender. Neil H. Jaffee, Assistant Federal Public Defender, entered an appearance.
Elizabeth H. Danello, Assistant U.S. Attorney, argued the cause for appellee. With her on the brief were Ronald C. Machen Jr., U.S. Attorney, and Roy W. McLeese, III and John P. Mannarino, Assistant U.S. Attorneys.
Before: SENTELLE, Chief Judge, and WILLIAMS and RANDOLPH, Senior Circuit Judges.
Opinion for the Court filed by Senior Circuit Judge WILLIAMS.
WILLIAMS, Senior Circuit Judge:
In 1993 appellant Patrick C. David was convicted of several drug and firearm offenses relating to his possession of 427 grams of crack cocaine. In 1997, after his conviction under 18 U.S.C. § 924(c)(1) was overturned in light of Bailey v. United States, 516 U.S. 137, 116 S.Ct. 501, 133 L.Ed.2d 472 (1995), he was resentencedto 188 months in prison. In 2008 he filed a motion under 18 U.S.C. § 3582(c)(2), which authorizes district courts to reduce sentences when the Sentencing Commission has amended the United States Sentencing *472 Guidelines ("USSG") to reduce the applicable sentencing range for an offense and has made the amendment retroactive. In this case David invoked the Sentencing Commission's reductions in the offense level (and thus the sentencing range) for certain crack cocaine offenses. The district court denied David's motion, noting on the record a host of facts about David's criminal record and his disciplinary infractions in prison. David appeals, arguing that the district court failed to determine the extent of the reduction for which he was eligible before denying his motion. In particular, he believes that the court may have underestimated the permissible reduction in the sentencing range, and that this hypothetical underestimate might have played a role in the court's refusal to make any reduction at all. Although we agree with David that a motion under § 3582(c)(2) requires the court first to compute the sentence reduction available, we find that the record here establishes that it did so.
* * *
Section 3582(c)(2) allows the court, "upon motion of the defendant or the Director of the Bureau of Prisons," to reduce a sentence in cases where the applicable guideline range has been reduced. In responding to such a motion, the district court must engage in a "two-step inquiry." Dillon v. United States, ___ U.S. ___, 130 S.Ct. 2683, 2691, 177 L.Ed.2d 271 (2010). The court must first "determine the prisoner's eligibility for a sentence modification and the extent of the reduction authorized." Id.; see USSG § 1B1.10(b). Only then may the court consider the factors set forth in 18 U.S.C. § 3553(a) to decide "whether the authorized reduction is warranted, either in whole or in part." Dillon, 130 S.Ct. at 2691. Dillon thus structures the district court's decision so that it first resolves the range of its legal authority, and then looks to a broad array of factors that may influence its discretion within that range.
David contends that the district court never met its obligation to determine the extent of the sentence reduction for which he was eligible. He faults the court for not explicitly stating that he was eligible for a 37-month reduction, particularly in light of two probation office memoranda submitted to the court that confused both David's original sentencing range and the new range to which his sentence could have been reduced.
Although David's sentencing history was complex, we find no trace of the probation office's confusion in the court's ruling. He had been sentenced in 1994 for possession with intent to distribute cocaine base, and the court correctly noted that this implied an offense level of 33; given his criminal history category of II (which has never changed), the court observed that that level entailed a range of 151 to 188 months. See Mem. & Order, United States v. David, No. 93-306, at 1-2 (D.D.C. Mar. 8, 2010) ("District Court Decision"). Thus the court clearly understood the range resulting from offense level 33 for someone with David's criminal history. With an additional mandatory and consecutive five years added for use of a firearm during a drug trafficking offense under 18 U.S.C. § 924(c)(1), the total 1994 sentence was 211 months. Id.
On appeal we vacated David's five-year sentence under § 924(c)(1). United States v. David, 96 F.3d 1477, 1482 (D.C.Cir. 1996). As removal of that sentence brought related gun possession enhancements under USSG § 2D1.1(b) into play, we remanded to the district court for application of those enhancements. See United States v. Rhodes, 106 F.3d 429, 432-33 & n. 3 (D.C.Cir.1997) (finding no constitutional or statutory bar to such a *473 procedure). Resentencing David in 1997, the district court added two offense levels, yielding a level of 35. The court here correctly observed that offense level 35 entailed a range of 188 to 235 months and that David had been resentenced, at the lower end of that range, to 188 months. District Court Decision at 2.
Finally, the court observed that the Sentencing Commission's 2007 amendment for crack cocaine provided for a "two level reduction." Id.
In short, the court expressed a clear understanding (1) that the 1997 188-month sentence had been at level 35, with a 188 to 235 month range, (2) that offense level 33 implied a 151 to 188 month range, and (3) that David was eligible for a two-level reduction in offense level. David in effect asks us to believe that the court, having handled all these numbers completely accurately, either failed to do the simple arithmetic of subtracting two from 35 and getting 33, or that somehow after making that subtraction it had forgotten its statement, about 12 lines higher on the same page, that level 33 entailed a range of 151 to 188 months. We cannot believe that.
Of course the district court could have averted any risk of appellate (or defendant) doubt by expressly stating the maximum reduction permitted by § 3582(c)(2). As we have said, "Justice is better served through clarity on the record." In re Sealed Case, 199 F.3d 488, 491 (D.C.Cir. 1999).
But where, as here, the court's ruling reflects an accurate grasp of all the relevant information as to offense levels and sentencing ranges, as discussed above, we are confident in inferring that the district court performed the basic arithmetic needed to understand its authority to grant a reduction of up to 37 months. Unlike the situation in United States v. Lawson, 494 F.3d 1046 (D.C.Cir.2007), where we could not be sure of the "starting point" for the court's application of the § 3553(a) factors, id. at 1058, here we have adequate grounds for inferring that the court knew that point exactly. The court fulfilled its obligation to determine the extent of the reduction authorized. We thus have no basis for thinking that a misunderstood starting or ending point could have skewed its exercise of discretion.
* * *
The decision of the district court is
Affirmed.
