
524 F.3d 358 (2008)
UNITED STATES of America, Appellee,
v.
Jose NEGRON, Rafael Gonzales, Angel Maldonado, Alexis Pratts, Christian Silverio, John Rodriguez, Lionel Pineiro, Defendants,
Julio Silverio,[1] Defendant-Appellant.
Docket No. 06-3614-cr.
United States Court of Appeals, Second Circuit.
Argued: April 1, 2008.
Decided: April 24, 2008.
*359 Lawrence Mark Stern, New York, NY, for Defendant-Appellant.
Jeffrey H. Knox, Assistant United States Attorney (Susan Corkery, Assistant United States Attorney, on the brief), for Benton J. Campbell, United States Attorney for the Eastern District of New York, Brooklyn, NY, for Appellee.
Before: JACOBS, Chief Judge, KEARSE and POOLER, Circuit Judges.
PER CURIAM:
Julio Silverio appeals from an order entered on August 2, 2006, in the United States District Court for the Eastern District of New York (Weinstein, J.), declining to resentence him after remand pursuant to United States v. Crosby, 397 F.3d 103 (2d Cir.2005). Silverio's sole argument on this appeal is that the district court erroneously refused to consider the terms of a *360 rejected plea offer in which the government had offered to recommend a lower prison term than ultimately imposed. We affirm because nothing in 18 U.S.C. § 3553(a) or controlling precedent requires a sentencing court to consider a rejected plea offer.
Silverio was one of the ringleaders of a criminal gang that engaged in a series of home and business robberies over an 18-month period. The victims, including families with small children, were held hostage and threatened and terrorized at gunpoint until cash and valuables were turned over. During plea negotiations, the government expressed willingness to enter an agreement under Fed.R.Crim.P. 11(e)(1)(C) (2000), which would include a binding sentence recommendation of 17 years' imprisonmentnotwithstanding an estimated Sentencing Guidelines range of approximately 22 to 27 years. Against counsel's advice, Silverio rejected this offer, believing he might obtain greater leniency from the sentencing judge. Silverio later accepted a plea agreement that contained no binding sentence recommendation. Pursuant to that agreement, he was convicted of kidnapping in aid of racketeering in violation of 18 U.S.C. §§ 1959(a)(1) and (2), conspiracy to commit robbery in violation of 18 U.S.C. § 1951, and use of a firearm in furtherance of crimes of violence in violation of 18 U.S.C. §§ 924(c)(1)(A)(ii) and (2). He was sentenced principally to 272 months of incarceration.
Silverio's initial appeal argued (inter alia) that the district court erred in restricting a downward departure for diminished capacity to a single level. By summary order dated May 21, 2004, this Court affirmed the sentence, specifically finding each of Silverio's arguments without merit. See United States v. Negron, 96 Fed.Appx. 788 (2d Cir.2004) (unpublished), vacated on other grounds sub nom. Silverio v. United States, 543 U.S. 1102, 125 S.Ct. 1026, 160 L.Ed.2d 1011 (2005). Subsequently, the Supreme Court vacated that summary order and remanded in light of United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005); and this Court remanded to the district court for a Crosby review. See United States v. Silverio, No. 01-1210 (2d Cir. Nov. 15, 2005) (unpublished). However, our May 21, 2004 decision as to the arguments presented in the initial appeal was explicitly made part of our November 15, 2005 remand order to the extent it was consistent with Crosby, and thus remains the law of the case. See United States v. Williams, 475 F.3d 468, 475-76 (2d Cir.2007).
On appeal from the district court's decision following the Crosby remand, Silverio argues that: (a) his rejection of the earlier plea offer was a manifestation of his diminished capacity at the time; and (b) the rejected offer was an acknowledgment by the government that a lesser sentence would have been sufficient. We review a sentence for reasonableness, under an abuse-of-discretion standard, see Gall v. United States, ___ U.S. ___, 128 S.Ct. 586, 594, 169 L.Ed.2d 445 (2007), including when the district court has declined to resentence pursuant to Crosby, see Williams, 475 F.3d at 474. Insofar as Silverio is asserting an error in the extent of the downward departure for diminished capacity in the original sentence, the argument is barred by the law of the case doctrine because it was adjudicated on his direct appeal. See United States v. Quintieri, 306 F.3d 1217, 1229 (2d Cir.2002).
"The law of the case doctrine will not, however, bar a defendant who is not resentenced after a Crosby remand from challenging the procedures used by the district court during the Crosby remand." Williams, 475 F.3d at 476. Here, the district court fully complied with Crosby's *361 procedural requirements, including appropriate consideration of the factors set forth in 18 U.S.C. § 3553(a). Nothing in § 3553(a) or controlling precedent requires a district court to consider a rejected plea offer. See Rita v. United States, ___ U.S. ___, 127 S.Ct. 2456, 2465, 168 L.Ed.2d 203 (2007) ("[The sentencing judge] may hear arguments by prosecution or defense that the Guidelines sentence should not apply. . . ." (emphasis added)); cf. United States v. Hamdi, 432 F.3d 115, 124 (2d Cir.2005) (noting "the well-settled legal principle that `the sentencing judge is of course not bound by the estimated range' in a plea agreement" (quoting United States v. Rosa, 123 F.3d 94, 98-99 (2d Cir.1997))).
In any event, the record shows that during the Crosby remand, defense counsel was given full opportunity to make this argument. "[W]e entertain a strong presumption that the sentencing judge has considered all arguments properly presented to [him], unless the record clearly suggests otherwise. This presumption is especially forceful when, as was the case here, the sentencing judge makes abundantly clear that [he] has read the relevant submissions and that [he] has considered the § 3553(a) factors." United States v. Fernandez, 443 F.3d 19, 29 (2d Cir.2006). The sentencing decision carefully applied the § 3553(a) factors to Silverio's case, and specifically considered the kinds of sentences available and the location of the sentence within the Guidelines range. The district court declined to resentence Silverio, in large part because of the "horrendous" and "serious" nature of the offense. See id. at 27 ("[I]n the overwhelming majority of cases, a Guidelines sentence will fall comfortably within the broad range of sentences that would be reasonable in the particular circumstances."). In doing so, the district court committed no procedural or substantive error.

CONCLUSION
For the foregoing reasons, the order of the district court is affirmed.
NOTES
[1]  We direct the Clerk of the Court to amend the official caption to reflect this spelling of Silverio's name.
