
556 F.3d 238 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Larry Donnell LINDSEY, a/k/a Donnell, Defendant-Appellant.
United States of America, Plaintiff-Appellee,
v.
Lonnie Dewayne Robinson, a/k/a Black Lonnie, Defendant-Appellant.
Nos. 08-7715, 008-7728.
United States Court of Appeals, Fourth Circuit.
Argued: December 2, 2008.
Decided: February 20, 2009.
*239 ARGUED: Matthew Segal, Federal Defenders of Western North Carolina, Inc., Asheville, North Carolina, for Appellants. Amy Elizabeth Ray, Office of the United States Attorney, Asheville, North Carolina, for Appellee. ON BRIEF: Claire J. Rauscher, Executive Director, Federal Defenders of Western North Carolina, Inc., Asheville, North Carolina; Cecilia Oseguera, Steven Slawinski, Charlotte, North Carolina, for Appellants. Gretchen C.F. Shappert, United States Attorney, Charlotte, North Carolina, for Appellee.
Before WILLIAMS, Chief Judge, and NIEMEYER and MOTZ, Circuit Judges.
No. 08-7715 affirmed; No. 08-7728 vacated and remanded by published opinion. Judge NIEMEYER wrote the opinion, in which Chief Judge WILLIAMS and Judge MOTZ joined.

OPINION
NIEMEYER, Circuit Judge:
In light of Amendment 706 to the Sentencing Guidelines, which retroactively reduced the offense levels for crack cocaine offenses, Larry Donnell Lindsey and Lonnie DeWayne Robinson filed motions in the district court to reduce their sentences, relying on 18 U.S.C. § 3582(c)(2), which authorizes a district court to reduce a sentence where "a defendant ... has been sentenced to a term of imprisonment based on a sentencing range that has subsequently been lowered by the Sentencing Commission." (Emphasis added). Both defendants' sentences were based on sentencing ranges determined under U.S.S.G. § 2D1.1, which Amendment 706 amended, and both defendants' sentences were reduced by the district court under U.S.S.G. § 5K1.1 for their substantial assistance to the government. But, even though Amendment 706 reduced these defendants' offense levels, it did not lower their sentencing ranges of 360 months' to life imprisonment. Yet, Lindsey and Robinson contend that because the district court departed downward nine offense levels under § 5K1.1, their sentencing ranges should be modified to correspond to an offense level first reduced two levels under Amendment 706 and then reduced by the nine levels for substantial assistance. The district court rejected this approach and denied the defendants' motions.
As to Lindsey, we affirm. Amendment 706, when applied to Lindsey in accordance with U.S.S.G. § 1B1.10(b)(1), does not lower his "sentencing range" or "applicable guideline range," as required by 18 U.S.C. § 3582(c)(2) and U.S.S.G. § 1B1.10(a)(2)(B). The district court's departure from the "applicable guideline range" to impose a lower sentence under U.S.S.G. § 5K1.1, based on Lindsey's substantial assistance to the government, has no legal effect on this analysis.
As to Robinson, we vacate and remand to a different district judge on the ground that the sentencing judge operated unwittingly under a conflict of interest that disqualified him under 28 U.S.C. § 455(b)(3).

I

Larry Donnell Lindsey
Lindsey pleaded guilty, pursuant to a written plea agreement, to one count of conspiracy to possess with intent to distribute cocaine and cocaine base, in violation of 21 U.S.C. §§ 841(a)(1) and 846. In the plea agreement, Lindsey stipulated that he was responsible for in excess of 1.5 kilograms of crack cocaine.
The presentence report recommended a sentence within the Guidelines range of 360 months' to life imprisonment. The report began with a base offense level of *240 38 under U.S.S.G. § 2D1.1 for an offense involving 1.5 or more kilograms of cocaine base. The probation officer then recommended a two-level increase because a dangerous weapon was possessed, a four-level increase because Lindsey led the drug organization, and a three-level reduction for acceptance of responsibility, yielding a final offense level of 41. With Lindsey's criminal history category of IV, the resulting Guidelines range was 360 months' to life imprisonment.
At sentencing, after the district court adopted the presentence report, the government made a motion under U.S.S.G. § 5K1.1 for a downward departure based on Lindsey's substantial assistance to the government. The government stated that Lindsey "was debriefed [and] provided truthful information. He was the leader of the conspiracy and his cooperation, which occurred roughly halfway through the process, led to, I think, the conclusion of the conspiracy. Furthermore, he testified at trial some three to four weeks ago against one of his co-defendants." Based on this assistance, the government recommended a downward departure "to offense level 32, criminal history category IV, which is a range of 168 to 210 months," and it recommended a sentence at "the low end of that range." The district court granted the government's motion, noting that it
[found] that the defendant ha[d] rendered substantial assistance; that it justifie[d] a departure to level 32, category IV. The court would sentence at the low end of that range with the hope that the defendant will be rehabilitated when he comes out of prison.
The court then sentenced Lindsey to 168 months' imprisonment, entering judgment on April 23, 1999.
Three years later, in April 2002, the government filed a motion under Federal Rule of Criminal Procedure 35(b) to reduce further Lindsey's 168-month sentence based on his additional substantial assistance rendered after his sentence had been imposed. The district court granted the motion and reduced Lindsey's sentence to a term of 150 months' imprisonment.
In June 2008, because of Amendment 706 to the Sentencing Guidelines, which retroactively lowered the base offense levels applicable to crack cocaine offenses under U.S.S.G. § 2D 1.1 by two levels, Lindsey filed a motion under 18 U.S.C. § 3582(c)(2) for a further reduction of his sentence. In his motion, Lindsey maintained that after the sentencing court's departure under U.S.S.G. § 5K1.1 and its subsequent reduction of his sentence under Rule 35(b), his 150-month sentence was based on a sentencing range for offense level 32, not on the range for offense level 41 reflected in his pre-sentence report. Arguing that Amendment 706 lowered his sentencing range to the range that corresponds to offense level 30, Lindsey claimed that he was eligible for a revised sentencing range of 135 to 168 months' imprisonment. Specifically, he requested a revised sentence of 120 months' imprisonment, reflecting a reduction proportionate to the original sentence after the district court had granted the government's Rule 35 motion.
The probation officer submitted a supplemental presentence report providing that under Amendment 706, Lindsey's offense level was lowered from level 41 to level 39. With Lindsey's criminal history category of IV, his Guidelines range for imprisonment, after application of Amendment 706, remained 360 months' to life imprisonment. The probation officer concluded that "[t]here was no change in the guideline range, therefore, no reduction is recommended."
The district court denied Lindsey's § 3582(c)(2) motion, stating:

*241 After giving defendant the benefit of Amendment 706's two-level reduction, his revised offense level (prior to any downward departures for substantial assistance) is 39 with a criminal history category IV, corresponding to a guideline range of 360 months to life imprisonment. Since this defendant's guideline range is not lowered by application of the amendment, he is not eligible for a sentence reduction.... The fact that this defendant was originally given a sentence below the applicable guideline range on account of the government's 5K1.1 and Rule 35 motions has no impact on this conclusion....
From the district court's order of August 22, 2008, denying Lindsey's § 3582(c)(2) motion, Lindsey now appeals.

Lonnie De Wayne Robinson
Robinson pleaded guilty, pursuant to a written plea agreement to one count of conspiracy to possess with intent to distribute crack cocaine near a protected location, in violation of 21 U.S.C. §§ 841(a)(1), 846, and 860. In his plea agreement, Robinson stipulated that he was responsible for in excess of 1.5 kilograms of crack cocaine.
The presentence report recommended a Guidelines sentence in the range of 360 months' to life imprisonment. The report began with a base offense level of 40 under U.S.S.G. § § 2D 1.1 and 2D1.2 for an offense involving at least 1.5 kilograms of crack cocaine (for which § 2D1.1 assigns a base level of 38) where the violation occurred near a protected location (for which § 2D1.2 assigns a base level of 2). The probation officer recommended a two-level increase for possession of a dangerous weapon and a three-level reduction for acceptance of responsibility, yielding a final offense level of 39. The probation officer also found Robinson to be a career offender within the meaning of U.S.S.G. § 4B1.1 on account of his prior North Carolina state convictions, but the calculations under § 4B1.1 left his offense level at 39. With Robinson's offense level of 39 and criminal history category of VI, the resulting Guidelines range was 360 months' to life imprisonment.
At sentencing, the district court began by adopting the pre-sentence report, finding that it accurately calculated Robinson's Guidelines sentencing range. The government then made a motion under U.S.S.G. § 5K1.1 for a downward departure based on Robinson's substantial assistance to the government. The government stated:
Mr. Robinson was one of the earliest cooperators and the second person in this 12-person indictment to enter a plea.... [H]e provided significant information about the Greer Heights drug trade and about Jamaican Harry.... Significant information he provided was actually used to indict Jamaican Harry. The Government contemplates a possible Rule 35 motion in the future if he testifies against Jamaican Harry.
In view of this assistance to the government, the government recommended a sentence of 180 months' imprisonment. The government explained:
That's a level 30, Category VI. The Government notes that 180 months is a lengthy sentence for someone to plead to, but Mr. Robinson faces 360 to life and is a career offender with 11 points for crimes plus three more points for enhancements, a total of 14 points. His sentence is so significant not because of this crime but because of his life of crime.
The district court granted the government's motion for a downward departure,
find[ing] the appropriate level of departure would be to level 30, category VI, which is 168 to 210 range. The Court *242 accept[ed] the recommendation of the Government as to the appropriate extent of the departure. The Court [found] there [was] substantial assistance meriting that departure. The Court recognize[d] the Defendant's change of heart and his sincerity.
The court sentenced Robinson to 180 months' imprisonment, entering judgment on November 4, 1996.
In March 2008, because of Amendment 706 to the Sentencing Guidelines, which retroactively lowered the base offense levels applicable to crack cocaine offenses under U.S.S.G. § 2D 1.1 by two levels, Robinson pro se filed a motion under 18 U.S.C. § 3582(c)(2) for a further reduction of his sentence. Counsel was appointed for him, and a formal brief was filed in June 2008. Robinson contended that even though the offense level calculated in his presentence report was 39, after the district court departed downward pursuant to U.S.S.G. § 5K1.1, his 180-month sentence was based on a sentencing range for offense level 30 and criminal history category VI. Claiming that Amendment 706 lowered the offense level from 30 to 28, Robinson argued that he was eligible for a reduced sentence in the corresponding range of 140 to 175 months' imprisonment. He specifically requested a revised sentence of 150 months' imprisonment, reflecting a reduction that was proportionate to his original sentence.
The probation officer submitted a supplemental presentence report that provided that under Amendment 706, Robinson's revised offense level was lowered from level 39 to level 37. With Robinson's criminal history category of VI, the revised Guidelines range for imprisonment remained 360 months' to life imprisonment. The probation officer concluded that there should be "no reduction" in Robinson's sentence by reason of Amendment 706.
The district court denied Robinson's § 3582(c)(2) motion, applying the same reasoning that it had applied in denying Lindsey's motion. The court stated:
After giving defendant the benefit of Amendment 706's two-level reduction, his revised offense level (prior to any downward departures for substantial assistance) is 37 with a criminal history category VI, corresponding to a guideline range of 360 months' to life imprisonment. Since this defendant's guideline range [was] not lowered by application of the amendment, he is not eligible for a sentence reduction.... The fact that this defendant was originally given a sentence below the applicable guideline range on account of the government's 5K1.1 motion has no impact on this conclusion....
From the district court's order of August 22, 2008, denying Robinson's § 3582(c)(2) motion, Robinson now appeals. In his brief on appeal, he raised for the first time the objection that the judge who denied his § 3582(c)(2) motion was also the Assistant United States Attorney handling his sentencing in 1996.

II. Lindsey
Section 3582(c)(2) authorizes a district court to modify a defendant's term of imprisonment "based on a sentencing range that has subsequently been lowered by the Sentencing Commission." 18 U.S.C. § 3582(c)(2). It also provides that any such reduction of a sentence must be "consistent with applicable policy statements issued by the Sentencing Commission." Id.
The applicable policy statement issued by the Sentencing Commission provides that a sentence reduction under § 3582(c)(2) "is not authorized" if the amendment to the Sentencing Guidelines *243 "does not have the effect of lowering the defendant's applicable guideline range." U.S.S.G. § 1B1.10(a)(2)(B). The Sentencing Guidelines also provide specific instructions for a court when "determining whether, and to what extent, a reduction in the defendant's term of imprisonment ... is warranted." Id. § 1B1.10(b)(1). They instruct that "the court shall determine the amended guideline range that would have been applicable to the defendant if the amendment[ ] ... had been in effect at the time the defendant was sentenced[,] ... substitut[ing] only the amendment[ ] ... for the corresponding guideline provision[ ] that [was] applied" and "leav[ing] all other guideline application decisions unaffected." Id.
Amendment 706, which was made effective November 1, 2007, and retroactive effective March 3, 2008, amended § 2D 1.1 of the Sentencing Guidelines by reducing the offense levels associated with crack cocaine quantities by two levels. See U.S.S.G. supp. to app. C, amend. 706 (Nov. 1, 2007); id. amend. 713 (May 1, 2008); U.S.S.G. § 2D1.1; U.S.S.G. § 1B1.10(c). Amendment 706, by retroactively lowering a sentencing range, enables a defendant to seek a reduced sentence through a motion filed under 18 U.S.C. § 3582(c)(2). To be the basis of a reduction under § 3582(c)(2), however, Amendment 706 must have "the effect of lowering the defendant's applicable guideline range." U.S.S.G. § 1B1.10(a)(2)(B) (emphasis added).
Lindsey contends that even though his sentencing range was 360 months' to life imprisonment, corresponding to offense level 41, after the district court departed downward under U.S.S.G. § 5K1.1, his sentence was "based on a sentencing range" of 168 to 210 months, corresponding to offense level 32. He argues that Amendment 706 should therefore be applied to reduce his offense level from level 32 to level 30 with a corresponding sentencing range of 135 to 165 months' imprisonment. And because the district court sentenced him at the low end of the range corresponding to level 32, his sentence should be at the low end of the revised range, or 135 months' imprisonment.[*] Lindsey thus argues that "sentencing range" as used in § 3582(c)(2) refers to the range that the district court may consult in fashioning its departure, based on substantial assistance under U.S.S.G. § 5K1.1, from the otherwise applicable Guidelines range.
While Lindsey acknowledges that Amendment 706 did not lower his pre-departure sentencing range of 360 months' to life imprisonment, he contends that he was not sentenced based on this pre-departure range because his sentence was the result of a downward departure under U.S.S.G. § 5K1.1. He argues that his sentence was the product of a nine-level departure from the applicable pre-departure offense level and that his final sentence was within the sentencing range corresponding to offense level 32. He contends that when Amendment 706 is applied to reduce his original offense level from 41 to 39 and his nine-level departure is applied, his ultimate offense level should become 30, yielding a sentencing range of 135 to 168 months' imprisonment. A sentence at *244 the low end of that range would therefore be 135 months' imprisonment.
Even though Lindsey's argument is logically sound, the calculation he espouses is not the one prescribed by 18 U.S.C. § 3582(c)(2) and U.S.S.G. § 1B1.10. Lindsey's analysis focuses on offense levels, whereas the calculations mandated by § 1B1.10 focus on sentencing ranges, and, in this case, that difference in focus makes a difference in outcome.
Section 1B1.10 of the Sentencing Guidelines, issued by the Sentencing Commission to implement § 3582(c)(2), states that a reduction under § 3582(c)(2) is "not authorized" if Amendment 706 "does not have the effect of lowering the defendant's applicable guideline range." U.S.S.G. § 1B1.10(a)(2)(B) (emphasis added). To determine whether Amendment 706 lowers the "applicable guideline range," § 1B1.10(b)(1) provides the specific calculation that we must make. It provides that we "substitute [Amendment 706] for the corresponding guideline provisions that were applied when [Lindsey] was sentenced" and that we "leave all other guideline application decisions unaffected." Id. § 1B1.10(b)(1).
To apply Amendment 706 in this manner, we return to Lindsey's original sentencing. The district court began in the original sentencing with offense level 38 derived from U.S.S.G. § 2D 1.1 (the guideline amended by Amendment 706) and then applied a two-level firearms enhancement, a four-level leadership-role enhancement, and a three-level reduction for acceptance of responsibility, ending with a final offense level of 41. Because the initial offense level of 38 (derived from U.S.S.G. § 2D 1.1) was amended by Amendment 706, reducing it by two levels, we "substitute" the amended offense level for "the corresponding guideline provision[ ] that [was] applied when [Lindsey] was sentenced." U.S.S.G. § 1B1.10(b)(1). Thus, instead of beginning with offense level 38, we begin with offense level 36 and then "leave all other guideline application decisions unaffected." Id. Following those instructions, we begin with amended offense level 36 and apply a two-level firearms enhancement, a four-level leadership-role enhancement, and a three-level reduction for acceptance of responsibility, ending with a revised offense level of 39 and an "amended guideline range" of 360 months' to life imprisonment. Because this "amended guideline range" is the same as the original Guidelines range, Amendment 706 does not "have the effect of lowering [Lindsey's] applicable guideline range" and therefore no reduction of Lindsey's sentence is authorized by 18 U.S.C. § 3582(c)(2). Id. § 1B1.10(a)(2)(B).
Under this specified method of applying Amendment 706 to determine whether a reduction under § 3582(c)(2) "is warranted," id. § 1B1.10(b)(1), the Sentencing Guidelines require the recalculation of Lindsey's "applicable guideline range" as if the amendment were in place from the beginning. Because this recalculation leads to the same "applicable guideline range," no modification of Lindsey's sentence is authorized by § 3582(c)(2). A modification is authorized only if, after performing this specific substitution, Lindsey's "applicable guideline range" is lowered. See U.S.S.G. § 1B1.10(a)(2)(B).
Lindsey seeks to avoid the inescapable outcome of this analysis by directing our attention to the manner in which the district court applied U.S.S.G. § 5K1.1 to depart downward nine offense levels. There are, however, several flaws in his approach.
First, Lindsey's approach bypasses the threshold determination required by U.S.S.G. § 1B1.10(b)(1) to determine if a reduction "is warranted" at all. That determination *245 has as its object whether the amendment lowered the "guideline range applicable to [Lindsey]." Id. § 1B1.10(a)(1) (emphasis added). Lindsey applies his calculation based on a downward departure and offense levels, without first determining whether the sentencing range was lowered by Amendment 706. Yet, had he made that threshold calculation in the manner specified by § 1B1.10(b)(1), he would have faced the conclusion that a reduction is "not authorized," U.S.S.G. § 1B1.10(a)(2), and he would not have been able conceptually to perform some other calculation to suggest that Amendment 706 somehow affected his sentence.
Second, if the focus of Lindsey's calculation is how to apply a downward departure in a later reduction under § 3582(c)(2), then his calculation is still flawed because he overlooks the limitations imposed by § 1B1.10(b)(2). That provision directs that only after it is determined that a reduction under § 3582(c)(2) is warranted via the calculation in § 1B1.10(b)(1), a downward departure may be made from the amended sentence. Thus, if the sentencing range is lowered, then, and only then, may we apply a comparable downward departure. And even then the departure is reduced only proportionately. If, for example, the original departure represented a 20% downward departure from the Guidelines sentence, a 20% downward departure could be given from the amended Guidelines sentence. See U.S.S.G. § 1B1.10(b)(2) cmt. n. 3. Of course, if no reduction is warranted as determined under § 1B1.10(b)(1) because his sentencing range is not lowered, any calculation of his downward departure becomes irrelevant.
Third, a downward departure under U.S.S.G. § 5K1.1 is an authorized departure "from the guidelines" based on the defendant's substantial assistance. It does not provide a Guidelines range of its own but rather a departure from the Guidelines range, made after the applicable Guidelines range has been calculated. See U.S.S.G. § 1B1.10(b)(2)(B) (explaining how a departure is applied to an amended Guidelines range after the threshold determination is made that a § 3582(c)(2) reduction is warranted). As the district court correctly noted:
This methodology is reflected in [the] Sentencing Guidelines manual itself (which treats downward departures as Part K of Chapter 5, after the applicable guideline range is tabulated in Part A) and also the Statement of Reasons given by the court at sentencing (which requires a pre-departure determination of the defendant's applicable guideline range on the record prior to the court's final sentencing determination, which would be reflective of any departure or variances).
United States v. Lindsey, No. 3:98-CR-50-1-FDW (W.D.N.C. Aug. 22, 2008).
Finally, the district court's downward departure was not determined by any applicable Guidelines range. Section 5K1.1 of the Sentencing Guidelines gives the sentencing judge discretion to award a defendant an "appropriate reduction," consistent with the non-exclusive list of factors for consideration by the judge, all related to the nature and quality of a defendant's assistance. See U.S.S.G. § 5K1.1; Hood, 556 F.3d at 235, 2009 WL 416979; United States v. Pearce, 191 F.3d 488, 492 (4th Cir.1999) (holding that under § 5K1.1, a sentencing court may only consider the "nature, extent, and significance" of the defendant's assistance). But the Sentencing Commission has not adopted a Guidelines range to apply in departing downward under § 5K1.1. Rather, the district court was exercising its discretion when it sought to quantify its downward departure *246 by referring to level 32 and category IV. It could just as well have used a percentage-based departure or stated a flat number of months to depart based on Lindsey's substantial assistance. Accordingly, the district court's reference to offense levels in making its discretionary decision of how far to depart did not amount to the application of a "sentencing range" authorized and made applicable by the Sentencing Guidelines and therefore was of no legal significance to the analysis under § 3582(c)(2). See United States v. Hood, 556 F.3d 226, 235-36, No. 08-7019, 2009 WL 416979 (4th Cir. Feb. 20, 2009).
Lindsey argues that United States v. Goines, 357 F.3d 469, 473-80 (4th cir.2004), entitled him to relief. In Goines, we considered whether a clarifying amendment to the Sentencing Guidelines lowered a sentencing range as required by § 3582(c)(2). In holding that "a defendant may rely on a clarifying ... amendment to support a § 3582(c)(2) motion, so long as the amendment has been designated for retroactive application and would result in application of a sentencing range lower than the range applied at the original sentencing proceeding," id. at 480, we stated that "sentencing range" is "the range actually applied by the district court," as distinct from the range "prescribed by the sentencing guidelines." Id. at 474, 475 (emphasis added). Lindsey thus argues that Goines requires us to determine whether Amendment 706 lowers not the range "prescribed by the guidelines," but rather the range "applied by the district court," which here was a post-departure sentencing range "derived from offense level 32."
Lindsey's argument, however, is neither advanced nor supported by Goines. In Goines, the issue was whether a court, in determining whether an amendment lowered a sentencing range, should consider the Guidelines range that should have been applied to the defendant or the Guidelines range actually applied by the district court. In order to permit consideration of the clarifying amendment in connection with the sentence actually imposed, we held that we had to consider the Guidelines range actually applied by the district court that the clarifying amendment changed retroactively. Unlike the sentencing court in Goines, however, the range "actually applied by the district court" in this case was in fact the range "prescribed by the Guidelines" under § 2D1.1. Thus, distinguishing between the "prescribed" range and the "applied" range does not contribute to or change the analysis we apply to Lindsey. When we apply Amendment 706applied according to the formula in U.S.S.G. § 1B1.10(b)  to the range actually applied by the district court, it does not "result in application of a sentencing range lower than the range applied at the original sentencing proceeding," id. at 480, as required by § 3582(c)(2) and Goines. Thus, Goines does not entitle Lindsey to relief. In short, even though Amendment 706 reduced Lindsey's offense level to 39, it did not lower his Guidelines sentencing range. The "applicable guideline range" was and remains 360 months' to life imprisonment. And because Amendment 706 "does not have the effect of lowering [Lindsey's] applicable guideline range," Lindsey is not eligible for relief under § 3582(c)(2).

III. Robinson
Robinson's § 3582(c)(2) motion was denied by District Judge Frank Whitney, who also, it was later learned, participated in Robinson's case in 1996 (12 years earlier) as an Assistant United States Attorney. Counsel for Robinson stated that after filing this appeal, he received transcripts from Robinson's 1996 sentencing *247 hearing and, for the first time, learned that Judge Whitney was the Assistant United States Attorney involved in the case at Robinson's sentencing hearing. Robinson now contends that we must vacate Judge Whitney's order denying his § 3582(c)(2) motion and remand, even though the judge's violation of 28 U.S.C. § 455(b)(3) was unwitting. The government agrees.
Section 455 provides in relevant part that a judge "shall disqualify himself in any proceeding ... [w]here he has served in governmental employment and in such capacity participated as counsel, adviser or material witness concerning the proceeding or expressed an opinion concerning the merits of the particular case in controversy." 28 U.S.C. § 455(a), (b)(3). Although there is no evidence to suggest that Judge Whitney recalled his participation in Robinson's original sentencing proceeding, nor did anyone bring it to his attention, his participation at that time is nonetheless undisputed. Accordingly, in light of 28 U.S.C. § 455(b)(3), we vacate the order denying Robinson's § 3582(c)(2) motion and remand for reconsideration before a different district judge in accordance with this opinion.

IV
Finally, both Lindsey and Robinson argue that this court's practice of placing appeals from the orders denying relief under § 3582(c)(2) on the informal briefing calendar under Local Rule 34(b) results in a "delay or denial of relief" that presents "serious constitutional problems." Under the reasoning set forth in Hood, 556 F.3d at 237-38, we conclude that no due process violation occurred.
The dockets in Lindsey's and Robinson's cases show that they filed their notices of appeal on August 27, 2008. By December 2, 2008, this court had ordered and received formal briefs and heard oral argument, less than four months after the defendants first filed their notices of appeal. We cannot conclude that "these processes denied [the defendants] due process." Hood, 556 F.3d at 238, (holding that a six-month period between a notice of appeal and oral argument did not violate the defendant's due process rights).
In sum, the order denying Lindsey's § 3582(c)(2) motion is affirmed, and the order denying Robinson's § 3582(c)(2) motion is vacated and remanded for proceedings before a different district judge in accordance with this opinion.
IT IS SO ORDERED.
NOTES
[*]  In the district court, because the sentencing court had reduced Lindsey's sentence a second time to 150 months' imprisonment on the government's Rule 35(b) motion, Lindsey argued that his sentence should correspondingly be reduced to 120 months' imprisonment, relying on U.S.S.G. § 1B1.10(b)(2)(B). On appeal, however, he has modified his request, asking for only a 135-month sentence, based on a sentence at the low end of the range corresponding to offense level 30, because even under this sentence, he is currently eligible for immediate release from prison.
