
625 F.3d 277 (2010)
UNITED STATES of America, Plaintiff-Appellee,
v.
Vincent L. WATKINS, Defendant-Appellant.
No. 09-3966.
United States Court of Appeals, Sixth Circuit.
Argued: October 21, 2010.
Decided and Filed: November 3, 2010.
*279 ARGUED: Matthew M. Robinson, Robinson & Brandt, P.S.C., Covington, Kentucky, for Appellant. Segev Phillips, Assistant United States Attorney, Columbus, Ohio, for Appellee. ON BRIEF: Matthew M. Robinson, Robinson & Brandt, P.S.C., Covington, Kentucky, for Appellant. William E. Hunt, Assistant United States Attorney, Cincinnati, Ohio, for Appellee.
Before: MARTIN, COLE, and CLAY, Circuit Judges.

OPINION
BOYCE F. MARTIN, JR., Circuit Judge.
Defendant-appellant Vincent Watkins appeals the district court's denial of a sentence reduction pursuant to 18 U.S.C. § 3582(c)(2). We AFFIRM.

I. BACKGROUND
On May 13, 1993, a jury convicted Watkins of conspiracy to possess with intent to distribute cocaine base in violation of 21 U.S.C. § 846. The district court found Watkins responsible for transporting 7.7957 kilograms of cocaine base, which resulted in a base offense level of forty under the United States Sentencing Guidelines. Watkins received a two-point enhancement for obstruction of justice and a two-point enhancement for his managerial role in the offense, which brought his total offense level to forty-four. Under the Guidelines, an offense level greater than forty-three was treated as a level forty-three. Coupled with a criminal history category of VI, Watkins's offense level produced a Guidelines sentence of life in prison. The district court sentenced Watkins to life in prison on September 15. Watkins appealed and this Court affirmed the district court's sentence. See United States v. Watkins, Nos. 93-4019, 93-4020, 1994 WL 464193, at *4 (6th Cir. Aug. 26, 1994).
Later in 1993, the United States Sentencing Commission amended the drug quantity table under U.S.S.G. § 2D1.1(c). See U.S.S.G. app. C, amend. 505. Amendment 505 lowered the base offense level from forty to thirty-eight for quantities of cocaine base equal to or greater than 1.5 kilograms. See U.S.S.G. § 2D1.1(c)(1). The amended drug quantity table reduced Watkins's base offense level from forty to thirty-eight. With his enhancements, his total offense level was forty-two, which reduced his Guidelines sentencing range from life to between thirty years and life. Following the enactment of Amendment 505, Watkins filed three motions pursuant to section 3582(c)(2) requesting that the district court apply Amendment 505 to his case and resentence him to the low end of the Guidelines range. The district court rejected each motion after noting its discretion to grant a reduction and evaluating the 18 U.S.C. § 3553(a) sentencing factors.
On November 1, 2007, Amendment 706 to the Guidelines went into effect, reducing the base offense level for most crack cocaine offenses by two levels. See U.S.S.G. supp. to app. C, amend. 706. On March 3, 2008, Amendment 713 went into effect, giving Amendment 706 retroactive effect. See U.S.S.G. supp. to app. C, amend. 713.
On February 25, 2008, Watkins filed a motion for reduction of sentence pursuant to section 3582(c)(2) based on Amendment 505, Amendment 706, consideration of the section 3553(a) sentencing factors, and application of United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). The district court denied Watkins's motion. The district court declined to consider a reduction based on Amendment 505 because it had previously denied three similar motions and it found no justification *280 for a reduction. The district court also found that Watkins's sentencing range was not affected by Amendment 706 and it thus lacked authority to reduce his sentence based on Amendment 706. Watkins appeals.

II. STATUTORY FRAMEWORK AND STANDARD OF REVIEW
A district court may modify a defendant's sentence only as authorized by statute. See United States v. Johnson, 564 F.3d 419, 421 (6th Cir.2009). Under section 3582(c)(2), a district court may modify a term of imprisonment:
in the case of a defendant who has been sentenced to a term of imprisonment based on a sentencing range that has subsequently been lowered by the Sentencing Commission pursuant to 28 U.S.C. 994(o) ... after considering the factors set forth in section 3553(a) to the extent that they are applicable, if such a reduction is consistent with applicable policy statements issued by the Sentencing Commission.
18 U.S.C. § 3582(c)(2).
The Supreme Court has held that section 3582(c) establishes a two-step inquiry. See Dillon v. United States, ___ U.S. ___, 130 S.Ct. 2683, 2691, 177 L.Ed.2d 271 (2010). At step one of the inquiry, the court must determine the defendant's eligibility for a sentence modification under the Sentencing Commission's policy statements and the extent of reduction authorized. Id. The Sentencing Commission has identified the amendments that may apply retroactively and the procedure for deciding a motion for reduction of sentence in a policy statement. See U.S.S.G. § 1B1.10. Both Amendment 505 and Amendment 706 are included in the collection of retroactive amendments listed in section 1B1.10(c) that may be considered as a basis for sentence reduction. The court must "determine the amended guideline range that would have been applicable to the defendant" if the relevant amendment had been in effect at the time of the initial sentencing. Id. § 1B1.10(b)(1). We review de novo a district court's determination that a defendant is ineligible for a sentence reduction. See United States v. Curry, 606 F.3d 323, 327 (6th Cir.2010).
If a defendant is eligible for a sentence reduction, then under step two of the inquiry the court must consider the section 3553(a) factors and determine whether, in its discretion, the authorized reduction is warranted under the circumstances. See Dillon, 130 S.Ct. at 2692. A district court's decision whether a sentence reduction is warranted is reviewed for abuse of discretion. See United States v. Washington, 584 F.3d 693, 695 (6th Cir. 2009), cert. denied, ___ U.S. ___, 130 S.Ct. 3479, ___ L.Ed.2d ___ (2010). A district court abuses its discretion when it relies on clearly erroneous findings of fact, applies the law improperly, or applies the incorrect legal standard. Id.

III. ANALYSIS

A. Amendment 505
First, we find that the district court correctly concluded that Watkins was eligible for a sentence reduction based on Amendment 505 and did not abuse its discretion in finding that a reduction was not warranted.
The district court correctly concluded that Watkins was eligible for a sentence reduction based on Amendment 505. To be eligible for a sentence reduction under section 3582(c)(2), the defendant must have been "sentenced to a term of imprisonment based on a sentencing range that has subsequently been lowered *281 by the Sentencing Commission." 18 U.S.C. § 3582(c)(2). As discussed above, Amendment 505 lowered Watkins's base offense level from forty to thirty-eight, which reduced his total offense level from forty-four to forty-two and lowered his Guidelines range from life to between thirty years and life. Thus, Watkins was sentenced to a term of imprisonment based on a Guidelines range that was subsequently lowered by the Sentencing Commission, and the district court correctly held that Watkins was eligible for a sentence reduction.
Furthermore, the district court did not abuse its discretion in concluding that a reduction in Watkins's sentence based on Amendment 505 was not warranted. The decision whether to grant an authorized sentence reduction is discretionary. See Curry, 606 F.3d at 330. In determining whether to grant an authorized sentence reduction, the district court must consider the section 3553(a) factors to the extent that they are applicable and the impact on public safety. See U.S.S.G. § 1B1.10, cmt. n.1(B)(i)-(iii). In addition, the court may consider the defendant's post-sentencing conduct. See id. Section 3582(c)(2) proceedings are not full resentencings, and we do not require the district court to articulate its analysis of each sentencing factor as long as the record demonstrates that the court considered the relevant factors. See Curry, 606 F.3d at 330-31.
The district court noted that whether to grant a reduction of sentence pursuant to section 3582(c)(2) was within its discretion, and that it was required to consider the applicable section 3553(a) factors. The district court reasoned that it would not consider any reduction based on Amendment 505 because it had already considered and denied three motions by Watkins to reduce his sentence based on Amendment 505. In each case, the district court denied the motion after considering the section 3553(a) factors, including the nature and circumstances of the offense, Watkins's history and characteristics, the need for the sentence imposed to reflect the seriousness of the offense and to promote respect for the law, whether the sentence provided just punishment for the offense, whether the sentence was an adequate deterrent to criminal conduct, and whether the sentence would protect the public from further crimes by Watkins. In the motion at issue in this case, Watkins did not present any new evidence of post-offense rehabilitation or other relevant factors not addressed in previous motions. Although the district court stated that it would not consider any reduction based on Amendment 505, it also stated that it had reviewed all the documents submitted by Watkins and did not find any justification for reducing his sentence.
In Curry, this Court could not conclude that the district court abused its discretion in denying the defendant's motion for modification of his sentence when the record had been amply developed before the resentencing motion was filed, the district court had considered the relevant factors in depth at the original sentencing and resentencing, and the district court indicated that it had considered all the relevant section 3553(a) factors. See id. at 331. Similarly, here, the district court had considered the relevant factors in Watkins's three previous motions, and it indicated that it had considered the entire record and the section 3553(a) factors. Thus, the district court did not abuse its discretion in denying Watkins's current motion for reduction pursuant to Amendment 505.

B. Amendment 706
The district court correctly found that Watkins was ineligible for a sentence *282 reduction based on Amendment 706 because this Amendment did not reduce Watkins's sentencing range. For a defendant to be eligible for a sentence reduction under section 3582(c)(2), the reduction must be "consistent with applicable policy statements issued by the Sentencing Commission." 18 U.S.C. § 3582(c)(2). The policy statement governing section 3582(c)(2) proceedings provides that a reduction in the defendant's term of imprisonment is not authorized if an "amendment listed in subsection (c) does not have the effect of lowering the defendant's applicable guideline range." U.S.S.G. § 1B1.10(a)(2)(B).
Although Amendment 706 lowered the offense level for most crack cocaine offenses, it did not lower Watkins's applicable Guidelines range. Watkins's base offense level was originally forty, then thirty-eight after Amendment 505. Before Amendment 706, the Guidelines assigned offense level thirty-eight to any quantity of cocaine base 1.5 kilograms or more. After Amendment 706, the Guidelines apply level thirty-six to a quantity of 1.5 to 4.5 kilograms cocaine base, and level thirty-eight to a quantity of 4.5 kilograms or more. Watkins was held responsible for over seven kilograms of cocaine base. Thus, his offense level continues to be thirty-eight after Amendment 706. With his enhancements, Watkins's adjusted offense level remains at forty-two, and his Guidelines range remains at 30 years to life. Because Amendment 706 did not lower Watkins's Guidelines range, a reduction in his term of imprisonment is not consistent with the Sentencing Commission policy statement. Id. Thus, the district court correctly held that Watkins is ineligible for a sentence reduction under section 3582(c)(2).
The bulk of Watkins's brief is devoted to his argument that permitting a sentence reduction under section 3582(c)(2) only when the requirements of section 1B1.10 are met treats the Guidelines as mandatory in violation of Booker, 543 U.S. 220, 125 S.Ct. 738. The Supreme Court, however, has recently foreclosed this argument. In Dillon, the Supreme Court held that "[g]iven the limited scope and purpose of § 3582(c)(2), ... proceedings under that section do not implicate the interests identified in Booker." Dillon, 130 S.Ct. at 2692. Therefore, the Sentencing Commission's policy statements are mandatory in the sentence-modification context. See United States v. Hameed, 614 F.3d 259, 265 (6th Cir.2010). Thus, the district court correctly held that because the requirements of section 1B1.10 were not met in this case, it did not have the authority to permit a sentence reduction under section 3582(c)(2).
To the extent that Watkins appeals the denial of the sentence reduction under section 3582(c)(2) on Booker reasonableness grounds, we lack jurisdiction to entertain this argument. See United States v. Bowers, 615 F.3d 715, 717 (6th Cir.2010). Thus, we lack jurisdiction to consider Watkins's argument that the district court failed to consider disparities that persist between crack and powder cocaine offense sentencing even after Amendment 706. See id. at 723 n. 6.

IV. CONCLUSION
The district court's denial of Watkins's motion for reduced sentence is AFFIRMED.
