
512 F.3d 787 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Freddie. L. PETERS, Defendant-Appellant.
No. 05-6101.
United States Court of Appeals, Sixth Circuit.
Submitted: October 23, 2007.
Decided and Filed: January 14, 2008.
ON BRIEF: Kemper B. Durand, Thomason, Hendrix, Harvey, Johnson & Mitchell, Memphis, Tennessee, for Appellant. Linda Nettles Harris, Assistant United States Attorney, Memphis, Tennessee, for Appellee.
Before: MERRITT and CLAY, Circuit Judges; COX, District Judge.[*]


*788 OPINION
MERRITT, Circuit Judge.
On January 31, 2002, a Federal Grand Jury in the Western District of Tennessee returned a 22-count indictment against Freddie Peters. The indictment charged Peters with making, and causing to be made and presented, false claims to the Internal Revenue Service in violation of 18 U.S.C. § 287, and unlawfully disclosing, using, and compelling the disclosure of Social Security account numbers of other persons in violation of 18 U.S.C. § 2 and 42 U.S.C. § 408(a)(8). His trial began on August 12, 2002, before Judge Julia Gibbons in the Western District of Tennessee.
At trial, the government produced evidence that Peters had executed a tax fraud scheme wherein he recruited African immigrants to file false income returns listing foster children as dependents. In fact, the taxpayers had no relationship with the children; rather, Peters had acquired Social Security numbers and other information for the children by paying the children's mothers $100 per child. Peters then provided this information to the immigrants filing the fraudulent tax returns for a fee of $200.
The jury found Peters guilty on all 22 counts of the indictment and Judge Gibbons sentenced him to 71 months (60 months for the false claims counts and 11 months for the fraudulent use of Social Security numbers) in prison followed by three years of supervised release. The sentence reflected four enhancements found by Judge Gibbons.
Peters appealed his conviction, challenging both the calculation of the sentence and the sufficiency of the evidence. The Sixth Circuit affirmed the conviction and sentence. United States v. Peters, 98 Fed. Appx. 449 (6th Cir.2004). The Supreme Court granted the writ, vacated the judgment of the Sixth Circuit, and remanded the case for further consideration in light of United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). The Sixth Circuit, in turn, remanded to the District Court for re-sentencing, where Peters received a new sentence of 57 months. The new 57-month sentence included three enhancements based on facts found by the judge: (1) a four-point enhancement for Peters' organizational role, (2) a two-point enhancement for obstruction of justice, and (3) a six-point enhancement because the losses exceeded $30,000. Peters again appeals his case, arguing both that his new sentence continues to violate the Sixth Amendment's prohibition of judicial fact-finding and that the sentence fails reasonableness review under 18 U.S.C. § 3553(a).
Peters requested that the sentencing judge impose a "time-served" sentence by presenting a document called "Statement of Reasons" that set out a number of mitigating factors, including the abandonment and many other adversities he suffered as a child, his new family ties and responsibilities as a result of his engagement to be married and other mitigating factors.
Besides a cursory statement acknowledging Peters' arguments, the District Court did not address the defendant's "time-served" argument or the mitigating factors indicating that a "time-served" sentence would satisfy the so-called "parsimony provision" of 18 U.S.C. § 3553(a) requiring a "sentence sufficient but not greater than necessary" to comply with the purposes of sentencing outlined in the statute.
The failure of the District Court to address Peters'"time-served" argument does not satisfy the "procedural reasonableness" requirement outlined in Section III of Justice Breyer's majority opinion in Rita v. United States, ___ U.S. ___, 127 *789 S.Ct. 2456, 2468-69, 168 L.Ed.2d 203 (2007). When the defendant or prosecutor "presents nonfrivolous reasons for imposing a different sentence," such as the statement of reasons submitted by Peters, a sentencing judge should address the "parties' arguments" and "explain why he has rejected those arguments." Id. at 2468. That did not happen in our case. See United States v. Thomas, 498 F.3d 336, 341 (6th Cir.2007) (vacating and remanding the district court's sentence because the factors raised by the defendant "went unmentioned and unaddressed, save the general statement by the district court that it had received, read, and understood the sentencing memorandum").
Accordingly, for these reasons, the judgment of the District Court sentencing the defendant to 57 months is reversed, and the case is remanded for re-sentencing.
NOTES
[*]  The Honorable Sean F. Cox, United States District Judge for the Eastern District of Michigan, sitting by designation.
