
    UNITED STATES of America, Plaintiff-Appellee, v. Tyrone D. HOWARD, Defendant-Appellant.
    No. 04-5240.
    United States Court of Appeals, Sixth Circuit.
    March 17, 2005.
    Terry M. Cushing, Monica Wheatley, U.S. Attorney’s Office, Louisville, KY, for Plaintiff-Appellee.
    Mark Wettle, Louisville, KY, for Defendant-Appellant.
    Before KENNEDY, MOORE, and SUTTON, Circuit Judges.
   OPINION

MOORE, Circuit Judge.

After a jury trial, Defendant-Appellant Tyrone D. Howard (“Howard”) was convicted of bank fraud in violation of 18 U.S.C. § 1344. The district court sentenced Howard to the lowest sentence possible, absent a downward departure, under the then-mandatory U.S. Sentencing Guidelines (“Guidelines”). Howard raises only one argument on appeal: that the district court unconstitutionally increased his sentence on the basis of facts neither admitted by Howard nor proved to a jury beyond a reasonable doubt. Conceding that he failed to raise this issue in the district court, Howard nonetheless argues that the district court’s plain error warrants our review. We agree, and accordingly VACATE Howard’s sentence and REMAND the case to the district court for resentencing in light of United States v. Booker, — U.S.-, 125 S.Ct. 738,160 L.Ed.2d 621 (2005).

We briefly set out the facts relevant to this appeal. At sentencing, the district court determined that Howard should be sentenced at Offense Level 12, Criminal History Category II, mandating a Guidelines imprisonment range of twelve to eighteen months. See U.S. Sentencing Guidelines Manual (“U.S.S.G.”) Sentencing Table (2002). In calculating this Guidelines range, the district court began with a Base Offense Level of 6. See U.S.S.G. § 2Bl.l(a). The district court then added four levels after determining that the amount of loss involved in the offense was more than $10,000 but not greater than $30,000, Joint Appendix (“J.A.”) at 484 (Feb. 2, 2004 Sentencing Hr’g); U.S.S.G. § 2Bl.l(b)(l)(C), plus an additional two levels based on its finding that Howard had obstructed justice by testifying falsely under oath about matters material to his guilt or innocence of the crime charged. J.A. at 530 (Feb. 9, 2004 Sentencing Hr’g); U.S.S.G. § 3C1.1. The district court sentenced Howard to a total term of imprisonment of one year and one day.

In United States v. Oliver, 397 F.3d 369, 380-81 (6th Cir.2005), we held that a sentence enhancement imposed in violation of the Sixth Amendment constitutes plain error warranting remand for resentencing. Howard contends that such an error occurred in this case. Absent the enhancements, Howard would have been sentenced at Offense Level 6, Criminal History Category II, for a Guidelines range of only one to seven months’ imprisonment. U.S.S.G. Sentencing Table. As the maximum seven-month sentence permissible under this Guidelines range is shorter than the year- and-a-day sentence actually imposed, the sentence imposed violates the Sixth Amendment unless based on facts “admitted by the defendant or proved to a jury beyond a reasonable doubt.” Booker, 125 S.Ct. at 756.

In this case, Howard maintained his innocence during trial. Nevertheless, he was found guilty by the jury. The jury’s verdict made no finding as to the amount of loss, but Howard’s attorney conceded at sentencing (conducted prior to the Supreme Court’s decision in Blakely v. Washington, — U.S.-, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004)) that it was appropriate for the district court to apply the four-level § 2B1.1 (b)(1)(C) amount-of-loss enhancement. J.A. at 457-59 (Feb. 2, 2004 Sentencing Hr’g). However, Howard’s attorney did successfully object to the government’s request that the district court instead apply the six-level § 2B1.l(b)(1)(D) amount-of-loss enhancement. J.A. at 483-84 (Feb. 2, 2004 Sentencing Hr’g). We need not decide whether counsel’s § 2B1.1(b)(1)(C) concession — made under a preponderance-of-the-evidence standard and prior to the Blakely decision — would constitute, for Booker purposes, an admission by the defendant sufficient to avoid a Sixth Amendment violation, because the sentence imposed in this case requires remand even absent a Sixth Amendment violation.

In United States v. Barnett, 398 F.3d 516, 529-530 (6th Cir.2005), we held that in certain circumstances remand of a preBooker sentence is required even absent a Sixth Amendment violation. As Howard was sentenced at the bottom of the applicable Guidelines range, Barnett requires that we remand the case to the district court. Accordingly, we VACATE Howard’s sentence and REMAND the case to the district court for resentencing in light of Booker. 
      
      . Although this sentence is technically one day longer than the minimum Guidelines term of imprisonment, it is in effect the lowest possible sentence the district court could have imposed within the applicable Guidelines range. Inmates sentenced to serve more than one year of imprisonment become eligible for up to fifty-four days of credit for good conduct during each year of imprisonment. See 18 U.S.C. § 3624(b). Accordingly, a year- and-a-day sentence can result in an inmate serving up to fifty-three days less than he or she would serve under a one-year sentence.
     
      
      
        . In its supplemental letter brief, the United States asserts that we should follow United States v. Bruce, 396 F.3d 697 (6th Cir. Feb.3, 2005), rather than United States v. Oliver, 397 F.3d 369 (6th Cir. Feb.2, 2005). However, as Oliver was decided prior to Bruce, we are bound by our longstanding rules to follow Oliver. 6th Cir. R. 206(c); see also United States v. Davis, 397 F.3d 340, 350 n. 7 (6th Cir.2005).
     
      
      . If we did conclude that defense counsel's concession allowed the district court to apply the amount-of-loss enhancement without violating the Sixth Amendment, the district court's application of the obstruction-of-justice enhancement, standing alone, would not be sufficient to establish a Sixth Amendment violation. Without the obstruction-of-justice enhancement, Howard would have had an Offense Level of 10 and a Criminal History Category of II, for a Guidelines range of eight to fourteen months’ imprisonment. U.S.S.G. Sentencing Table. As the year-and-a-day sentence imposed by the district court would have fallen within this Guidelines range, Howard’s sentence would not violate the Sixth Amendment.
     