McKEAGUE, J., delivered the opinion of the court, in which SUTTON, J., joined. CLAY, J. (pp. 757-63), delivered a separate dissenting opinion.
OPINION
McKEAGUE, Circuit Judge.Defendant-appellant appeals from a judgment sentencing him to a prison term of twelve months and a day, followed by three years of supervised release. Appellant contends the district court erred by granting the government’s motion to strike its amended judgment of sentence, under which he had been sentenced to probation only. In addition, appellant contends the reinstated original sentence is procedurally and substantively unreasonable. Finding *746that the district court did not err by striking the amended judgment and that the sentence ultimately imposed is not unreasonable, we affirm the judgment of the district court.
I. FACTUAL AND PROCEDURAL BACKGROUND
This appeal stems from an illegal gambling enterprise known as “the numbers.” From 2000 to 2005, defendant James E. Houston, of Knoxville, Tennessee, and several co-conspirators ran an illegal gambling operation in the states of Alabama, Georgia and Tennessee that resembled a state lottery in many respects. Defendant, an otherwise legitimate and apparently successful businessman, served as the “bank” for the operation and derived substantial benefit from his participation.
In March 2006, a two-count bill of information was filed in the U.S. District Court for the Eastern District of Tennessee, alleging that defendant conspired to conduct an illegal gambling business involving a numbers lottery, in violation of 18 U.S.C. §§ 371 and 1955, and conspired to launder the proceeds of an illegal gambling operation, in violation of 18 U.S.C. §§ 1956(h) and 1957. Defendant pleaded guilty to both charges in April 2006. Pursuant to the plea agreement, defendant agreed to forfeit money and property obtained as a result of the gambling operation. The plea agreement includes the government’s acknowledgment that defendant had provided “substantial assistance” by encouraging his co-defendants to plead guilty, based upon which the government agreed to file a motion for downward departure pursuant to § 5K1.1 of the Sentencing Guidelines. The government further agreed to “represent to the Court that any lawful sentence that the Court deems appropriate is acceptable to the United States.” Plea Agreement ¶ 7, JA 57.
Defendant was sentenced by the district court on July 19, 2006. According to the presentence report (“PSR”) prepared by the Probation Department, defendant’s base offense level under the Sentencing Guidelines was 12. The PSR recommended a four-level increase due to defendant’s role as an organizer or leader of a scheme involving five or more participants, pursuant to § 3Bl.l(a) of the Guidelines. Defendant’s offense level was reduced by three levels due to his acceptance of responsibility. Defendant’s single prior misdemeanor conviction in 1990 placed him in criminal history category I. The resulting Guidelines sentencing range was 15 to 21 months. Defendant did not object to the PSR.
During sentencing, the district court noted that defendant had worked hard to establish himself as a businessman, had cooperated with the government, and had agreed to a substantial forfeiture of property. Accordingly, the court granted the government’s motion for downward departure. The court declined defendant’s request to impose a sentence of probation only, finding that defendant was the “organizer,” “the main man,” whom the other co-conspirators had trusted. Sentencing tr. pp. 16-17, JA 202-03. The court imposed a sentence of 12 months’ imprisonment on each count, the two sentences to run concurrently. This sentence, the court observed, would afford “adequate deterrence” and “just punishment.” Id. The court also imposed a supervised release term of three years. Upon request of defense counsel, the court changed the prison sentence to twelve months and a day so that defendant would be eligible for an earlier release from the Federal Bureau of Prisons. The court then asked if the parties had any objections to the sentence. Defendant did not object.
*747On July 24, 2006, five days after sentencing and prior to entry of the judgment, defendant filed a “motion for reconsideration.” Defendant contended the sentence imposed, representing a downward departure of three months from the low end of the advisory Guidelines range, was still greater than necessary to comply with the purposes of sentencing set forth at 18 U.S.C. § 3553(a)(2). He noted that the court had not expressly considered his arguments: (1) that he grew up in a community where playing the numbers was culturally accepted; and (2) that he had a history of assisting others in the community, had strong familial relationships, and provided support for his children and mother. Further, he complained that the sentence was disproportionately harsh in comparison with sentences imposed on other similarly situated defendants in the Northern Division of the Eastern District of Tennessee. In this respect, the motion was supported by the affidavit of defendant’s attorney, David M. Eldridge, stating in pertinent part:
Accordingly, based upon my personal experience as well as following cases in this court since 1988, to the best of my personal knowledge, no individual who has pled guilty to involvement in an illegal gambling business, cooperated, and received a Motion for Downward Departure has ever been sentenced to a term of incarceration in the Northern Division of the Eastern District of Tennessee. This category of defendants, who have not been incarcerated, includes those who have been denominated as an organizer or leader under the guidelines.
Eldridge aff. ¶ 5, JA 128. The motion represented that the government “does not oppose this motion for reconsideration if the Court deems it appropriate to reconsider Mr. Houston’s sentence.” Motion ¶ 11, JA 125.
Three days later, without conducting a hearing, the district court issued a memorandum and order granting defendant’s motion. JA 148. The court confirmed that it had previously considered defendant’s history and personal characteristics raised in the motion for reconsideration. The court acknowledged, however, that it had not previously considered the sentencing disparities issue. After considering the “new information” presented by defense counsel and “independently researching” the matter, the court concluded that defense counsel was correct and that a term of incarceration was too harsh and greater than necessary to comply with the purposes of sentencing. Memorandum and Order pp. 2-3, JA 149-50. The court ordered that the judgment of sentence be amended by substituting a period of two years’ probation for the original prison term of twelve months and a day. The judgment of sentence was entered on July 31, 2006.
On August 3, 2006, the government moved to strike the amended judgment for three reasons: (1) because the court lacked authority to amend defendant’s sentence under Rule 35(a) of the Federal Rules of Criminal Procedure; (2) because defendant had misrepresented the government’s position on the motion for reconsideration; and (3) because the factual basis for the sentence reduction was inaccurate. The district court granted the government’s motion to strike the amended judgment on October 3, 2006. In a 10-page memorandum and order, the court explained that it had granted the motion for reconsideration and reduced defendant’s sentence for two reasons. First, the court had been persuaded by defendant’s new argument, as well as its own independent research, concerning the need to avoid unwarranted sentence disparities under 18 U.S.C. § 3553(a)(6). Memorandum and *748Order p. 3, JA 172. Second, despite being “acutely aware that it was on legal ground of questionable firmness when it granted defendant’s motion for reconsideration,” the court had relied on defendant’s representation that the government had no objection to the motion. Id. at 9, JA 178.
When the government belatedly raised its objection through the motion to strike, explaining that the earlier, inaccurate representation of its position had been the product of a miscommunication, the court was constrained to acknowledge that it was without authority to correct the original sentence under Rule 35(a). Id. at 8-9, JA 177-78. The court nevertheless maintained that it had not fully considered the sentence disparities factor when it originally sentenced defendant. Id. at 9, JA 178. Further, the court acknowledged that the government’s opposition to the reduced sentence demonstrated that the record remained incomplete and inadequate to enable fair comparison of similarly situated defendants. Hence, the record remained insufficiently developed to permit a determination whether defendant’s twelvemonths-and-a-day prison term constituted an unwarranted disparity under § 3553(a)(6). Yet, being without authority to alter the originally imposed sentence, the court was “compelled to reimpose the sentence originally announced on July 19, 2006.” Id. at 10, JA 179. The amended judgment was entered on October 10, 2006 and this appeal followed.
II. ANALYSIS
A. Order Striking Amended Judgment
The district court concluded that it did not have authority to correct the originally pronounced sentence and therefore granted the motion to strike. Defendant contends that the district court erred when it granted the government’s motion to strike the amended judgment, insisting that the district court did have authority to correct “clear error” in the original sentencing. The asserted “clear error” the district court was asked to correct was twofold. See Memorandum in Support of Reconsideration pp. 4-6, JA 132-34. First, defendant contended the district court had not adequately explained why its consideration of two factors under 18 U.S.C. § 3553(a)(1) did not warrant a downward variance greater than three months. Specifically, these two asserted factors are “the nature and circumstances of the offense” (i.e., the fact that defendant grew up in a community where playing the numbers was culturally accepted); and “the history and characteristics of the defendant” (i.e., his strong familial relationships and his history of generosity to others and good citizenship). Id. Second, the district court was said not to have expressly considered, under 18 U.S.C. § 3553(a)(6), “the need to avoid unwarranted sentence disparities.” Arguing that these failures by the district court represented “clear errors” that were correctable by the district court, defendant now would have us vacate the order striking the amended sentence and remand the case to the district court for entry of the original amended sentence of two years’ probation.
Whether the district court had the authority to resentence defendant is a question of law subject to de novo review. United States v. Ross, 245 F.3d 577, 585 (6th Cir.2001). The authority of a district court to resentence a defendant is limited by statute. Id. at 585.1 Specifically, 18 U.S.C. § 3582(c)(1)(B) provides in relevant part that a “court may not modify a term *749of imprisonment once it has been imposed except that ... the court may modify an imposed sentence of imprisonment to the extent otherwise expressly permitted by statute or by Rule 35 of the Federal Rules of Criminal Procedure.”
Rule 35(a) represents the only arguably applicable authority for correction of the original sentence in this case. It provides that, “[w]ithin 7 days after sentencing, the court may correct a sentence that resulted from arithmetical, technical, or other clear error.” The authority to correct a sentence conferred by Rule 35(a) is “extremely limited.” United States v. Arroyo, 434 F.3d 835, 838 (6th Cir.2006). As the Rule 35 Advisory Committee Note makes clear, the rule “is not intended to afford the court the opportunity to reconsider the application or interpretation of the sentencing guidelines or ... simply to change its mind about the appropriateness of the sentence ... [or] to reopen issues previously resolved at the sentencing hearing through the exercise of the court’s discretion with regard to the application of the sentencing guidelines.” See also United States v. Galvan-Perez, 291 F.3d 401, 406-07 (6th Cir.2002) (noting that a sentencing judge may not use Rule 35(a) to alter a discretionary decision merely because he later had a “change of heart”). Unless an error is an “obvious error or mistake” that would have resulted in a remand by the appellate court, it is outside of Rule 35(a)’s narrow purview. Arroyo, 434 F.3d at 838.
The original sentence imposed by the district court in this case was not marked by any arithmetical or technical error. Hence, the district court had authority to modify its original sentence only if it suffered from some other “clear error” that would have necessitated an appellate remand for re-sentencing. In granting defendant’s motion for reconsideration, the district court did not identify such an error. Rather, it relied on the government’s purported non-objection to reconsideration and the “new information” produced by defense counsel and confirmed by the court’s own independent research concerning sentences imposed on other “similarly situated” defendants in the Northern Division of the Eastern District of Tennessee. In other words, based on new information, the district court reconsidered, or changed its mind concerning, the extent of the appropriate downward adjustment from the low end of the advisory Guidelines sentencing range.
When the government belatedly lodged its objection, the district court characterized its amended sentence as having been premised on a “perceived misinterpretation of sentencing factors,” an error the district court conceded was beyond its power to correct, citing United States v. Durham, 178 F.3d 796, 800 (6th Cir.1999). Memorandum and Order p. 8, JA 177. Thus, although the district court regretted not having fully considered the sentence disparities issue when it first sentenced defendant, it concluded that its failure to do so did not constitute the sort of “clear error” that it was at liberty to correct. In this, defendant contends, the district court erred. For the reasons that follow, we disagree.
The gravamen of defendant’s argument is that the district court’s failure to explicitly consider the required § 3553(a) factors constitutes “clear error” within the meaning of Rule 35(a), i.e., an error that obviously “would have resulted in remand by this Court.” Arroyo, 434 F.3d at 838 (quoting Galvan-Perez, 291 F.3d at 407). In support of this argument, defendant has relied in part on United States v. Vonner, 452 F.3d 560 (6th Cir.2006) (vacating a sentence for failure to provide adequate explanation). See Memorandum in Sup*750port of Reconsideration pp. 4-6, JA 132-34. The Vonner decision has been vacated, however, by the Sixth Circuit sitting en banc, which recently issued a new ruling, applying plain-error review and affirming the district court judgment. United States v. Vonner, 516 F.3d 382 (6th Cir.2008). The en banc court’s Vonner decision is important to our resolution of the instant appeal for a couple of reasons.
As a threshold matter, Vonner applied plain-error review, per United States v. Bostic, 371 F.3d 865 (6th Cir.2004), because defendant Vonner had not, when given the opportunity at sentencing, expressly stated an objection to the adequacy of the court’s explanation for the sentence. Vonner, 516 F.3d at 385-86. This teaching is relevant here, too, as we consider whether the district court’s asserted errors were of such a nature that they should have been viewed, in the eyes of the district judge, as obviously warranting an appellate remand. Vonner confirms the already well-established Bostic rule: If, at the conclusion of a sentencing hearing, the judge asks the parties whether they have any objections to the proposed sentence that have not previously been raised, and the relevant party does not object, then plain-error review applies on appeal to those arguments not preserved in the district court. Id. at 385. Here, when the district court asked the parties whether there was any objection to the proposed sentence, no objection was made. That is, defendant did not challenge the adequacy of the court’s explanation of its sentence and did not raise the sentence disparities issue. It follows that appellate scrutiny would have been limited to plain-error review. And because, as we demonstrate below, defendant has not shown plain error, we agree with the district court that he did not show clear error either.
Under plain-error review, relief is granted only under “exceptional circumstances.” Id. at 386. That is, defendant Houston would have been required to show “(1) error (2) that was ‘obvious or clear,’ (3) that ‘affected defendant’s substantial rights’ and (4) that ‘affected the fairness, integrity, or public reputation of the judicial proceedings.’” Id. (quoting United States v. Gardiner, 463 F.3d 445, 459 (6th Cir.2006)).
In Vonner, the en banc court applied plain-error review to the question whether re-sentencing was required where the district court had imposed a within-Guidelines sentence without explicitly stating why it denied the defendant’s request for a downward variance. The court acknowledged that the sentencing court’s explanation was not “ideal;” that it failed to specifically address all of Vonner’s arguments for leniency. Yet, the record demonstrated that the district court had considered the nature and circumstances of the offense and the history and characteristics of the defendant. Nothing in the record suggested that the sentencing court did not listen to, consider and understand every argument Vonner made. Citing Rita v. United States, — U.S. -, 127 S.Ct. 2456, 2469, 168 L.Ed.2d 203 (2007), the court observed that a lengthy reasoned explanation was not required because the request for leniency was “conceptually straightforward.” Vonner, 516 F.3d at 388. Further, the court noted that Vonner’s arguments in mitigation were not disputed by the government and therefore did not amount to “controverted matters” on which the district court was required to rule under Rule 32 of the Federal Rules of Criminal Procedure, Fed.R.Crim.P. 32(i)(3)(B). Id. at 388-89. Hence, the en banc court concluded the sentencing court had not plainly violated its duty to analyze the relevant sentencing factors or Vonner’s arguments for leniency. Id. Vonner’s inadequate-ex*751planation objection was overruled, his procedural-unreasonableness challenge was denied, and the district court’s judgment of sentence was affirmed.
Here, defendant Houston’s request for reconsideration was based on two asserted errors. First, he argued that the district court did not adequately explain why such circumstances as cultural acceptance of gambling, familial relationships, and his history of generosity were not deemed to merit a greater-than-three-months downward variance. Id. In response, the district court confirmed that it had fully considered these circumstances. Memorandum and Order p. 2, JA 149; Memorandum and Order p. 2, JA 171. Clearly, the district court’s mere failure to fully explain the extent of its consideration of sentencing factors, which it had in fact fully considered, could not have been viewed by the district court as plain error so affecting Houston’s substantial rights and impugning the fairness of the proceeding that appellate correction would have been clearly warranted. This conclusion is further buttressed, of course, by Vomer's holding on the merits of a similar adequacy-of-explanation challenge. The district court did not err, therefore, in its determination that this first basis for reconsideration did not constitute “clear error” that it had authority to correct under Rule 35(a).
The second basis for defendant’s motion for reconsideration was the district court’s failure to expressly consider the need to avoid unwarranted sentence disparities. The district court freely acknowledged that it had not fully considered this factor. Based on defense counsel’s affidavit, attesting to his knowledge and belief concerning sentences received by other gambling offenders in the area, the district court undertook confirmatory research and, in view of the government’s supposed non-objection, amended the original sentence. “In light of this new information,” the court explained, “[and][g]iving due weight to the [sentencing] factors, the court is now of the opinion that a sentence of twelve months and one day is greater than necessary ...” Memorandum and Order p. 3, JA 150. In other words, the district judge changed his mind in his application of the Sentencing Guidelines, thereby acting outside the bounds of his authority under Rule 35(a), as he later freely conceded.
Further, this sentence disparities factor was not mentioned in the PSR (to which defendant did not object), and neither party made an issue of the factor prior to or during the sentencing hearing. Because defendant did not preserve the issue per Bostic, an appellate challenge to the sentence on this basis would also have been subject to plain error review. It is also apparent that, since the sentence disparities factor had not been raised, it had not become a manifestly “relevant” sentencing factor at the time of sentencing and, per Vonner, the court’s failure to consider it could hardly have been viewed as “clear” or “plain” error, if error at all. See also United States v. Kirchhof, 505 F.3d 409, 413 (6th Cir.2007) (“If the record demonstrates that the sentencing court addressed the relevant factors in reaching its conclusion, the court need not explicitly consider each of the § 3553(a) factors or engage in a rote listing or some other ritualistic incantation of the factors.)” (citing United States v. Dexta, 470 F.3d 612, 614-15 (6th Cir.2006)(emphasis added)); United States v. Simmons, 501 F.3d 620, 625 (6th Cir.2007) (holding that district judge is required to explicitly consider only those factors raised by defendant or otherwise particularly relevant).
In Simmons, moreover, the court specifically addressed the § 3553(a)(6) sentence *752disparities issue and held that the sentencing court was under a duty to explicitly consider it only if raised by the defendant or if it was otherwise shown to be “particularly relevant.” Simmons, 501 F.3d at 625. See also United States v. Husein, 478 F.3d 318, 330-32 (6th Cir.2007) (upholding sentence over procedural-unreasonableness challenge where five of six sentencing factors were considered, even though § 3553(a)(6) was left undiscussed). Otherwise, a failure to explicitly consider the § 3553(a)(6) factor could be deemed to evidence a procedurally unreasonable sentence only if the failure were shown to stem from a “complete ignorance of that factor.” Simmons, 501 F.3d at 626.
Here, the sentence disparities issue had not been raised by defendant at the time of sentencing and there was no reason to believe it was particularly relevant. When, post-sentencing, the sentencing judge was confronted with “new information” concerning sentencing practices in the vicinity, he believed that he had ignored this factor. In this belief, however, the sentencing judge misconceived the nature of the factor. “Subsection 3553(a)(6) is concerned with national disparities among the many defendants with similar criminal backgrounds convicted of similar criminal conduct.” Id. at 623 (emphasis added). This factor is designed to “ensure nationally uniform sentences among like offenders.” Id. Considering that one of the fundamental purposes of the Guidelines is to help maintain national uniformity in sentences, and considering that most sentences are within the Guidelines, the Guidelines themselves represent the best indication of national sentencing practices. Id. at 626.
Hence, by initially and correctly determining what defendant Houston’s advisory Guidelines range would be, the sentencing court necessarily — albeit implicitly and even unwittingly — took account of the national uniformity concern embodied in § 3553(a)(6). See id. Contrary to his own belief, the sentencing judge did not fail to consider the sentence disparities factor. The Supreme Court recently elaborated on this very point:
As with the seriousness of the offense conduct, avoidance of unwarranted disparities was clearly considered by the Sentencing Commission when setting the Guidelines ranges. Since the District Judge correctly calculated and carefully reviewed the Guidelines range, he necessarily gave significant weight and consideration to the need to avoid unwarranted disparities.
Gall v. United States, — U.S. -, 128 S.Ct. 586, 599, 169 L.Ed.2d 445 (2007). See also United States v. Phinazee, 515 F.3d 511, 520 (6th Cir.2008) (observing that Guidelines as a whole embrace the need to avoid unwarranted sentence disparities). The district court did not, therefore, clearly err by failing to expressly describe its consideration of the unassert-ed sentence disparities issue.
Moreover, the representations made by defense counsel in support of reconsideration, i.e., the representations that triggered the sentencing judge’s misapprehension that he had committed error, did not even implicate national sentence disparities. They pertained to local sentence disparities, which are not a concern of § 3553(a)(6). The district judge, in his discretion, might have considered local disparities to be a relevant consideration if timely raised. We cannot hold, however, that he clearly erred by failing to take such a non-mandatory consideration into account where it had not been timely raised.
We therefore conclude that neither of the asserted grounds for reconsideration presented the sort of clear error that *753would have warranted appellate remand. The district court lacked authority under Rule 35(a) to alter the sentence originally imposed. Of course, this is the very conclusion that the district court correctly reached when it granted the government’s motion to strike the amended sentence.2 Inasmuch as this is the only basis on which defendant Houston challenges the district court’s order granting the government’s motion to strike, we overrule the objection and uphold the order vacating the amended judgment.3
As a consequence of that order, the district court proceeded to re-impose the original sentence, sentencing defendant to a prison term of twelve months and a day. Defendant challenges this sentence as procedurally and substantively unreasonable.
B. Procedural Unreasonableness
Even though the sentence ultimately imposed represents a three-month downward variance from the low-end of the advisory Guidelines range, defendant contends the sentence is marked by procedural unreasonableness because the sentencing judge admitted that he failed to fully consider the § 3553(a)(6) sentence disparities issue. Had this factor been properly considered, defendant argues, it is evident that the sentencing judge would have granted a greater downward variance. That is, notwithstanding our holding that the district court did not “clearly err,” defendant maintains that the court “erred” by imposing a procedurally unreasonable sentence.
We review a judgment of sentence for reasonableness under an abuse-of-discretion standard. Gall, 128 S.Ct. at 594. To obtain relief, an appellant must show that the sentence is either procedurally or substantively unreasonable. Id. at 597; United States v. Vowell, 516 F.3d 503, 509-10 (6th Cir.2008). A sentence may be held procedurally unreasonable if it is marked by “significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the § 3553(a) factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentence-including an explanation for any deviation from the Guidelines range.” Gall, 128 S.Ct. at 597. Hence, a sentencing court’s failure to consider a § 3553(a) factor may render a sentence procedurally unreasonable.
As the above analysis makes clear, defendant Houston’s sentencing was not procedurally infirm. Again, because defendant did not timely object to the court’s failure to explicitly consider the matter of sentence disparities, and raised the issue only after sentencing, at a time when the district court was without authority to al*754ter the sentence already imposed, we review only for plain error. Vonner, 516 F.3d at 386, 392 (“While we do not require defendants to challenge the “reasonableness” of their sentences in front of the district court, we surely should apply plain-error review to any arguments for leniency that the defendant does not present to the trial court.”).
The first step in plain-error review is to determine whether the lower court erred. Did the district court commit procedural error? The district judge believed, post-sentencing, that he had failed to consider § 3553(a)(6) and that this failure constituted error, albeit not “clear error.” In the foregoing analysis, however, we have explained that it was the district judge’s belief, rather than the sentence imposed, that was erroneous. By correctly calculating defendant Houston’s Guidelines range, the district judge had necessarily taken into account the need to avoid unwarranted sentence disparities, viewed nationally. The matter of supposed local sentence disparities, brought to his attention post-sentencing, which he believed could be relevant, is not a matter within the contemplation of § 3553(a)(6). Notwithstanding the district judge’s post-sentencing misunderstanding about the nature of this sentencing factor, the sentence ultimately imposed is not procedurally infirm because he failed to consider an unassert-ed, non-mandatory factor.4 Contrary to defendant’s argument, the record demonstrates that the district court did adequately consider the national sentencing disparities concern embodied in § 3553(a)(6). We therefore reject defendant’s procedural-unreasonableness challenge.5,6
*755C. Substantive Unreasonableness
Defendant also argues that his sentence is substantively unreasonable, i.e., greater than necessary to comply with the purposes of sentencing. Defendant need not have asserted a substantive-unreasonableness objection in the district court to preserve the issue for appeal. Vonner, 516 F.3d at 389 (observing that, because “reasonableness” is the standard of appellate review, a litigant has no duty to object in the district court to the unreasonableness of the length of the sentence). Hence, we review the substantive-unreasonableness challenge not for plain error, but for abuse of discretion. The Supreme Court has defined the scope of this review as follows:
When conducting this review, the court will, of course, take into account the totality of the circumstances, including the extent of any variance from the Guidelines range. If the sentence is within the Guidelines range, the appellate court may, but is not required to, apply a presumption of reasonableness. [Rita v. United States, — U.S. -, 127 S.Ct. 2456, 2462-68, 168 L.Ed.2d 203 (2007) ]. But if the sentence is outside the Guidelines range, the court may not apply a presumption of unreasonableness. It may consider the extent of the deviation, but must give due deference to the district court’s decision that the § 3553(a) factors, on a whole, justify the extent of the variance. The fact that the appellate court might reasonably have concluded that a different sentence was appropriate is insufficient to justify reversal of the district court.
Gall, 128 S.Ct. at 597.
Arguably, the presumption of reasonableness validated in Rita, as recognized in Gall, may not apply here, as the district court did not impose a sentence within the advisory Guidelines range, but granted a three-month downward variance from the low end of the range. See Phinazee, 515 F.3d at 514; Kirchhof, 505 F.3d at 414-15. Yet, the fact that the sentence imposed is outside the Guidelines range does not give rise to a presumption of unreasonableness, Gall, 128 S.Ct. at 597, especially where the variance results in a sentence even more favorable to the challenging defendant than a within-Guidelines sentence. After determining that the district court made no significant procedural error in calculating the Guidelines range, we must assess the substantive reasonableness of the sentence in light of the totality of the circumstances, giving “due deference” to the sentencing judge, in recognition of his greater familiarity with the case, his superior position to find facts and assess credibility, and the institutional advantage that comes with frequent sentencing of offenders. Id. at 597-98.
We have already explained why the district court’s failure to explicitly consider § 3553(a)(6) was not a significant procedural error. Defendant maintains the sentence is substantively unreasonable because the three-month downward variance granted in the original sentence is insufficient. Defendant insists that the original amended sentence, imposing a two-year term of probation and no term of imprisonment, was sufficient to comply with the purposes of sentencing. This is said to be clearly evidenced by the fact that the district judge, when he believed he had the discretion to do so because the government had no objection, amended the sentence to eliminate incarceration. Defendant thus urges us to defer to the district judge’s exercise of discretion in the second of the three sentencing rulings, rather than the first and third.
The district judge’s ambivalence clearly stemmed in part from his misunderstanding about the government’s position, but *756even more fundamentally from his misunderstanding of the sentence disparities factor. Whether he would have continued to question the fairness of the sentence if he had properly understood the requirements of § 3553(a)(6) is a matter of sheer speculation. Speculation, however, will not support a holding that the district judge abused his discretion when he initially (and ultimately) granted a three-month downward variance and imposed a sentence of twelve months and a day. To the contrary, the sentencing transcript and opinion vacating the original amended sentence affirmatively demonstrate that the sentence originally (and ultimately) imposed is not unreasonable in length.
No one has challenged the correctness of the advisory Guidelines range identified by the district judge, being fifteen to twenty-one months. After identifying this range and deciding to grant the government’s motion for downward variance based on defendant’s substantial assistance, the sentencing judge engaged in a weighing of circumstances. The district judge expressly considered that defendant profited greatly from his unlawful conduct; that he conducted the illegal gambling business for over five years; that he was the organizer of this criminal enterprise and had persuaded other “good people” who trusted him to become involved; and that defendant had a prior criminal history — albeit not a terribly serious one. Hrg. tr. pp. 14-16, JA 200-02. The judge also took note of mitigating circumstances, i.e., that defendant had cooperated with the government and had agreed to forfeit substantial property to the government; that defendant had strong family ties and responsibilities; and that he had been a good citizen, supporting local civic organizations and helping others less privileged than himself. Id.; Memorandum and Order p. 2, JA 149. The district judge concluded that a prison sentence of twelve months and a day afforded “adequate deterrence” and “just punishment.” Hrg. tr. pp. 16-17, JA 202-03.
The district judge thus appears to have reasonably weighed the totality of the circumstances in arriving at a sentence. The district judge also appears to have reasonably justified the extent of the variance granted. Apart from his contention that the sentence is unreasonably long in comparison with sentences imposed on other local gambling offenders, defendant has not explained why this sentence should be deemed so unreasonably long as to constitute an abuse of discretion. Even if the local sentence disparities issue were deemed to have been timely raised below, the record was not sufficiently developed, as the district court recognized, to enable a sound determination that the other putatively comparable offenders were in fact similarly situated in all relevant respects. Defendant’s substantive-unreasonableness argument thus boils down to either (1) a contention that the sentencing judge should have weighed the circumstances differently, or (2) a mere allegation that the sentence is greater than necessary. Both contentions are beyond the scope of proper appellate review for substantive unreasonableness. See United States v. Sexton, 512 F.3d 326, 332 (6th Cir.2008) (recognizing that substantive-unreasonableness review does not look to whether the appellate court would have imposed the same sentence in the first instance); Phinazee, 515 F.3d at 519 (observing that since review is not de novo, the appellate court must be wary to avoid substituting its judgment for that of the district court).
Defendant has not carried his burden of demonstrating that the sentence ultimately imposed represents an abuse of discretion. In fact, he has failed to identify a single Sixth Circuit case in which a sentence *757reflecting a downward variance from the advisory Guidelines range was vacated because unreasonably long. See Phinazee, 515 F.3d at 519. According due deference to the district judge’s discretion in assessing the extent of the downward variance warranted by the circumstances properly before him, see Gall, 128 S.Ct. at 597-98, we therefore overrule defendant’s substantive-unreasonableness challenge as well.
III. CONCLUSION
Notwithstanding the confused nature of post-sentencing proceedings in the district court, we conclude that the sentence originally, and ultimately, imposed is marked neither by clear error that was correctable by the district court under Rule 35(a) of the Federal Rules of Criminal Procedure, nor by other procedural or substantive unreasonableness. Accordingly, we AFFIRM the judgment of the district court.
. The Ross court rejected the argument that a sentencing court has any inherent power to modify a sentence of imprisonment. 245 F.3d at 586.
. This conclusion is further buttressed, as the district court ultimately recognized, by the fact that, in the sentencing context, "there is simply no such thing as a 'motion to reconsider’ an otherwise final sentence.” United States v. Dotz, 455 F.3d 644, 648 (6th Cir.2006). Rather, as discussed above, the sentencing court’s authority to alter a sentence of imprisonment after it has been imposed is narrowly circumscribed, per 18 U.S.C. § 3582(c)(1)(B).
. In his reply brief, defendant argues that the government should have been deemed barred from moving to strike the amended sentence in the first place. In ¶ 7 of the plea agreement, defendant correctly asserts, the prosecution had agreed to accept “any lawful sentence that the Court deemed appropriate.” JA 57. The motion to strike did not contravene this promise, however. As the foregoing analysis demonstrates, the amended sentence was beyond the court’s authority to issue and was, to this extent, not a “lawful sentence.” See United States v. Moncivais, 492 F.3d 652, 662 (6th Cir.2007) ("Plea agreements are to be enforced according to their terms.”).
. To be sure, defendant was free to argue for leniency, prior to or at the sentencing hearing, based on local trends in sentencing of gambling offenders. If he had so argued, it would have been within the district court's discretion to accept the argument as warranting an even greater downward variance. We hold simply that the sentence imposed is not procedurally unreasonable merely because the court did not consider a potentially relevant, but unasserted, non-mandatory sentencing factor.
. This case is distinguishable from United States v. Christman, 509 F.3d 299 (6th Cir.2007), where a sentence which the district court acknowledged was marked by procedural error, but which the district court was powerless to correct under Rule 35(a), was vacated and the matter remanded for re-sentencing. In Christman, the sentencing judge had committed a legal error which impacted the length of sentence; here, the district judge erroneously believed he had committed legal error, when in fact he had not.
. In his separate opinion, our dissenting colleague strains to characterize the district court as confused and our affirmance as "astounding” and "inexplicable.” The characterizations are inapt.
Twice, the dissent describes the district court as having gotten "turned around.” In actuality, the "turned around” reference in the sentencing transcript, JA 188, does not evidence confusion in the sentencing proceeding at all. Rather, it is derived from a quip made by the district judge before the sentencing even began as he entered the courtroom and reacted, ostensibly, to the defendant and his counsel having seated themselves at the table ordinarily occupied by the Assistant U.S. Attorney. It was a trivial irregularity that played no role in the sentencing proceeding.
No less inaccurate is the dissent's description of our procedural-unreasonableness analysis as astounding and inexplicable. As explained in quite some detail, our affirmance is the product of rather ordinary application of plain-error review. Our dissenting colleague would prefer not to be constrained by plain-error review. Yet, as justification for avoiding the clear, well-established and binding teaching of Sixth Circuit rulings like Vonner and Bostic, the dissent cites no authority but an Eighth Circuit opinion, United States v. Ellis, 417 F.3d 931, 933 (8th Cir.2005). Ellis carries no weight in this context, however, because the Eighth Circuit, in its application of Rule 35(a), was unconstrained by a Bostic-type prophylactic rule, whereas we remain bound by Bostic.