ORDER
On December 27, 2004, we issued an opinion vacating Corey A. Smith’s sentence and remanding for re-sentencing in light of the Supreme Court’s opinion in Blakely v. Washington, 542 U.S. 296, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004), and this court’s opinion in United States v. Booker, 375 F.3d 508 (7th Cir.2004), judgment aff'd & remanded, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). United States v. Smith, 393 F.3d 717 (7th Cir. 2004). On remand, the district court re-sentenced Smith to the same prison term that it had originally imposed. R.101. Smith again appeals. His lawyer has filed a brief pursuant to Anders v. California, 386 U.S. 738, 87 S.Ct. 1396, 18 L.Ed.2d 493 (1967), contending that there are no non-frivolous grounds for appeal at this juncture. Having reviewed the Anders brief, we conclude that there are two potentially non-frivolous grounds on which Smith might challenge his sentence that Smith’s counsel has not considered. For that reason, we find the Anders brief to be deficient, and we direct Smith’s counsel to consider the issues we have identified and either to brief those issues on the merits or to file a new Anders brief explaining why Smith could not make non-frivolous arguments on those issues.
Following Smith’s conviction by a jury for distributing and conspiring to distrib*521ute crack cocaine in violation of 21 U.S.C. §§ 841(a)(1), 841(b)(1)(B), and 846, the district court in 2003 ordered Smith to serve a prison term of 115 months. That term was within the sentencing range of 108 to 135 months called for by the U.S. Sentencing Guidelines. In calculating the Guidelines range, the district court found as a matter of fact that Smith had perjured himself when he testified in his own defense; and based on that finding, the court adjusted Smith’s offense level upward by two levels for obstruction of justice. See U.S.S.G. § 3C1.1. Because the court’s obstruction finding had the effect of boosting the Guidelines sentencing range, Smith argued in the prior appeal that the enhancement was inconsistent with his Sixth Amendment right to a jury trial in light of the Supreme Court’s then-recent decision in Blakely and this court’s decision in Booker. We agreed and accordingly vacated Smith’s sentence and remanded for re-sentencing. Smith, 393 F.3d at 720.
On May 20, 2005, the district court re-sentenced Smith. In the intervening months between our decision in Smith’s appeal and the re-sentencing, two important developments had occurred. First, the Supreme Court had issued its own opinion in Booker, concluding as we had that a federal sentencing judge cannot, consistent with the Sixth Amendment, make factual determinations that have the effect of increasing the sentencing range mandated by the U.S. Sentencing Guidelines. 125 S.Ct. at 749-50. However, the Supreme Court resolved the Sixth Amendment problem with the Guidelines by excising the provision of the enabling statute that obligated sentencing judges to apply them. Id. at 764. The Court similarly excised the statutory provision setting for the standards of review for appeals of Guidelines sentences, as that provision cross-referenced the provision mandating application of the Guidelines. Id. at 765. As a result, the Guidelines are now advisory rather than mandatory, see id. at 764, and sentences are subject to “review for ‘unreasonable[ness],’” id. at 765 (quoting 18 U.S.C. § 3742(e)(3)). Second, in United States v. Paladino, 401 F.3d 471, 483-84 (7th Cir.2005), cert. denied, 2005 WL 1304753 (U.S. Oct.3, 2005), we had outlined the procedure we would henceforth follow in cases where, as here, Booker challenges were raised for the first time on appeal and were therefore subject to review for plain error.1 We explained in Paladino that where a Booker-type of Sixth Amendment error had occurred and it was possible that the error had an impact on the defendant’s sentence, we would order a limited remand to the district court for the purpose of allowing the sentencing judge to consider whether he would be inclined to impose a different sentence knowing that the Sentencing Guidelines are to be treated as advisory rather than binding. Id. When the sentencing judge discloses an inclination to impose a lesser sentence, we will deem the Booker error “plain” in the sense that it was prejudicial, vacate the sentence, and remand for re-sentencing. Id. at 484. Where the sentencing judge reveals an inclination to impose the same sentence, we will instead proceed to consider whether the sentence is plainly erroneous in the sense that it is “unreasonable,” reasonableness being the standard of review prescribed by Booker. Id. (citing Booker, 125 S.Ct. at 765).
With the benefit of these two decisions, the district court understood that although we had gone so far as to vacate Smith’s original sentence and remand for re-sentencing, rather than ordering the limited *522remand we had subsequently described in Paladino, the question before it on remand was, in practical terms, the same one that Paladino posed: Was the court inclined to impose a sentence outside of the Guidelines range, knowing that it had the discretion to do so after Booker? See R. 106 at 4. The court concluded that it was not so inclined, notwithstanding the suggestion of Smith’s counsel that the Guidelines enhancement for obstruction of justice might have increased the sentencing range out of proportion to Smith’s actual conduct in testifying. See id.
Under Paladino, ... all I would have to say is no, I don’t think I would change the sentence if I had known about Booker when I sentenced [Smith] before. And the fact that the sentence was in the mid-range certainly confirms that, and I will tell you that is the fact.
And so my conclusion is that the sentence should be exactly the same, for the same reasons, I thought it was an appropriate sentence at the time. The — I recall the obstruction issue. It was not simply a denial [of guilt], there was a lot of misinformation and obfuscation in the testimony [Smith] offered, and that’s the reason, I think, that I gave him the mid-range initially.
Id. at 6. The court subsequently entered a fresh judgment and commitment order reimposing a sentence of 115 months. R. 101.
In his Anders brief, Smith’s counsel contends that there is no longer any issue to pursue on Smith’s behalf, now that the district court has considered the possibility of imposing a sentence outside of the Guidelines range and rejected it. Counsel notes that although the court did not solicit the views of the parties’ counsel in writing as we instructed in Paladino, 401 F.3d at 474, the court nonetheless gave both parties the opportunity to place their arguments on the record and there is no indication that had the court followed a different procedure, it might have affected the court’s decision to re-impose the original sentence. Anders Br. at 10. With that contention, we agree.
There is, however, a potentially more important omission in the re-sentencing that counsel has not considered in his Anders brief. As the Supreme Court’s opinion in Booker makes clear, in choosing an appropriate sentence the district judge must consider not only the sentencing range advised by the Guidelines, but also the other factors set forth in 18 U.S.C. § 3553(a), including the nature and circumstances of the offense along with the history and characteristics of the defendant, as well as the need for a sentence which reflects the gravity of the offense, provides for just punishment, promotes respect for the law, deters and protects the public from future criminal conduct by the defendant, and provides the defendant with appropriate care and rehabilitation. 125 S.Ct. at 764-65. Although we have stated that “|j]udges need not rehearse on the record all of the considerations that 18 U.S.C. § 3553(a) lists,” United States v. George, 403 F.3d 470, 472-73 (7th Cir. 2005), the district court nonetheless is obliged to weigh them. See United States v. Dean, 414 F.3d 725, 728 (7th Cir.2005) (“[N]ow that [the Guidelines] are advisory, while section 3553(a) remains unchanged, judges will have to consider the factors that the section tells them to consider.”); id. at 729 (“Section 3553(a), unlike the guidelines themselves after Booker, is mandatory.”). The transcript of Smith’s re-sentencing does not confirm that the district court considered the section 3553(a) factors in its decision to re-impose the original sentence; there is, in fact, no mention of section 3553(a) (or the types of factors that the statute identifies) at all. *523Cf. United States v. Mykytiuk, 415 F.3d 606, 608 (7th Cir.2005) (“On the limited Paladino remand, the court considered the relevant factors in § 3553(a) and found that they did not necessitate a shortening of Mykytiuk’s sentence.”). Because the court elected to reimpose a sentence within the Guidelines range, we may infer that the court at least considered “ ‘all the factors for a fair sentence set forth in the Guidelines.’ ” See Dean, 414 F.3d at 730 (quoting United States v. Mares, 402 F.3d 511, 519 (5th Cir.2005), cert. denied, — U.S. -, 126 S.Ct. 43, — L.Ed.2d-(2005)). But the Guidelines themselves do not encompass all of the sentencing factors set forth in section 3553(a); if they did, there would be no need for a court to independently assess those factors. See id. at 728 (“ ‘Booker suggests that the sentencing factors articulated in § 3553(a), which the mandatory application of the Guidelines made dormant, have a new vitality in channeling the exercise of sentencing discretion.’ ”) (quoting United States v. Trujillo-Terrazas, 405 F.3d 814, 819 (10th Cir.2005)). And although we repeatedly have made clear that the sentencing judge is under no obligation to discuss the section 3553(a) factors at any length, e.g., United States v. Alburay, 415 F.3d 782, 787 (7th Cir.2005); Dean, 414 F.3d at 728-30; George, 403 F.3d at 472-73, without some acknowledgment that the court has in fact considered these factors, it may be difficult for us on appeal to determine whether the court appropriately exercised its discretion in selecting a sentence. Perhaps there are indicia elsewhere in the record that the court considered the section 3553(a) factors. It may also be that the omission to explicitly acknowledge consideration of these factors was harmless in Smith’s case. However, counsel nonetheless is obliged to consider whether Smith might have a non-frivolous argument to make with respect to this apparent omission.
There is a second, related question that counsel has not considered in his Anders brief. Following Booker, sentences are subject to review for reasonableness. 125 S.Ct. at 765. Thus, as we explained in Paladino, when a district court concludes after Booker that a sentence within the Guidelines range remains appropriate notwithstanding the now-advisory nature of the Guidelines, the task falls to us as an appellate body to consider whether that sentence is reasonable. 401 F.3d at 484. “The proviso is important; the mere reimposition of the original sentence does not insulate it from appellate review under the new standard.” Id. This court recently concluded in Mykytiuk that a sentence within the Guidelines range, properly calculated, is presumptively reasonable. 415 F.3d at 608. A defendant may rebut that presumption, however, by demonstrating that a lesser sentence is called for by the sentencing factors identified in section 3553(a). Id.
Although our opinion in Mykytiuk suggests that it will be the rare Guidelines sentence that we would find unreasonable, see id., the possibility is one that a defendant’s appellate counsel must consider. The Anders brief that Smith’s counsel has filed does not reflect a consideration of whether the sentence re-imposed on Smith is arguably unreasonable in light of the factors set out in § 3553(a). We express no opinion on that possibility, beyond saying that it is one that must be considered.
Finding the Anders brief to be deficient in these respects, we direct Smith’s counsel to evaluate the apparent omission to consider the section 3553(a) factors in re-sentencing Smith and the related question of whether Smith’s sentence is unreasonable in light of those factors. If counsel concludes that Smith has a non-frivolous *524argument to make as to either of these questions, then he may file a brief on the merits of that question no later than October 28, 2005. If he concludes that there is no reasonable argument to make on either question, he should file a supplemental Anders brief giving his reasons for that conclusion no later than October 28, 2005.
SO ORDERED.
. Although our prior opinion did not so note, Smith had challenged the obstruction enhancement in the district court, but he had not made a Booker-type argument doing so.