
602 F.3d 346 (2010)
UNITED STATES of America, Plaintiff-Appellee,
v.
David RODRIGUEZ, Defendant-Appellant.
No. 09-20181.
United States Court of Appeals, Fifth Circuit.
March 25, 2010.
*348 Renata Ann Gowie (argued), and James Lee Turner, Asst. U.S. Attys., Houston, TX, for U.S.
Thomas B. Dupont, II (Court-Appointed), Heather Elizabeth Morrow (argued), Houston, TX, for Defendant-Appellant.
Before KING, BARKSDALE and ELROD, Circuit Judges.
RHESA HAWKINS BARKSDALE, Circuit Judge:
David Rodriguez challenges a greater sentence imposed on remand by a different *349 judge from the one who imposed his first sentence. Previously, based on the Government's breach of his plea agreement, Rodriguez successfully appealed his first sentence. In remanding for resentencing, our court ordered it to be conducted by a different judge because of that breach. United States v. Rodriguez, 306 Fed.Appx. 135 (5th Cir.2009) (unpublished).
Primarily, Rodriguez claims his new sentence was vindictive. For this point, the principal issue is whether United States v. Floyd, 519 F.2d 1031 (5th Cir. 1975), has been overruled by Texas v. McCullough, 475 U.S. 134, 106 S.Ct. 976, 89 L.Ed.2d 104 (1986). In the alternative, he claims the advisory guidelines sentencing range used in imposing his sentence was not supported by the requisite preponderance of the evidence. Although plain-error review applies to each issue, there was no error. AFFIRMED.

I.
Rodriguez, a former Houston police officer, operated a private security company in Houston, Texas, where he employed several illegal aliens as armed security guards. Rodriguez directed them to apply for commissions to carry firearms, which required submission of false information. He also purchased firearms and transferred them to those employees.
In June 2006, Rodriguez was indicted for conspiracy, making false statements in the acquisition of firearms, selling firearms to prohibited persons, and selling firearms without a license. See 18 U.S.C. §§ 371, 922, 924. He pleaded guilty to conspiracy, in exchange for the Government's promise to dismiss the other counts and not to seek any offense-level increases at sentencing.
The presentence investigation report (PSR) recommended: a base offense level of 18 because the offense involved at least 39 firearms; a four-level aggravating-role increase for Rodriguez' being a leader or organizer; and, a two-level increase for obstruction of justice. Rodriguez' advisory guidelines sentencing range would have been 51 to 63 months, but the statutory maximum was 60 months, see 18 U.S.C. § 371; therefore, the range was 51 to 60 months.
Rodriguez filed sealed objections to the PSR's recommended offense-level increases. At sentencing, the Government's responses to those objections defended the PSR's recommended sentencing range. This arguably breached the Government's plea-agreement promise not to seek any offense-level increases.
After considering the parties' contentions, the district judge rejected some parts of the PSR and ruled: the offense involved 23, rather than the recommended 39, firearms, reducing the recommended base offense level by two; and a three-level aggravating-role enhancement, instead of the recommended four levels, along with the recommended two-level obstruction-of-justice enhancement, should be imposed. This resulted in an advisory guidelines sentencing range of 37 to 46 months. Rodriguez was sentenced to, inter alia, 37 months' imprisonment.
Rodriguez appealed his conviction and sentence. Among other things, he claimed the Government had breached its plea agreement by urging enhancements at sentencing; the Government conceded it had "arguably" done so. Rodriguez, 306 Fed.Appx. at 138. Our court affirmed the conviction; but, in the light of the Government's concession, it vacated Rodriguez' sentence and remanded for resentencing. Id. at 138-39.
In doing so, our court ruled that, because of the plea-agreement breach, a different judge would preside at resentencing:

*350 The government . . . conced[es] . . . that Rodriguez is entitled to be resentenced before a different district judge. See Santobello v. New York, 404 U.S. 257, 262-63, 92 S.Ct. 495, 30 L.Ed.2d 427 (1971) (providing for remedy of resentencing before a different district judge); United States v. Saling, 205 F.3d 764, 768 (5th Cir.2000) (same). In light of this concession, we grant the agreed-upon relief by vacating Rodriguez's sentence and remanding for resentencing before a different district judge. In so doing, we note that this vacatur is caused not by any error on the part of the district judge, but rather by the government's error. Id.

306 Fed.Appx. at 138-39 (footnotes omitted). Our court also stated: "[R]emand to a different judge is not a reflection upon the original judge". Id. at 138 n. 3 (citing Santobello, 404 U.S. at 263, 92 S.Ct. 495).
At resentencing, Rodriguez renewed his prior objections to the PSR; they were denied. Based upon his independent analysis, the second judge ruled, contrary to the original judge's ruling, that Rodriguez was responsible for 27 firearms (instead of 23). The second judge also ruled, as had the first, that Rodriguez should receive a three-level aggravating-role enhancement (again, instead of the PSR-recommended four levels) and a two-level obstruction-of-justice enhancement. The resulting advisory guidelines sentencing range was 46 to 57 months. Rodriguez was sentenced to, inter alia, 46 months' imprisonmentnine months more than his original sentence.

II.
Rodriguez claims: his sentence on remand was vindictive (either presumed or actual vindictiveness); and, in the alternative, the advisory guidelines sentencing range used for imposing his sentence was not supported by the requisite preponderance of the evidence. For those two claims, this appeal presents several instances in which we must decide whether to exercise our discretion to review an issue. In that regard, plain-error review will be applied to the two claims. (In his opening brief, Rodriguez also claimed he was not credited for time served; at oral argument, his counsel conceded that issue is moot.)

A.
The Fifth and Fourteenth Amendments guarantee due process, which obviously includes the right to be tried and sentenced absent prosecutorial or judicial vindictiveness. See, e.g., Thigpen v. Roberts, 468 U.S. 27, 30, 104 S.Ct. 2916, 82 L.Ed.2d 23 (1984) (citing Blackledge v. Perry, 417 U.S. 21, 27, 94 S.Ct. 2098, 40 L.Ed.2d 628 (1974)) (prosecutorial vindictiveness); North Carolina v. Pearce, 395 U.S. 711, 723-24, 89 S.Ct. 2072, 23 L.Ed.2d 656 (1969) (judicial vindictiveness), overruled in part by Alabama v. Smith, 490 U.S. 794, 109 S.Ct. 2201, 104 L.Ed.2d 865 (1989). Of course, because Rodriguez was convicted of a federal crime, only the Fifth Amendment is in play. Rodriguez claims the second judge's sentence violates his right against vindictiveness.

1.
Before reaching the vindictiveness claim, we must determine our standard of review for it. In contending the claim is unreviewable, the Government asserts Rodriguez' counsel either waived or invited this claimed error at resentencing.

a.
Waived errors are unreviewable. E.g., United States v. Arviso-Mata, 442 F.3d 382, 384 (5th Cir.2006) (citing United States v. Musquiz, 45 F.3d 927, 931-32 (5th Cir.1995)). Review of invited errors *351 is almost similarly precluded; such errors are reviewed only for "manifest injustice". United States v. Green, 272 F.3d 748, 754 (5th Cir.2001) (quoting United States v. Pankhurst, 118 F.3d 345, 359 (5th Cir. 1997)). Forfeited errors are reviewed under the least strict standard for these three types of error: plain error, as discussed infra. E.g., Arviso-Mata, 442 F.3d at 384 (citing United States v. Gracia-Cantu, 302 F.3d 308, 310 (5th Cir.2002)).
"Forfeiture is the failure to make the timely assertion of a right; waiver is the intentional relinquishment of a known right." Id. (citing United States v. Reveles, 190 F.3d 678, 683 (5th Cir.1999)). In other words, for waiver, Rodriguez' "counsel [must have known] of the . . . issue and. . . consciously chose[n] to forego it". Id. For the invited-error doctrine to apply, defendant (or his counsel) must have induced the error. Green, 272 F.3d at 754.
At resentencing, after sentence was imposed, Rodriguez stated he was confused about that greater sentence. In doing so, he questioned how, in the light of the Government's plea-agreement breach at the first sentencing, he could now receive a greater sentence. In responding, the court explained to Rodriguez the process it had followed; and, after stating it was within the scope of our court's remand mandate as the district court understood it, the court asked Rodriguez' counsel if he had "any argument on the mandate". Counsel replied:
Judge, he was ordered a re-sentencing. And from the looks of it, you have done, you have went through that file extensively. We reurged [prior counsel's] objections, which were extensive; and you have just summed up exactly what you just did.
The Government maintains counsel's reply constitutes waiver or invited error. But, that reply, made after imposition of sentence, does not show counsel knew of the potential vindictiveness issue and chose intentionally to relinquish it (waiver). And, certainly, sentence having already been imposed, the reply did not induce the claimed error (invited error). Accordingly, the claimed error is reviewable.

b.
Nevertheless, because Rodriguez failed to object in district court on the basis of vindictiveness (forfeited error), review is only for plain error. E.g., United States v. Scott, 48 F.3d 1389, 1398 (5th Cir.1995) (citing United States v. Vontsteen, 950 F.2d 1086, 1089 (5th Cir.1992) (en banc)). (The Government states, and in his reply brief Rodriguez acknowledges, that such forfeited error results in plain-error review. Of course, we, not the parties, determine our standard of review. E.g., Vontsteen, 950 F.2d at 1091 ("But no party has the power to control our standard of review. A reviewing court may reject both parties' approach to the standard." (emphasis in original)).)
To establish reversible plain error, Rodriguez must show: an error was committed; it was clear or obvious; and, it affected his substantial rights. E.g., United States v. Baker, 538 F.3d 324, 332 (5th Cir.2008) (citing United States v. Thompson, 454 F.3d 459, 464 (5th Cir.2006), cert. denied, ___ U.S. ___, 129 S.Ct. 962, 173 L.Ed.2d 153 (2009)). Even if reversible plain error is established, we retain discretion whether to correct it and, generally, will do so only if it seriously affects the fairness, integrity, or public reputation of judicial proceedings. Id.

2.
In support of his vindictiveness claim, Rodriguez contends: pursuant to North *352 Carolina v. Pearce, 395 U.S. 711, 89 S.Ct. 2072, 23 L.Ed.2d 656 (1969), a presumption of vindictiveness applies to his sentence; or, alternatively, there was actual vindictiveness. For the reasons that follow, there was no error. Accordingly, that ends our plain-error review.

a.
Pearce held a presumption of vindictiveness arises when, after a new trial, a judge sentences a defendant to a harsher sentence. Id. at 723-24, 89 S.Ct. 2072; see also United States v. Resendez-Mendez, 251 F.3d 514, 517 n. 6 (5th Cir.2001) (applying Pearce rule to resentencing context, where new sentence imposed by judge who imposed original sentence (citing United States v. Campbell, 106 F.3d 64, 67 (5th Cir.1997))). At issue here is whether that presumption applies when a different judge of the same court imposes the new sentence.
In his opening and reply briefs here, Rodriguez asserted this issue is controlled by United States v. Floyd, 519 F.2d 1031 (5th Cir.1975), which held the presumption applies in this situation. The Government countered that, in the light of Texas v. McCullough, 475 U.S. 134, 106 S.Ct. 976, 89 L.Ed.2d 104 (1986), Floyd is no longer good law. At oral argument, Rodriguez' counsel conceded McCullough controls, but urged our criticizing McCullough as having strayed from the principles announced in Pearce.
Of course, counsel's request that we criticize McCullough is rejected; similarly, we do not rely on counsel's concession that Floyd has been overruled. Because our court has never rendered that holding, we must instead undertake an independent analysis to determine Floyd's validity vel non.
As is well known, "a panel of this court can only overrule a prior panel decision if [, inter alia,] `such overruling is unequivocally directed by controlling Supreme Court precedent'". Martin v. Medtronic, Inc., 254 F.3d 573, 577 (5th Cir.2001) (quoting United States v. Zuniga-Salinas, 945 F.2d 1302, 1306 (5th Cir. 1991)). Therefore, at issue is whether McCullough "explicitly or implicitly overrul[ed]" Floyd. United States v. Short, 181 F.3d 620, 624 (5th Cir.1999).
For that analysis, a review of the Supreme Court's extensive judicial-vindictiveness jurisprudence is required. The seminal case is North Carolina v. Pearce, rendered in 1969. There, the Court considered two consolidated cases. See 395 U.S. at 713, 89 S.Ct. 2072.
In the first, defendant was convicted and sentenced by the trial judge. Id. He successfully challenged his conviction in a state post-conviction proceeding and was retried, convicted, and given a greater sentence by the trial judge. Id. (Of great importance to our analysis, and although it was not mentioned in Pearce, it was noted 17 years later in Texas v. McCullough, 475 U.S. 134, 140 n. 3, 106 S.Ct. 976, 89 L.Ed.2d 104, is that this first case in Pearce "apparently involved different judges presiding over the two trials". As discussed infra, there being two judges in this first case in Pearce was a basis for this court's decision in Floyd in 1975, which predated McCullough (1986). Floyd also involved two judges, and the below-described presumption of vindictiveness adopted in Pearce was imposed in Floyd.)
In the second case considered in Pearce, defendant pleaded guilty and was sentenced. Id. at 714, 89 S.Ct. 2072. His plea and sentence were set aside in a state post-conviction proceeding; he was tried, convicted, and given a greater sentence (the Pearce Court did not specify whether the judge who accepted the guilty plea was *353 the judge who subsequently tried and resentenced this defendant). Id.
Both defendants pursued federal habeas relief, challenging their greater sentences. Id. at 713-14, 89 S.Ct. 2072. The Supreme Court rejected claims that either "the double jeopardy provision [or] the Equal Protection Clause imposes an absolute bar to a more severe sentence upon reconviction". Id. at 723, 89 S.Ct. 2072. On the other hand, it was obvious to the Court that due process of law forbids imposition of "a heavier sentence upon every reconvicted defendant for the explicit purpose of punishing the defendant for his having succeeded in getting his original conviction set aside". Id. at 723-24, 89 S.Ct. 2072.
The Court went further, however, and held: not only does actual vindictiveness violate due process, but also, the "apprehension of such a retaliatory motivation on the part of the sentencing judge" does so as well, because "the fear of such vindictiveness may unconstitutionally deter" defendants from exercising any rights to appeal and collateral attack. Id. at 725, 89 S.Ct. 2072. Therefore, the Court adopted a prophylactic rule, holding a presumption of vindictiveness applies when defendant receives a greater sentence after a new trial, unless: the sentencing court affirmatively states objective reasons for that sentence; and, those reasons are based upon "information concerning identifiable conduct on the part of the defendant occurring after the time of the original sentencing proceeding". Id. at 726, 89 S.Ct. 2072.
A few years after Pearce was rendered in 1969, the Supreme Court narrowed the application of this broad presumption of vindictiveness. Colten v. Kentucky, 407 U.S. 104, 92 S.Ct. 1953, 32 L.Ed.2d 584 (1972), considered whether the presumption should apply in the context of Kentucky's two-tier criminal court system: inferior courts of limited jurisdiction, which adjudicated misdemeanors; and those of general criminal jurisdiction. Id. at 112, 92 S.Ct. 1953. Kentucky law provided that, if defendant elected to do so, he could obtain a trial de novo in the latter after conviction in the former. Id. Defendant in Colten was sentenced to a fine in the inferior court; he elected to have a trial de novo in the general-jurisdiction court and received a greater fine. Id. at 108, 92 S.Ct. 1953. He claimed, inter alia, his sentence should be presumed vindictive. Id.
The Court disagreed. It "not[ed] first the obvious": the general-jurisdiction court was a different court than the inferior court"not the court with whose work [defendant] was sufficiently dissatisfied to seek a different result on appeal; and . . . not the court that is asked to do over what it thought it had already done correctly". Id. at 116-17, 92 S.Ct. 1953. Moreover, the general-jurisdiction court was not "even asked to find error in another court's work". Id. at 117, 92 S.Ct. 1953. The Court also noted:
It may often be that the superior court will impose a punishment more severe than that received from the inferior court. But it no more follows that such a sentence is a vindictive penalty for seeking a superior court trial than that the inferior court imposed a lenient penalty. The trial de novo represents a completely fresh determination of guilt or innocence.
Id.
Under those circumstances, "[t]he possibility of vindictiveness, found to exist in Pearce, [was] not inherent in the Kentucky two-tier system". Id. at 116, 92 S.Ct. 1953 (emphasis added). Therefore, the Pearce prophylactic rule was not required. Id. at 118-19, 92 S.Ct. 1953.
*354 Not long after, in Chaffin v. Stynchcombe, 412 U.S. 17, 93 S.Ct. 1977, 36 L.Ed.2d 714 (1973), the presumption's reach was restricted further. Chaffin addressed a circuit split: whether the vindictiveness presumption applied when, following successful appeal or collateral attack, a jury, rather than a judge, imposed a greater sentence after retrial. See id. at 21, 93 S.Ct. 1977. In Chaffin, defendant was convicted and sentenced by a jury; his conviction was affirmed. Id. at 18-19, 93 S.Ct. 1977. He received federal habeas relief (retrial). Id. at 19, 93 S.Ct. 1977. On retrial before a new judge and jury, defendant received a greater sentence from the jury. Id. Defendant appealed unsuccessfully and then again sought federal habeas relief, claiming his sentence should be presumed vindictive. Id. at 20, 93 S.Ct. 1977.
The Court reasoned that the presumption exists to protect against the possibility of vindictiveness; therefore, the circumstances of resentencing must be examined to determine whether they carry such an inherent threat. Id. at 26-27, 93 S.Ct. 1977. If not, there was no reason to apply the presumption. Id.
The Court held sentencing by a jury does not carry such a threat of vindictiveness. It reasoned a jury would not (should not) know of the prior sentence; would have no institutional interest in discouraging meritless appeals; and was not the "same judicial authority whose handling of the prior trial was sufficiently unacceptable to have required a reversal of the conviction. Thus, the jury, unlike the judge who has been reversed, will have no personal stake in the prior conviction and no motivation to engage in self-vindication". Id. at 27, 93 S.Ct. 1977.
Over the next 11 years, the Court considered prosecutorial vindictiveness several times. See Blackledge v. Perry, 417 U.S. 21, 94 S.Ct. 2098, 40 L.Ed.2d 628 (1974); Bordenkircher v. Hayes, 434 U.S. 357, 98 S.Ct. 663, 54 L.Ed.2d 604 (1978); United States v. Goodwin, 457 U.S. 368, 102 S.Ct. 2485, 73 L.Ed.2d 74 (1982); Thigpen v. Roberts, 468 U.S. 27, 104 S.Ct. 2916, 82 L.Ed.2d 23 (1984). In Bordenkircher, 434 U.S. at 363, 98 S.Ct. 663, the Court summarized its vindictiveness precedents through its first prosecutorial-vindictiveness decision in Blackledge v. Perry:
The Court has emphasized that the due process violation in cases such as Pearce and Perry lay not in the possibility that a defendant might be deterred from the exercise of a legal right, see Colten v. Kentucky, 407 U.S. 104, 92 S.Ct. 1953, 32 L.Ed.2d 584; Chaffin v. Stynchcombe, 412 U.S. 17, 93 S.Ct. 1977, 36 L.Ed.2d 714, but rather in the danger that the State might be retaliating against the accused for lawfully attacking his conviction. See Blackledge v. Perry, 417 U.S. at 26-28, 94 S.Ct. 2098.
Goodwin explained further the reason for the presumption:
Both Pearce and Blackledge involved the defendant's exercise of a procedural right that caused a complete retrial after he had been once tried and convicted. The decisions in these cases reflect a recognition by the Court of the institutional bias inherent in the judicial system against the retrial of issues that have already been decided. The doctrines of stare decisis, res judicata, the law of the case, and double jeopardy are all based, at least in part, on that deep-seated bias. While none of these doctrines barred the retrials in Pearce and Blackledge, the same institutional pressure that supports them might also subconsciously motivate a vindictive prosecutorial or judicial response to a defendant's exercise of his right to obtain a retrial of a decided question.
*355 457 U.S. at 376-77, 102 S.Ct. 2485 (emphasis added).
In these prosecutorial-vindictiveness decisions, the Court articulated the reasonable-likelihood-of-vindictiveness standard in play here. For example, 16 months before our court's 1975 decision in Floyd, the Court stated in Blackledge: "The lesson that emerges from Pearce, Colten, and Chaffin is that the Due Process Clause is not offended by all possibilities of increased punishment upon retrial after appeal, but only by those that pose a realistic likelihood of `vindictiveness'". 417 U.S. at 27, 94 S.Ct. 2098 (emphasis added). Similarly, in Goodwin, the Court stated: "Given the severity of such a presumption [of vindictiveness,] . . . the Court has [imposed it] only in cases in which a reasonable likelihood of vindictiveness exists". 457 U.S. at 373, 102 S.Ct. 2485 (emphasis added). And, in Goodwin, the Court reaffirmed its earlier statement of the law from Blackledge: "As Blackledge makes clear, `the Due Process Clause is not offended by all possibilities of increased punishment. . . but only by those that pose a realistic likelihood of vindictiveness'". 457 U.S. at 384, 102 S.Ct. 2485 (quoting Blackledge, 417 U.S. at 27, 94 S.Ct. 2098) (omission in Goodwin) (emphasis added).
Following the 1973 decision in Chaffin, judicial vindictiveness was not addressed again until Texas v. McCullough, 475 U.S. 134, 106 S.Ct. 976, 89 L.Ed.2d 104 (1986). As noted, we must decide whether McCullough overruled our court's 1975 decision in Floyd, discussed infra.
McCullough addressed whether the Pearce presumption applied where: a jury imposed the initial sentence; because of prosecutorial misconduct, however, the trial judge granted a new trial; upon retrial before the same judge, defendant asked that the judge, rather than the jury, impose sentence; and that judge imposed a greater sentence than had the jury for the first trial. 475 U.S. at 136, 106 S.Ct. 976. The judge, on defendant's motion, made findings of fact on why her sentence was greater. Id.
Noting that "vindictiveness of a sentencing judge is the evil the Court [in Pearce] sought to prevent rather than simply enlarged sentences after a new trial", id. at 138, 106 S.Ct. 976, McCullough held the presumption inapplicable for the following three reasons. First, the trial judge had ordered the new trial; therefore, she "had `no motivation to engage in self-vindication'", because she had not been reversed. Id. at 139, 106 S.Ct. 976 (quoting Chaffin, 412 U.S. at 27, 93 S.Ct. 1977). Second, it was unlikely that the greater sentence arose from a desire to dissuade defendants from requesting new trials. Id. And, third, "different sentencers assessed the varying sentences". Id. at 140, 106 S.Ct. 976.
For this third reason, the Court looked to the two-tier system in Colten, for which the presumption of vindictiveness had been held not applicable. As further support, it noted: "Here [in McCullough], the second sentencer provide[d] an on-the-record, wholly logical, nonvindictive reason for the sentence. We read Pearce to require no more[,] particularly since trial judges must be accorded broad discretion in sentencing". Id. (citing Wasman v. United States, 468 U.S. 559, 563-64, 104 S.Ct. 3217, 82 L.Ed.2d 424 (1984)).
Moreover, regarding this third reason (different sentencers), the Court clarified a point that "ha[d] led some courts to conclude by implication that the presumption of vindictiveness applies even where different sentencing judges are involved". Id. at 140 n. 3, 106 S.Ct. 976. The Court stated that such conclusion (which was also reached earlier in Floyd, discussed infra) had resulted from the fact that, as noted *356 supra, the first case in Pearce "apparently involved different judges presiding over the two trials". Id. The Court noted the Pearce opinion had not addressed that point; accordingly, McCullough "decline[d] to read Pearce as governing this issue". Id.
The Court last addressed judicial vindictiveness in Alabama v. Smith, 490 U.S. 794, 109 S.Ct. 2201, 104 L.Ed.2d 865 (1989). There, after pleading guilty, defendant was sentenced. Id. at 795-96, 109 S.Ct. 2201. He appealed and was granted a trial. Id. at 796, 109 S.Ct. 2201. That trial was before the judge who had accepted the earlier guilty plea. Id.
At trial, the victim gave graphic testimony. Id. Defendant was convicted, and the judge imposed a greater sentence. Id. The judge explained that his doing so was based on evidence at trial of which he had been unaware when imposing the first sentence (pursuant to the guilty plea). Id. at 796-97, 109 S.Ct. 2201.
Defendant appealed, contending his sentence was due the Pearce vindictiveness presumption. Id. at 797, 109 S.Ct. 2201. The state supreme court agreed. Id.
The Supreme Court granted review "[b]ecause of the conflicting results reached by the lower courts on the question whether the Pearce presumption of vindictiveness applies when a sentence imposed after trial is greater than that previously imposed after a guilty plea". Id. at 798, 109 S.Ct. 2201 (emphasis added). The Court denied application of the presumption and, in doing so, partially overturned Pearce. Id. at 801-02, 109 S.Ct. 2201. (As noted supra, Pearce consisted of two consolidated cases. The latter was factually similar to that before the Court; therefore, that portion of Pearce was overruled.)
The Court held: where a guilty plea is successfully appealed and followed by a trial, a higher sentence should not be presumed vindictive, because the increase is much more likely to be the result of increased information presented to the judge, rather than based on vindictiveness. Id. Utilizing the reasonable-likelihood standard first announced in Blackledge, 417 U.S. at 27, 94 S.Ct. 2098, the Court emphasized that the Pearce presumption applies only where

there is a reasonable likelihood that the increase in sentence is the product of actual vindictiveness on the part of the sentencing authority. Where there is no such reasonable likelihood, the burden remains upon the defendant to prove actual vindictiveness.

Id. at 799-800, 109 S.Ct. 2201 (internal citations and quotation marks omitted) (emphasis added).

i.
Against the backdrop of this Supreme Court precedent, we turn to this court's split-panel decision in United States v. Floyd, 519 F.2d 1031 (5th Cir.1975), which pre-dated a great deal of the Court's vindictiveness decisions, including McCullough (1986). Floyd considered whether the Pearce presumption applies when a second judge, after trial, imposes a greater sentence than that imposed by a first judge, after a guilty plea. Id. at 1032. That issue was joined by two great, former judges (later, chief judges) on our court: Judge Charles Clark, writing for the majority; and Judge James Plemon Coleman, in dissent.
Defendant pleaded guilty and was sentenced by the judge who accepted the plea. Because that judge had not advised defendant about an aspect of the sentence prior to accepting the plea, however, he granted defendant's § 2255 motion and withdrew the guilty plea; and defendant received a jury trial before a different judge. Defendant *357 was found guilty and received a greater sentence than that imposed on his guilty plea. Id. at 1032.
At sentencing, the second judge stated that, in addition to reviewing the presentence investigation report, he had talked with counsel and the probation officer. But, the judge stated he had admonished them that he "did not want to know anything about the circumstances in connection with [the withdrawn] plea before another judge in this court". Id. at 1033 (emphasis added). At sentencing, the second judge also stated he was basing the sentence, as he had "done in similar cases in the past", solely on the offense and evidence. Id.
In reviewing Supreme Court precedent, Floyd noted correctly that, "[a]bsent vindictiveness or the possibility of vindictiveness, more severe sentences imposed following reconviction are constitutionally valid". Id. (citing Chaffin, 412 U.S. at 29, 93 S.Ct. 1977; Colten, 407 U.S. at 116, 92 S.Ct. 1953; Pearce, 395 U.S. at 723, 89 S.Ct. 2072) (emphasis added). Floyd then noted that, "Blackledge [in 1974] . . . most recently reaffirmed this principle"; and it next quoted the above-described, resulting "realistic likelihood of `vindictiveness'" standard developed in Pearce, Colten, and Chaffin. Id. (quoting Blackledge, 417 U.S. at 27, 94 S.Ct. 2098).
If such "realistic likelihood" exists, Floyd acknowledged the above-discussed Pearce standard regarding the sentencing-judge-stated objective reasons that would permit the greater sentence. Id. Reflecting the extremely careful analysis employed in Floyd, the majority opinion then addressed the above-discussed factor not addressed in Pearce: "that the second sentencing judge . . . was a different judge from the first". Id. at 1034. (As discussed supra, this two-judges-in-Pearce point was acknowledged ten years later in McCullough.)
Floyd contrasted any prior-sentence knowledge of the second judge in Floyd with that of the second judge in Pearce, noting that, in Floyd, "the second . . . affirmatively avoided knowledge of the original sentence. Such lack of knowledge is clearly probative of an absence of actual vindictiveness". Id. (emphasis added). Of course, there being no actual vindictiveness did not end Floyd's inquiry; it moved to application of the reasonable-likelihood-of-vindictiveness standard. The majority opinion's painstaking, insightful analysis is reflected in how it framed the question:
However, the broader question we face is whether, in and of itself, such intentional insulation (together with the judge's independent basis for his more severe sentence) so negates the possibility of vindictiveness as to render unnecessary Pearce's prophylactic showing that subsequent conduct was the basis for the increase.
Id. at 1034.
After careful analysis of the existing precedent, Floyd held the Pearce presumption applied. Id. In doing so, ten years before its being noted by the Supreme Court in McCullough, the Floyd court observed: "The meaning of Pearce for today's case must take into account that the second sentencing judge in Pearce was a different judge from the first sentencing judge"a fact not mentioned in Pearce, but clear from the underlying state court opinion. Id. at 1034 n. 5 (citing State v. Pearce, 268 N.C. 707, 151 S.E.2d 571 (1966)) (emphasis added). As a result, Floyd focused on "the institutional interests involved and procedures to be followed", id. (emphasis added), and concluded that the same threat of vindictiveness present in Pearce was present in Floyd: "The same sort of hazard exists that defendants *358 will be deterred in exercising their right to seek review because of a reasonable apprehension that judges who work together daily and must preside at each other's retrials will have a stake in discouraging such reviews", id. at 1035 (emphasis added). The majority vacated the sentence, because the requisite, stated bases for imposing the greater sentence had not been provided. Id. The matter was "remanded for proceedings consistent with Pearce". Id.
The dissent from applying the Pearce presumption was based on concluding that "resentencing [had been] affirmatively shown to have been utterly bereft of any `realistic likelihood of vindictiveness'". Id. at 1036. In that regard, the dissent was "unwilling to accept as a matter of law the idea expressed in the majority opinion that there can be `a reasonable apprehension that judges who work together daily and must preside at [each] other's retrials will have a stake in discouraging such reviews'". Id. (emphasis added). It also found that apprehension "wholly unsupported by the facts in [the] case". Id.
Since Floyd was announced in 1975, it has been cited by our court only four timesmost recently in 1983. See United States v. Henry, 709 F.2d 298, 315 n. 24 (5th Cir.1983); Gamble v. Estelle, 551 F.2d 654, 655 (5th Cir.1977); Hardwick v. Doolittle, 558 F.2d 292, 299 (5th Cir.1977); Dan J. Sheehan Co. v. Occupational Safety and Health Review Comm'n, 520 F.2d 1036, 1041 (5th Cir.1975). None of these cases relied on Floyd's holding.
Our court is bound not only by the result of an opinion, "but also [by] those portions of the opinion necessary to that result . . . ." Seminole Tribe v. Florida, 517 U.S. 44, 67, 116 S.Ct. 1114, 134 L.Ed.2d 252 (1996) (citations omitted). McCullough expressly rejected part of the basis for Floyd's reasoningthere having been different sentencing judges in Pearce. Moreover, McCullough held having different sentencers was one of the primary reasons that the presumption was unnecessary. Restated, the possible same-court institutional and collegial pressures that were of concern to Floyd were held in McCullough not to require the presumption. Accordingly, we hold, as Rodriguez' counsel conceded at oral argument, that Floyd was overruled by McCullough.
In doing so, we join our seven sister circuits that, as discussed below, do not apply the presumption when different judges preside over the first and second sentencing. See United States v. Anderson, 440 F.3d 1013, 1016 (8th Cir. 2006) (collecting cases); Gonzales v. Wolfe, 290 Fed.Appx. 799, 813 (6th Cir.2008) (unpublished), cert. denied, ___ U.S. ___, 129 S.Ct. 1016, 173 L.Ed.2d 306 (2009). Some of these circuits, however, hold the presumption is inapplicable in this different-sentencers situation only if the second states objective, non-vindictive reasons for imposing the greater sentence (added condition). See Anderson, 440 F.3d at 1016; Macomber v. Hannigan, 15 F.3d 155, 156-57 (10th Cir.1994); Rock v. Zimmerman, 959 F.2d 1237, 1257 (3d Cir.1992), overruled on other grounds by Brecht v. Abrahamson, 507 U.S. 619, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993); see also United States v. Newman, 6 F.3d 623, 630-31 (9th Cir. 1993) (seeming to impose the added condition). But see Gonzales, 290 Fed.Appx. at 813; United States v. Cheek, 3 F.3d 1057, 1064 (7th Cir.1993); United States v. Perez, 904 F.2d 142, 146 (2d Cir.1990). The Third and Tenth Circuits cite McCullough in support of imposing this added condition. See Macomber, 15 F.3d at 157; Rock, 959 F.2d at 1257-58. McCullough stated, as quoted supra: "Here [in McCullough], the second sentencer provide[d] an on-the-record, wholly logical, nonvindictive *359 reason for the sentence. We read Pearce to require no more[,] particularly since trial judges must be accorded broad discretion in sentencing". 475 U.S. at 140, 106 S.Ct. 976 (citing Wasman, 468 U.S. at 563-64, 104 S.Ct. 3217).
It may be that this added-condition difference of opinion in the seven circuits arises, as can happen, from the Supreme Court's repeated summarization and quotation from its vindictiveness decisions. And, none of these circuits addresses this added-condition difference of opinion.
Arguably, the evolved reasonable-likelihood-of-vindictiveness standard negates this added condition. See Alabama v. Smith, 490 U.S. at 798-800, 109 S.Ct. 2201. Neither party, however, has raised this added-condition issue. See Vontsteen, 950 F.2d at 1086 (holding it is within our discretion to decline to consider issues not raised on appeal). In any event, as discussed infra, because the second judge stated more than sufficient reasons for the greater sentence, we do not need to reach the issue. In other words, even assuming the added condition is required, the record amply demonstrates that the second judge more than fulfilled that condition. Along that line, regardless of whether the added condition is required, the second judge should obviously state such reasons. They assist not only in our reviewing a vindictiveness challenge but also in reviewing other challenges to the sentence as well.

ii.
Therefore, we are not bound by Floyd to presume vindictiveness per se. Nonetheless, as noted above and as addressed, for example, in Alabama v. Smith, 490 U.S. at 799-800, 109 S.Ct. 2201, we must still consider whether there was a reasonable likelihood that the increase in Rodriguez' sentence was due to actual vindictiveness.
As noted, in remanding this matter, the prior panel required "resentencing before a different district judge". Rodriguez, 306 Fed.Appx. at 138-39. In doing so, it stated: "The remedy of resentencing by a different district judge is not based on any misstep by the original sentencing judge; instead, it reflects a need to remove the taint of the original error by the government" its breach of the plea agreement. Id. at 139 n. 3 (emphasis added). As support for the different-judge requirement, our court cited Santobello v. New York, 404 U.S. 257, 263, 92 S.Ct. 495, 30 L.Ed.2d 427 (1971) (requiring that defendant who seeks to have his sentence vacated for breach of a plea agreement be resentenced by a different judge, though the original judge committed no error), and United States v. Saling, 205 F.3d 764, 768 (5th Cir.2000) (holding such a defendant may choose between "specific performance [of the plea agreement], which requires that the sentence be vacated and that the defendant be resentenced by a different judge; or . . . withdrawal of the guilty plea, and the opportunity to plead anew, which requires vacation of both the conviction and the sentence" (citing United States v. Palomo, 998 F.2d 253, 256 (5th Cir.1993))). Needless to say, this different-judge requirement, because of breach of a plea agreement, also decreased greatly the possibility of vindictiveness.
In addition, there is absolutely no evidence that the second judge was reasonably likely to impose a vindictive sentence. Rodriguez has not shown, for example, some relationship between the first and second judges, or a desire to enforce decisions by their court, that would induce the second judge to act in that fashion. Nor, as another example, has Rodriguez shown that the second judge has some sort of bias against him, including because Rodriguez showed breach of his plea agreement by the Government. Nor, as a final example, *360 has he shown the second judge seeks to discourage appeals.
In short, based on this record, there is no reason to think any likelihood of vindictiveness is inherent in this situationquite the contrary. The second judge conducted not only an independent review of the record and PSR, but he also took the further step of having "the probation officer. . . provide the [judge] with the underlying ATF reports regarding the weapons purchases" and independently examining that evidence. There being no reasonable likelihood of vindictiveness is reflected in the judge's response, after imposing sentence, when Rodriguez, as discussed supra, expressed his confusion to the judge regarding receiving that greater sentence, even though, as Rodriguez noted, the Government had breached the plea agreement at the first sentencing. The judge stated:
I have ruled on the objections your lawyer told me were extant. I based my own independent recollection of the evidence. I have read the entire file. I am not basing my ruling on any statement made to [the first judge]. I made my own independent assessment of the evaluations. I reviewed the ATF file. This is clearly within the scope of the 5th Circuit's mandate as I perceive the mandate to read.
In sum, because there is no reasonable likelihood of vindictiveness, the presumption of vindictiveness does not apply. Again, because there was no error, our plain-error review ends at this point regarding presumed vindictiveness.

b.
Of course, as discussed supra, where, as here, that presumption does not apply, defendant may still show a due-process violation by showing actual vindictiveness. E.g., McCullough, 475 U.S. at 138, 106 S.Ct. 976 (citing Wasman, 468 U.S. at 569, 104 S.Ct. 3217); see Pearce, 395 U.S. at 725, 89 S.Ct. 2072. As noted, Rodriguez also claims such vindictiveness; but, he did not raise this contention until his reply brief here. As discussed infra, that point, however, was addressed in the Government's brief.
For obvious reasons, our court generally will not consider an issue raised for the first time in a reply brief. E.g., United States v. Brown, 305 F.3d 304, 307 n. 4 (5th Cir.2002) (citing United States v. Prince, 868 F.2d 1379, 1386 (5th Cir.1989)). Adding insult to procedural injury here is that the actual-vindictiveness issue, not raised until the reply brief, was not even raised in district court. As discussed supra, no form of vindictivenesspresumed or actualwas claimed there.
Nevertheless, also for obvious reasons, "we ordinarily have the discretion to decide legal issues that are not timely raised". Vontsteen, 950 F.2d at 1091 (citing United States v. Giovannetti, 928 F.2d 225 (7th Cir.1991) (plain-error review)). Accordingly, that includes "consider[ing] issues not raised in an initial brief" on appeal. Estate of Lisle v. Comm'r of Internal Revenue, 341 F.3d 364, 384 (5th Cir.2003), mandate recalled and modified on other grounds by 431 F.3d 439 (5th Cir.2005); cf. United States v. Whitfield, 590 F.3d 325, 346-47 (5th Cir.2009) ("As a general rule, a party waives any argument that it fails to brief on appeal. However, this court has recognized an exception to this rule whereby we will consider a point of error not raised on appeal when it is necessary to prevent a miscarriage of justice." (citation and quotation marks omitted)); Martinez v. Mukasey, 519 F.3d 532, 545-46 (5th Cir.2008) ("For obvious reasons, we generally do not consider contentions raised for the first time at oral argument. . . . In our discretion, because this *361 is a question of statutory construction, we will consider it."). Present here is one of those exceptions to not reviewing an issue first raised in a reply brief.
This exception arises out of the Government's, as noted, addressing actual vindictiveness in its brief. The general rule against not considering an issue not raised until the reply brief is
view[ed] ... differently when a new issue is raised in the appellee's brief and the appellant responds in his reply brief. Cousin v. Trans Union Corp., 246 F.3d 359, n. 22 (5th Cir.2001) and Vallecillo v. United States HUD, 155 Fed.Appx. 764, 766 n. 1 (5th Cir.2005). In that situation, the court avoids the more unfair scenario that occurs when "an appellant raises a completely new issue in its reply brief, disadvantaging the appellee, and for which the procedural bar concerning initial briefs was properly developed and utilized." Cousin, 246 F.3d at 373. This situation is not present in this case because the government raised the issue presented by [appellant,] eliminating any surprise.
United States v. Ramirez, 557 F.3d 200, 203 (5th Cir.2009).
Although Rodriguez' opening brief had not claimed actual vindictiveness, the Government asserted in its brief that "Rodriguez has not shown any actual vindictiveness". Considering this assertion, there is no prejudice to the Government for our exercising our discretion to consider Rodriguez' quite belated actual-vindictiveness claim.
Because this reply-brief claim was not raised in district court, we will assume review is for plain error. Arguably an even more strict standard of review could apply, such as that to prevent a manifest miscarriage of justice. Cf. United States v. Miller, 576 F.3d 528, 529-30 & n. 2 (5th Cir.2009) (applying manifest-miscarriage-of-justice standard where defendant failed in district court to move for judgment of acquittal; relief is granted only if there has been a "manifest miscarriage of justice, which is found if the record is devoid of evidence pointing to guilt". (quoting United States v. Green, 293 F.3d 886, 895 (5th Cir.2002)) (internal quotation marks omitted)). We need not decide that question because the claim fails even under the more lenient review for plain error.
Along that line, it is well established that there can never be plain error if the issue is a factual one, which could have been resolved in district court upon proper objection. E.g., United States v. Lee, ___ Fed.Appx. ___, ___, 2010 WL 742592, at *3 (5th Cir.2010) (quoting United States v. Lopez, 923 F.2d 47, 50 (5th Cir. 1991)). Although an issue of fact, actual vindictiveness vel non is not, however, within that category. It is questionable such an actual-vindictiveness objection could be resolved in district court. Cf. Vontsteen, 950 F.2d at 1090 (presumed vindictiveness). Moreover, it is the reviewing, not the district, court that decides whether the district court's sentence was pursuant to actual vindictiveness.
Our exercising our discretion to review this claim is, in large part, to make absolutely clear that the second judge committed no error. Acting entirely within our mandate, the second judge conducted an independent, objective analysis of the PSR and the ATF reports.
Rodriguez contends the record shows the second judge acted vindictively because: he summarily overruled Rodriguez' objections to the PSR; and, he did not allow the Government to contribute to the sentencing hearing. Neither matter even remotely suggests vindictiveness.
*362 The record reflects that the second judge carefully considered Rodriguez' objections. Moreover, Rodriguez has offered no authority requiring the second judge to state his reasons for denying them. Cf. United States v. Rocha, 916 F.2d 219, 239 (5th Cir.1990) (affirming district court's having "summarily overruled [defendant's] objections to such evidence").
Rodriguez does, apparently, recognize the patent absurdity of his contention that the second judge's stated intention not to engage the Government at resentencing somehow evinces vindictiveness. He admits in his reply brief that his contention creates a Catch-22 for the district court: according to Rodriguez, the second judge is vindictive for not having engaged the Government; but, had the judge done so, he would have caused the Government, once again, to breach its plea agreement. The record shows, as discussed infra, that the second judge was entitled to rely on other bases, negating any need to solicit input from the Government.
Again, there is simply no evidence of actual vindictiveness. Therefore, there was no error. In sum, our plain-error review for vindictivenesspresumed or actualends.

B.
In the alternative, Rodriguez claims the advisory guidelines sentencing range used to impose his sentence was not supported by the requisite preponderance of the evidence. Although, post-Booker, the Guidelines are advisory only, and an ultimate sentence is reviewed for reasonableness under an abuse-of-discretion standard, the district court must still properly calculate the advisory guidelines sentencing range for use in deciding on the sentence to impose. Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007).
In that respect, for properly preserved claims, a sentencing court's application of the guidelines is reviewed de novo; its factual findings, only for clear error. E.g., United States v. Cisneros-Gutierrez, 517 F.3d 751, 764 (5th Cir.2008) (citing United States v. Juarez-Duarte, 513 F.3d 204 (5th Cir.), cert. denied, ___ U.S. ___, 128 S.Ct. 2452, 171 L.Ed.2d 248 (2008)); United States v. Villegas, 404 F.3d 355, 359 (5th Cir.2005). In that regard, those factual findings must be supported by a preponderance of the evidence. E.g., United States v. Duhon, 541 F.3d 391, 395 (5th Cir.2008) (citing United States v. Mares, 402 F.3d 511, 519 (5th Cir.2005)).
Here, however, as Rodriguez acknowledges, review is only for plain error because, at resentencing, he objected on bases different from those presented here. Villegas, 404 F.3d at 358. As discussed supra, to establish reversible plain error, Rodriguez must show a clear or obvious error that affected his substantial rights. E.g., Baker, 538 F.3d at 332 (citing Thompson, 454 F.3d at 464). Again, if reversible plain error is established, we still retain discretion whether to correct such error and, generally, will do so only if it seriously affects the fairness, integrity, or public reputation of judicial proceedings. Id.
Rodriguez contends: the district court's calculations for the base offense level and the aggravating-role and obstruction-of-justice enhancements were not supported by a preponderance of the evidence; and, therefore, each claimed error constitutes reversible plain error for which we should grant relief. Rodriguez asserts that the district court's claimed error for each of these calculations lies in its relying on the PSR.
*363 "[A] district court may adopt the facts contained in a PSR without further inquiry if those facts have an adequate evidentiary basis with sufficient indicia of reliability and the defendant does not present rebuttal evidence or otherwise demonstrate that the information in the PSR is unreliable". United States v. Cabrera, 288 F.3d 163, 173-74 (5th Cir.2002). For the following reasons, the PSR contained sufficient facts to provide an adequate evidentiary basis for calculating the three belatedly challenged sentencing elements: the base offense level and the aggravating-role and obstruction-of-justice enhancements to it.
For the base offense level, the PSR contains numerous details regarding Rodriguez's firearms dealings. (Moreover, in addition to considering the PSR, the second judge considered the ATF reports and, on the record, identified each of the weapons for which he deemed Rodriguez responsible.) For the aggravating-role enhancement, the PSR shows Rodriguez was in charge of the daily operations of this private security company (BCPD) and possessed final decision-making authority. Finally, for the obstruction-of-justice enhancement, the PSR shows that, during the raid, federal agents learned that BCPD guards had received advance warnings from their supervisors that law enforcement agents were arresting the guards and had been told to vacate their job sites if their work documents were not in order.
Rodriguez, however, insists he provided rebuttal evidence that prevented the district court's being entitled to rely on the PSR. "If information is presented to the sentencing judge with which the defendant would take issue, the defendant bears the burden of demonstrating that the information cannot be relied upon because it is materially untrue, inaccurate or unreliable." United States v. Angulo, 927 F.2d 202, 205 (5th Cir.1991). Rodriguez maintains he met this burden by submitting written objections to the PSR. These objections, however, are not evidencethey are merely "unsworn assertions". United States v. Lghodaro, 967 F.2d 1028, 1030 (5th Cir.1992) (citing United States v. Sanders, 942 F.2d 894, 897-98 (5th Cir. 1991)).
Because no testimony or other evidence was submitted to rebut the information in the PSR, the district court was free to adopt the PSR's findings without further inquiry or explanation. United States v. Mir, 919 F.2d 940, 943 (5th Cir.1990) (citing United States v. Mueller, 902 F.2d 336, 346 (5th Cir.1990)). The district court committed no error. Again, our plain-error review draws to a close.

III.
For the foregoing reasons, the judgment is AFFIRMED.
