WILLIAMS, Circuit Judge.
In this successive appeal we consider the propriety of Mark A. White’s sentence on his convictions for participating in a drug conspiracy and money laundering. White contends that our remand order following his initial appeal was limited in scope, solely permitting the district court to recalculate his sentence without the vacated murder cross-reference. Therefore, he reasons, the district court exceeded its authority when it applied an obstruction of justice enhancement to White’s sentencing guideline calculation. White also asserts that the district court’s findings of fact do not support the obstruction of justice enhancement, and that the imposition of the enhancement was in violation of the Supreme Court’s recent decision in United States v. Booker, — U.S. —, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). Lastly, he argues that his Due Process rights were violated based on the lower prison sentence granted his codefendant. While we find that our remand order allowed the district court to consider the obstruction of justice enhancement, and that the sentence did not violate due process, we nonetheless remand White’s case to the district court for reconsideration of his sentence consistent with this opinion and Booker.
I. BACKGROUND
We assume familiarity with the general facts of this case as set forth in United States v. Thompson, 286 F.3d 950 (7th Cir.2002). As this appeal is limited to Mark A. White, we will repeat only those facts pertinent to his conduct. A jury convicted White of participating in a conspiracy to distribute cocaine in violation of 21 U.S.C. §§ 841(a)(1), 846, and three counts of money laundering in violation of 18 U.S.C. § 1956(a)(1)(A)(i), (B)(i), and (h). During White’s first sentencing hearing, the district court concluded, and we agreed, that Marcus Willis, an undercover law enforcement officer, was murdered in White’s vehicle, a white Yukon. Thompson, 286 F.3d at 956-57. White aided in the cover-up of Willis’s murder by lying to police officers about his whereabouts on the morning of and after the murder. He restated his lies under oath at his detention hearing, thereby actively participating in the cover-up. Moreover, he attempted to tamper with evidence of the murder by scheduling the Yukon to be repaired before police could examine the vehicle for evidence. Id. at 961 n. 4. However, after the conspirators’ [830]*830arrest but before the scheduled repair could take place, a police inspection of the Yukon revealed that the front passenger seat was removed, carpet from the front passenger side was cut out, damage to the left side of the front windshield was present, and Marcus Willis’s blood was in the vehicle.
A. The Original Sentencing and First Appeal
At his original sentencing hearing, the district court sentenced White to life imprisonment after concluding that the conspiracy trafficked in more than five kilograms of cocaine and that the United States Sentencing Guidelines (U.S.S.G.) § 2D1.1(d)(1) murder cross-reference enhancement was applicable. The Presentence Report (PSR) also recommended increasing White’s base offense level by two for obstruction of justice in accordance with U.S.S.G. § 3C1.1. The district court, however, chose not to apply the obstruction of justice enhancement because the murder cross-reference enhancement involved parallel relevant conduct and application of both enhancements would have amounted to double counting in violation of U.S.S.G. § 1B1.1.
In Thompson, 286 F.3d at 955, we affirmed White’s convictions but remanded his case for resentencing. We held that the district court’s factual findings did not sufficiently support the murder cross-reference enhancement because the record did not reveal that White could reasonably foresee that Willis could be killed with malice aforethought in furtherance of the conspiracy. Our remand language was general, instructing the district court to resentence White “consistent with our ruling.” Id. at 961.
B. The Resentencing Hearing
Pursuant to our instructions, the district court resentenced White on June 13, 2003. Prior to White’s resentencing, on November 15, 2002, Dennis Jones, White’s co-conspirator, was resentenced. He was found guilty of the same criminal offenses as White and also lied to police about his whereabouts and participated in the murder’s cover-up. At Jones’s resentencing hearing, also done pursuant to this court’s decision in Thompson, Chief Judge McKinney declined to add the obstruction of justice enhancement, reasoning:
It is true that those statements that I found to support the foreseeability of the murder aren’t related to the offense of conviction in one way, but in another way they are. They are related to the ability of this conspiracy to successfully pursue its ends. I think it is a relatively difficult call to make at this point, and it is my view that I will not add that obstruction of justice at this point.
Despite Chief Judge McKinney’s leniency with Jones, his analysis of the remand order and obstruction of justice enhancement led to a different result at White’s resentencing hearing:
It seems to me that the remand is a narrow remand and it is for me to resen-tence Mr. White without the murder cross-reference. It is, I think, true that the findings that I made at the time that supported what I thought, or that I thought at the time supported a murder cross-reference are the same findings that could possibly then have supported an obstruction of justice .... I was concerned about it then as double counting. And so the issue today is on this remand, would it be permissible for the Court to take the findings that the Appellate Court determined did not support a murder cross-reference and use those same findings to support an obstruction of justice addition because there isn’t any question of double counting anymore. [¶]... ] I think those findings made before do in fact support an [831]*831obstruction of justice conclusion. [¶]... ] Again, the issue is whether under this narrow remand I can take that step. I don’t believe there’s anything in that remand that requires that those facts no longer be considered. And I will consider them.
Then, in agreement with the PSR’s recommendation and the district court’s own findings of fact, Chief Judge McKinney imposed the obstruction of justice enhancement, sentencing White to 480 for the drug conspiracy charge and to 240 months on each of the other three convictions, to be served concurrently. Jones, however, as a result of the court’s decision not to apply the obstruction of justice enhancement, was sentenced to 350 months in prison.
II. DISCUSSION
White raises three issues on appeal. First, he asserts that the district court lacked jurisdiction to consider whether the obstruction of justice enhancement applies because it was beyond the scope of our remand. Second, he submits that even if the district court acted within the scope of remand, it clearly erred as its factual findings are not supported by the record, and were made in contravention of United States v. Booker, — U.S. —, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). Lastly, he claims that the disparity between his sentence and that of his co-conspirator Jones violates his Due Process rights. We address each of his arguments in turn.
A. Scope of Remand
White’s contention that the district court acted outside the scope of the remand by adding the obstruction of justice enhancement to his offense level calculation is a question of law that we review de novo. United States v. Sumner, 325 F.3d 884, 888 (7th Cir.2003); United States v. Husband, 312 F.3d 247, 251 (7th Cir.2002).
Title 28 U.S.C. § 2106 grants appellate courts flexibility in determining the scope of remand.1 This Court has previously stated that in the sentencing context, “the statute authorizes us to ‘limit a remand to specific issues or to order complete resentencing.’ ” United States v. Young, 66 F.3d 830, 835 (7th Cir.1995) (quoting United States v. Polland, 56 F.3d 776, 777 (7th Cir.1995)). Both the law of the case doctrine and the mandate rule require the district court to adhere to the commands of this Court. See Husband, 312 F.3d at 250 n. 3 (“ ‘law of the case’ generally requires the district court to confine its discussion to the issues remanded”) (internal citation omitted); Polland, 56 F.3d at 777-78 (“mandate rule requires a lower court to adhere to the commands of a higher court on remand”). The scope of a district court’s power on remand is determined by the language of the order of remand. United States v. Buckley, 251 F.3d 668, 669 (7th Cir.2001). There is no formula for determining its scope. See Husband, 312 F.3d at 251 (“The court may explicitly remand certain issues exclusive of all others; but the same result may also be accomplished implicitly.”). But see Young, 66 F.3d at 836 (suggesting that explicit language is required for a limited remand).
Our case law has characterized the scope of the remand issue using two analogies: (1) that upon remand the district [832]*832court is presented with a “clean slate” or (2) the district court may “unbundle the sentencing package.” There is no meaningful distinction in this phraseology. In United States v. Smith, 103 F.3d 531, 534 (7th Cir.1996), we held that the sentencing guidelines provide lower courts with the authority to restructure sentences when part of a sentence is vacated. We opined:
If a multicount sentence is a package— and we think it is — then severing part of the total sentence usually will unbundle it. And we do not think it matters what means are used to bring resentencing proceedings before the district court. Under the sentencing package concept, when a defendant raises a sentencing issue he attacks the bottom line.
Id.; see also United States v. Noble, 299 F.3d 907, 910 (7th Cir.2002) (“[I]t is settled that after the appellate court vacates the sentence on a particular count, the district court on remand may adjust the entire sentencing ‘package.’ ”); United States v. Binford, 108 F.3d 723, 729 (7th Cir.1997) (holding that package concept is applicable in the collateral attack context).
Likewise, in Polland, we explained, “the vacation of a sentence results in a ‘clean slate’ and allows the district court to start from scratch.” 56 F.3d at 777 (citing United States v. Atkinson, 979 F.2d 1219, 1223 (7th Cir.1992) (instructing trial court to write on a “clean slate” after vacating the original sentence)); see also United States v. Barnes, 948 F.2d 325, 330 (7th Cir.1991) (stating that the effect of a vacated sentence is to provide the trial judge with a “clean slate as far as sentencing [is] concerned”). In Polland, we further clarified that vacation of a sentence does not mean “we must always order, and the district court must always engage in, complete resentencing,” 56 F.3d at 779; rather the calculus is a practical one. We recognize that in a sentencing determination potential enhancements are inter-connected and the district court’s original sentencing intent may be undermined by altering one portion of the calculus. Furthermore, vacated aspects of a sentence may change the form of the sentence. We have ruled that “[a] court may increase a sentence on an unchallenged count without violating the Double Jeopardy Clause so long as the new sentence is lawful.” Smith, 103 F.3d at 535 (citing Pennsylvania v. Goldhammer, 474 U.S. 28, 106 S.Ct. 353, 88 L.Ed.2d 183 (1985)). Additionally, the district court should be “invited to resentence the defendant on all counts in order to achieve a rational, coherent structure in light of the remaining convictions.” United States v. Martenson, 178 F.3d 457, 465 (7th Cir.1999).
In Thompson, we found that the district court erred in applying the murder cross-reference enhancement to White’s offense level calculation. Further, we directed that “we remand for resentencing consistent with our ruling.” Taken as a whole, the remand order did not implicitly or explicitly suggest that the district court only eliminate the murder cross-reference enhancement.
White incorrectly asserts that the sentence was not vacated because we did not explicitly use the word “vacate” in our remand order, and therefore did not provide the district court with a “clean slate” or “unbundled package.” Our decision sufficiently altered the sentence to have the effect of vacating his sentence. As we have held, “when there is an alteration in the components of a sentence, the entire sentence is altered. If the alteration contains within itself potential for permeating the whole sentence, the entire sentence can be revisited .... ” Martenson, 178 F.3d at 463 (quoting Smith, 103 F.3d at 535 (affirming a trial court’s complete re-sentencing after vacating one of defendant’s three convictions)). Here, the [833]*833elimination of the murder cross-reference enhancement similarly permeated the entire sentence because it eliminated the life sentence imposed by the district court, leaving White’s sentence at 240 months, thereby sufficiently disturbing the district court’s sentencing intent.
Most importantly, the guidelines explicitly preclude the imposition of two enhancements which are based on the same relevant conduct. See U.S.S.G. § 1B1.1 (“Where two or more guideline provisions appear equally applicable, but the guidelines authorize the application of only one such provision, use the provision that results in the greater offense level.”); see United States v. Szakacs, 212 F.3d 344, 353 (7th Cir.2000) (double counting exists when enhancements are premised on identical facts) (quoting United States v. Haines, 32 F.3d 290, 293 (7th Cir.1994)); United States v. Austin, 54 F.3d 394, 403 (7th Cir.1995) (same). Therefore, once the district court chose to apply the murder cross-reference, it was no longer empowered to consider the obstruction of justice enhancement. The district court based the imposition of the murder cross-reference enhancement on the findings that White lied to police officers and participated in the cover-up of Willis’s murder — -the same findings of fact used for the obstruction of justice enhancement.
Our decision remanding stated that the district court’s initial decision to apply the murder cross-reference was not supported by sufficient factual findings. Thus, without a remand order to the contrary, the district court was free to determine whether an enhancement that it was previously precluded from applying based on double counting implications could now be supported by the record.2
B. Application of Obstruction of Justice Enhancement
White raises two challenges to the district court’s application of the obstruction of justice enhancement to his sentence. First he argues that the district court’s findings of fact do not support the enhancement because they fail to meet the requisite burden of persuasion. Second, he challenges the propriety of the very method through which those facts were found.
1. Meeting Burden of Persuasion
The guidelines provide that an obstruction of justice enhancement should be applied:
If (A) the defendant willfully obstructed or impeded, or attempted to obstruct or impede, the administration of justice during the course of the investigation, prosecution, or sentencing of the instant offense of conviction, and (B) the obstructive conduct related to (i) the defendant’s offense of conviction and any relevant conduct; or (ii) a closely related offense, increase the offense level by 2 levels.
U.S.S.G. § 3C1.1.
Our prior opinion approved the district court’s finding that White lied to authorities about his whereabouts on the morning of and after the murder of the undercover informant (Willis). Thompson, 286 F.3d at 960-61. We also noted that the district court properly concluded that “White participated in the cover-up because he often used the name ‘Demarco,’ the same name used by the party who scheduled the appointment to have the vehicle [in which the murder took place] repaired at Mobile Jamzz” before it could be examined by the [834]*834police for evidence. Id. at 961 n. 4. Based upon this evidence, the district court upon remand found that White had impeded law enforcement’s investigation, and applied the obstruction of justice enhancement accordingly.
White argues that this evidence is insufficient to support the obstruction of justice enhancement. However, if properly found, evidence establishing that White participated in a cover-up of an undercover informant’s murder by both lying under oath during his detention hearing about his whereabouts the night of the murder, and assisting in the attempted destruction of evidence, would certainly qualify him for the obstruction of justice enhancement. Indeed, White’s perjury alone—if properly found—may be sufficient to warrant the enhancement. See United States v. White, 240 F.3d 656, 661 (7th Cir.2001) (affirming obstruction of justice enhancement when witness committed perjury by flatly denying involvement in insurance fraud scheme); United States v. Hickok, 77 F.3d 992, 1006 (7th Cir.1996) (“Perjury is a well-established example of conduct that warrants an enhancement for obstruction of justice.”) (internal citations omitted).
Moreover, a legitimate finding that White had assisted in the attempted destruction of evidence would also be independently sufficient for the obstruction of justice enhancement, as the application note highlights. U.S.S.G. § 3C1.1, App. Note 4(d) (noting that “destroying or concealing or directing or procuring another person to destroy or conceal evidence that is material to an official investigation or judicial proceeding” is an example of obstructive conduct). White’s perjury coupled with his participation in the murder’s cover-up would—if properly found—more than sufficiently demonstrate that the district court did not clearly err in applying the obstruction of justice enhancement.
2. Propriety of the Factual Findings—United States v. Booker
However, as the repeated caveats above suggest, the ultimate propriety of applying the obstruction of justice enhancement here turns on the legitimacy of the method in which the facts supporting the enhancement were found. Toward this end, White argues that the district court’s application of the obstruction of justice enhancement to his sentence violated his rights as interpreted in United States v. Booker, — U.S. —, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). Because he did not raise this challenge before the district court (nor any related challenge invoking the Sixth Amendment, the since decided Blakely v. Washington, — U.S. —, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004), or Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000)), we review for plain error. See United States v. Paladino, 401 F.3d 471, 481 (7th Cir.2005); United States v. Olano, 507 U.S. 725, 731, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993).
“Under [the plain error] test, before an appellate court can correct an error not raised at trial, there must be (1) ‘error,’ (2) that is ‘plain,’ and (3) that ‘affects substantial rights.’ ” United States v. Cotton, 535 U.S. 625, 631, 122 S.Ct. 1781, 152 L.Ed.2d 860 (2002) (quoting Johnson v. United States, 520 U.S. 461, 466-67, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997)). “If all three conditions are met, an appellate court may then exercise its discretion to notice a forfeited error, but only if (4) the error ‘seriously affects the fairness, integrity, or public reputation of judicial proceedings.’ ” Id. (quoting Johnson, 520 U.S. at 467, 117 S.Ct. 1544).
We begin by assessing error. One error that White may argue is that the district court violated his Sixth Amendment right to a jury trial by increasing his sentence— [835]*835via the obstruction of justice enhancement — based on facts neither admitted by himself nor proven to his jury beyond a reasonable doubt. In United States v. Booker, the Supreme Court made clear that “the Sixth Amendment as construed in Blakely does apply to the Sentencing Guidelines.” 125 S.Ct. at 746. Accordingly, under the formerly mandatory regime, “[a]ny fact (other than a prior conviction) which is necessary to support a sentence exceeding the maximum authorized by the facts established by a plea of guilty or a jury verdict must be admitted by the defendant or proved to a jury beyond a reasonable doubt.” Id. at 756.
Indeed, both of the facts upon which the district court justified the obstruction of justice enhancement — namely, that White had (1) lied under oath during his detention hearing about his whereabouts on the night of the murder of the undercover informant; and (2) assisted in the attempted destruction of evidence by scheduling an appointment to have the vehicle in which the murder took place (the Yukon) repaired before it could be examined by the police for evidence — were found solely by the district court. Such sentencing in reliance on supplemental facts neither admitted by White nor proven to his jury beyond a reasonable doubt squarely violates our new understanding of the Sixth Amendment as divined by Booker, and thereby constitutes error.
The procedural posture of this case, however, presents an interesting wrinkle in assessing the propriety of the facts upon which the enhancement was based. The matter before us is a successive appeal. As noted above, we have already visited the findings upon which the district court based its imposition of the obstruction enhancement in our prior opinion. Thompson, 286 F.3d at 960-61 & n. 4. While the issue of the propriety of the facts found was before this court on prior appeal, White did not raise a Sixth Amendment challenge akin to that raised today.
We need not decide today, however, whether our prior decision precludes our ability to assess today a Sixth Amendment challenge to the propriety of these since settled facts. Increasing sentence under the mandatory scheme based on solely judge found facts is not the only error contemplated by Booker. As the government concedes, the mere mandatory application of the Guidelines — the district court’s belief that it was required to impose a Guidelines sentence — constitutes error. See Booker, 125 S.Ct. at 769 (holding. that parties in respondent Fanfan’s case “may seek resentencing under the system set forth in [Booker ]” though “Fanfan’s sentence d[id] not violate the Sixth Amendment”); Paladino, 401 F.3d at 480 (finding Booker error where a portion of defendant Velleff s sentence “was based on mandatory provisions of the sentencing guidelines”); United States v. Labastida-Segura, 396 F.3d 1140, 1142 (10th Cir.2005) (“We must apply the remedial holding of Booker to [defendant’s] direct appeal even though his sentence does not involve a Sixth Amendment violation.”). What’s more, that error is plain. Olano, 507 U.S. at 734, 113 S.Ct. 1770 (“ ‘Plain’ is synonymous with ‘clear’ or, equivalently, ‘obvious.’ ”); Johnson v. United States, 520 U.S. 461, 468, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997) (“[W]here the law at the time of trial was settled and clearly contrary to the law at the time of appeal[,] it is enough that an error be ‘plain’ at the time of appellate consideration.”) (emphasis added).
In turning to the third and fourth prongs of the plain error standard, we note that the difference between the two elements “is not entirely clear.” Paladino, 401 F.3d at 481. Under Paladino’s application of the plain error test in the [836]*836Booker context, the third element — providing that the error must “affect substantial rights” — requires the error to have been “prejudicial,” id., in that it “affected the outcome of the district court proceedings,” Olano, 507 U.S. at 734, 113 S.Ct. 1770. The fourth element, on the other hand, by limiting renewable error to those which “seriously affect the fairness, integrity, or public reputation of judicial proceedings,” requires that the uncorrected error be “intolerable,” or result in a “miscarriage of justice,” Paladino, 401 F.3d at 481 (citing cases). While an error cannot be intolerable without being prejudicial, “[a]n error can be prejudicial without being intolerable, because it might be apparent that a retrial or a resentencing would lead to the same result.” Id. “Here we can and have predetermined that if the defendant has been prejudiced by an illegal sentence, then allowing that illegal sentence to stand would constitute a miscarriage of justice.” United States v. Macedo, 406 F.3d 778, 790, 2005 WL 851501, *8 (7th Cir.2005); see also Paladino, 401 F.3d at 483 (“It is a miscarriage of justice to give a person an illegal sentence that increases his punishment, just as it is to convict an innocent person.”); United States v. Pawlinski, 374 F.3d 536, 540-41 (7th Cir.2004) (“[T]he entry of an illegal sentence is a serious error routinely corrected on plain-error review.”). What remains uncertain at this stage of our review, however, is whether the district court, operating under it new-found post-Booker discretion, would have sentenced the defendant any differently.
This is not a “case[ ] in which one can be certain that the judge would not have given a different sentence even if he had realized that the guidelines were merely advisory.” Paladino, 401 F.3d at 480. There are no “indicators” here that might dissipate the “fog” that surrounds our understanding of “what the district judge would have done with additional discretion.” Cf. United States v. Lee, 399 F.3d 864, 866 (7th Cir.2005) (listing several indicators that would suggest that the district court, notwithstanding its broader, post-Booker discretion, would not sentence differently). Here, with a final offense level of 42 and a criminal history category II, White’s sentencing range was 360 months to life. The district court sentenced him to 460 months. That the sentencing judge imposed a sentence higher than the guideline minimum tells us nothing, for “[a] conscientious judge — one who took the guidelines seriously whatever his private views — would pick a sentence relative to the guideline range.” Paladino, 401 F.3d at 482 (emphasis added). Vested with broader discretion, district courts may today find once mandated ranges wholly inapt, inexorably corrupting any sentence imposed relative to them.
Accordingly, so that we might complete our plain error analysis, we, “while retaining jurisdiction of the appeal, order a limited remand to permit the sentencing judge to determine whether he would (if required to resentence) reimpose his original sentence.” Id. at 484. Before reaching this decision on remand,
(whether the judge’s conclusion is that he would, or would not, adhere to the original sentence), ‘the District Court should obtain the views of counsel, at least in writing, but ‘need not’ require the presence of the Defendant, see Fed.R.Crim.P. 43(b)(3). Upon reaching its decision (with or without a hearing) whether to resentence, the District Court should either place on the record a decision not to resentence, with an appropriate explanation,’ United States v. Crosby, supra, at *13, or inform this court of its desire to resentence the defendant. (By ‘should’ in the quoted passage, we understand ‘must.’).
Paladino, 401 F.3d at 484. If the district court determines that it would nonetheless [837]*837reimpose the original sentence if required to resentence, we will affirm the original sentence, provided that the sentence is reasonable. Id. If the district court determines that it would, with its greater discretion, sentence White differently, we will vacate White’s original sentence and remand his case for resentencing. Id.
C. Due Process Claim
Finally, White argues that his Due Process rights were violated by the district court’s decision to apply the obstruction of justice enhancement to his sentence and not thát of his co-defendant, Jones, when the district court found that they both engaged in substantially identical conduct. Jones was sentenced to 350 months in prison and White was sentenced to'480 months. This court has explicitly rejected similar arguments. We have repeatedly stated, “a disparity among co-defendants’ sentences is not a valid basis to challenge a guideline sentence otherwise correctly calculated.” United States v. Simpson, 337 F.3d 905, 909 (7th Cir.2003) (quoting United States v. Simmons, 218 F.3d 692, 696 (7th Cir.2000)). White’s sentence was correctly calculated and falls within the guidelines’ range of 360 months to life. The propriety of Jones’s sentence is not relevant to White’s appeal. We will not disturb the appealing defendant’s sentence even when a co-conspirator’s sentence is lenient. See United States v. McMutuary, 217 F.3d 477, 489-90 (7th Cir.2000). The only time we will disturb a sentence based on an unjustifiable disparity between co-defendants is if it “actually creates a disparity between the length of the appellant defendant’s sentence and all other similar sentences imposed nationwide.” Simpson, 337 F.3d at 909 (quoting McMutuary, 217 F.3d at 490). White neither asserts nor presents evidence that his sentence creates such a national disparity. Therefore, he has not met his burden.
III. CONCLUSION
For the reasons stated above, we direct a limited RemaNd of White’s case in accordance with the procedure set forth in this opinion, thus retaining appellate jurisdiction.
This opinion was circulated to the entire court before issuance. All but one member of the court in regular active service voted not to hear the case en banc. Judge Easterbrook voted to hear it en banc.