
517 F.3d 801 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
George W. WILLIAMS, Defendant-Appellant.
No. 06-30010.
United States Court of Appeals, Fifth Circuit.
February 18, 2008.
*802 *803 *804 *805 Camille Ann Domingue, Asst. U.S. Atty. (argued), Lafayette, LA, for U.S.
Tara Selver (argued), Gig Harbor, WA, for Williams.
Before JOLLY, CLEMENT and OWEN, Circuit Judges.
OWEN, Circuit Judge:
George W. Williams was originally sentenced prior to the issuance of United States v. Booker,[1] under a mandatory Sentencing Guidelines regime. In a prior appeal, this court held that certain factors did not justify an upward departure from the mandatory Guidelines range. On remand, after Booker was decided, the district court imposed a non-Guidelines sentence greater than the advisory Guidelines range. We hold that the district court did not violate the law of the case in imposing the sentence and that the sentence was not unreasonable. We therefore affirm.

I
George W. Williams was convicted of federal conspiracy, fraud, money laundering, and criminal forfeiture. The facts underlying these convictions were described by this court in United States v. Williams.[2] The district court sentenced Williams to 172 months of imprisonment under the then-mandatory Guidelines. The district court grouped Williams's offenses, and applied the base-offense level of the money laundering guideline,[3] on the ground that it was the highest among the grouped offenses.[4] The district court enhanced this level by two based on its finding that Williams had obstructed justice by perjuring himself at trial,[5] and upwardly departed from the guidelines by four levels based on its finding that the money laundering scheme was complex and involved a large number of victims.[6]
*806 Williams appealed the sentence, claiming that both the enhancement and the upward departure were in error. This court held there was no error in the enhancement based on obstruction of justice[7] but held that the district court did err in its upward departure based on complexity and number of victims.[8] The court reasoned that the scheme was not exceptional in its complexity nor in the number of victims within the meaning of § 5K2.0,[9] as the district court had found.[10] This court therefore vacated the sentence and remanded to the district court in June, 2004.
In January, 2005, the Supreme Court decided United States v. Booker,[11] holding both that "[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,"[12] and that the guidelines must be non-mandatory in order to comply with the Sixth Amendment.[13]
In December, 2005, the district court held a re-sentencing hearing. The district court apparently believed that the enhancement based on obstruction of justice was invalid under Booker,[14] since the fact of perjury had not been found by a jury nor admitted by Williams. Without the obstruction of justice enhancement and the upward departure for complexity and number of victims, the advisory guideline sentencing range was 78 to 97 months. Citing the sentencing factors stated in 18 U.S.C. § 3553(a) and the specific circumstances of Williams's case, the court imposed a non-Guidelines sentence and again sentenced Williams to 172 months of imprisonment.
Williams has appealed. He claims (1) that the sentence violates the law of the case established by this court in the first appeal, because the district court's stated factors for ordering 172 months of imprisonment were many of the same factors that this court held did not justify a four-level upward departure under the Sentencing Guidelines in the initial sentencing; and (2) that the 172-month sentence is unreasonable.

II
We review a district court's interpretation of our remand order de novo, including whether the law of the case forecloses any of the district court's actions on remand.[15] The law of the case doctrine contemplates that "an issue of fact or law decided on appeal may not be reexamined either by the district court on remand or by the appellate court on a subsequent appeal."[16] "The law of the case doctrine, however, is not inviolate. We have explained that `a prior decision of this court will be followed without re-examination . . . unless (i) the evidence on a subsequent trial was substantially different, (ii) controlling *807 authority has since made a contrary decision of the law applicable to such issues, or (iii) the decision was clearly erroneous and would work a manifest injustice.'"[17] If it appears that this court's holding has not been followed in subsequent proceedings, we may nevertheless affirm the district court if one of the exceptions applies.[18]
In the prior appeal we held that the district court "erred by departing upward from the sentencing guidelines pursuant to § 5K2.0."[19] We concluded that the facts of Williams's case did not reveal an exceptional degree of complexity or number of victims, that the Sentencing Guidelines already took complexity and number of victims into account, and therefore that the Guidelines themselves did not allow an upward departure on those grounds.[20] Our earlier holding was an interpretation of the mandatory Sentencing Guidelines, and a non-Guidelines sentence could not be imposed at that time.
The Supreme Court's decision in Booker was intervening law that created one of the recognized exceptions to the law of the case doctrine. Booker rendered the Guidelines sentencing range advisory only.[21] This was a dramatic shift in sentencing law and permitted the district court to consider complexity and number of victims in selecting a sentence, even though we had ruled that those factors were improperly considered in upwardly departing pursuant to section 5K2.0 of the then-mandatory regime. The Booker decision was intervening controlling law that created an exception to the law of the case doctrine.[22]

III
Williams argues that his sentence is unreasonable, contending that his money laundering offenses are "run of the mill" and within the "heartland of money laundering offenses." He further asserts that the amount of loss is the relevant measure of harm, not the number of victims or complexity of the scheme because, he contends, the number of victims and the sophistication of the scheme is subsumed in the loss tables. The Guidelines range should be applied, he argues, absent extraordinary circumstances peculiar to the particular defendant. He asserts that his 172-month sentence (fourteen years and four months) is a 77% increase over the maximum guideline sentence calculated by the district court, which was 97 months (eight years and one month). A sentence of eight years and one month would more than satisfy the sentencing goals in 18 U.S.C. § 3553, he contends.

A
The Supreme Court has recently provided additional guidance in determining *808 whether a sentence is reasonable.[23] The Court reconfirmed that "[r]egardless of whether the sentence imposed is inside or outside the Guidelines range, the appellate court must review the sentence under an abuse-of-discretion standard."[24] In performing that review, we are to "first ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range. . . . "[25]
Although Williams asserts that the district court properly calculated the Guidelines range, the Government contends otherwise, arguing that the district court should have applied a two-level enhancement for perjury. We will consider the Government's contention since in reviewing the reasonableness of a sentence, we are to "take into account the totality of the circumstances, including the extent of any variance from the Guidelines range."[26] The Government has not cross-appealed and requested that we remand, so we do not consider whether a remand would be required if it had done so.
The district court found in its initial sentencing that Williams had committed perjury during his trial and imposed an obstruction enhancement under § 3C1.1.[27] We affirmed that enhancement in the first appeal. At the sentencing hearing on remand, the district court reconfirmed its conclusion that Williams committed perjury during his trial, but the district court did not apply an enhancement because Williams "was not charged with nor convicted of perjury." However, in order for the enhancement to apply, the fact of perjury need not be tried to a jury and may instead be found by the sentencing judge by a preponderance of the evidence.[28] The calculation of the Guidelines range at re-sentencing should have included a two-level enhancement for obstruction of justice, and the correct advisory sentencing range was 97 to 121 months. This error does not entitle Williams to any relief because his sentence was not "imposed as a result of an incorrect application of the sentencing guidelines"[29] since the properly calculated range was higher than that applied by the district court. Nor can it be said that Williams's sentence "would have been different but for the district court's error"[30] in calculating the applicable Guideline's range.
There is no contention that the district court "select[ed] a sentence based on clearly erroneous facts, or fail[ed] to adequately explain the chosen sentence. . . ."[31] Accordingly, we turn our consideration to "the substantive reasonableness of the sentence imposed under an abuse-of-discretion standard."[32]

B
When, as here, a sentence is outside the Guidelines range, we "may consider the extent of the deviation, but must give due deference to the district court's decision that the § 3553(a) factors, on [the] *809 whole, justify the extent of the variance."[33] We apply the familiar deferential standard: "The fact that the appellate court might reasonably have concluded that a different sentence was appropriate is insufficient to justify reversal of the district court."[34]
The district court considered a number of factors in selecting a sentence of 172 months, including the number of victims who were individuals, the harm to and disruption of the lives of those victims, the fact that the fraud and money laundering occurred across 26 states, and the complexity of the scheme. Among Williams's chief complaints is his contention that the Guidelines adequately accounted for these factors and therefore his sentence in excess of the Guidelines range is unreasonable.
The Supreme Court's decision in Booker[35] implicitly rejected the position that no additional weight could be given to factors included in calculating the applicable advisory Guidelines range, since to do otherwise would essentially render the Guidelines mandatory. In Gall[36] and Kimbrough v. United States[37] the Supreme Court has more explicitly set forth the permissible considerations in imposing a sentence, whether within or without an applicable Guidelines range. The Court explained in Gall that in selecting a sentence, the district court "may not presume that the Guidelines range is reasonable."[38] The court "must make an individualized assessment based on the facts presented."[39] This necessarily means that the sentencing court is free to conclude that the applicable Guidelines range gives too much or too little weight to one or more factors, either as applied in a particular case or as a matter of policy. The Supreme Court confirmed in Kimbrough that while "[a] district judge must include the Guidelines range in the array of factors warranting consideration," the sentencing "judge may determine, however, that, in the particular case, a within-Guidelines sentence is `greater than necessary' to serve the objectives of sentencing."[40] Obviously, the sentencing court may also conclude in a particular case that a sentence within the Guidelines range is not lengthy enough to serve the objectives of sentencing.
The Supreme Court reiterated in Kimbrough what it had conveyed in Rita v. United States,[41] which is that "as a general matter, `courts may vary [from Guidelines ranges] based solely on policy considerations, including disagreements with the Guidelines.'"[42] In Gall the Court held that a sentence imposing only probation was reasonable even though the applicable Guidelines range was 30 to 37 *810 months of imprisonment,[43] and the Guidelines did not recommend probation when such a range applied.[44] Accordingly, even though the Guidelines "state[d] that probation alone [was] not an appropriate sentence for comparable offenses," the Supreme Court admonished that "the Guidelines are not mandatory, and thus the `range of choice dictated by the facts of the case' is significantly broadened."[45] The Supreme Court reminded us that "the Guidelines are only one of the factors to consider when imposing sentence," and that even in a case in which only probation was imposed in direct contradiction of the Guidelines's policy, "§ 3553(a)(3) directs the judge to consider sentences other than imprisonment."[46]
Both Gall and Kimbrough emphasized that the Guidelines range is but one factor for a sentencing judge to consider.[47] The Guideline range is "the starting point and the initial benchmark."[48] "[I]n the ordinary case, the Commission's recommendation of a sentencing range will `reflect a rough approximation of sentences that might achieve § 3553(a)'s objectives.'"[49] But that range is not mandatory. The § 3553(a) factors must be considered.[50] "The sentencing judge . . . has `greater familiarity with . . . the individual case and the individual defendant before him than the Commission or the appeals court.' He is therefore `in a superior position to find facts and judge their import under § 3553(a)' in each particular case."[51] The Supreme Court further counseled, "[i]n light of these discrete institutional strengths, a district court's decision to vary from the advisory Guidelines may attract greatest respect when the sentencing judge finds a particular case `outside the "heartland" to which the Commission intends individual Guidelines to apply.'"[52] "On the other hand, while the Guidelines are no longer binding, closer review may be in order when the sentencing judge varies from the Guidelines based solely on the judge's view that the Guidelines range `fails properly to reflect § 3553(a) considerations' even in a mine-run case."[53]
In selecting a sentence for Williams, the district court was not prohibited from considering the number of victims, *811 the harm to individuals, the expansive reach of the crimes, or the complexity of the scheme, even though the Guidelines sentencing range for money laundering[54] may implicitly have taken complexity of the scheme and the number of victims into account by basing the term of imprisonment on the amount of loss. We find no merit in Williams's arguments that these factors could not support a sentence outside the guidelines, although we recognize that some of our pre-Rita, pre-Gall and pre-Kimbrough decisions indicate otherwise.[55] All of the factors about which Williams complains are permissible factors for consideration under 18 U.S.C. § 3553(a) in determining whether a sentence inside or outside the Guidelines would be appropriate.
Williams contends there must be extraordinary circumstances to justify a sentence 77% higher than 97 months, which was the top of the Guidelines advisory range found applicable by the district court. (We note that Williams's 172-month sentence is 42% greater than 121 months, the top of the properly calculated Guidelines range.)
Williams's argument that district courts may depart from the Guidelines only in "extraordinary circumstances peculiar to the particular defendant before the sentencing court" is directly foreclosed by Gall.[56] We may not require district courts to find "extraordinary" circumstances before they impose sentences outside of the guidelines range.[57] Nor may we use a "rigid mathematical formula that uses the percentage of a departure [from the Guidelines range] as the standard for determining the strength of the justifications required for a specific sentence."[58] Appellate systems of "`proportional review'" that "apply[] a heightened standard of review to sentences outside the Guidelines range" are inconsistent with the abuse-of-discretion standard that must be applied to all sentences, "whether inside or outside the Guidelines range."[59] To require "extraordinary circumstances" or to give "proportional review" would "come[] too close to creating an impermissible presumption of unreasonableness" for non-Guidelines sentences.[60]
We may, however, "take the degree of variance into account and consider *812 the extent of a deviation from the Guidelines."[61] The Guidelines range applicable to Williams is 97 to 121 months, which is a range between eight years, one month and ten years, one month. The 172-month sentence is fourteen years, four months, which is four years, three months longer than the top of the Guidelines range, and six years, three months longer than the bottom of the Guidelines range.
In imposing a 172-month sentence the district court enumerated each of the factors set forth in 18 U.S.C. § 3553(a) and considered their application to Williams's case. The court found that his offense "was horrendous and wrecked many people's lives," that Williams "[b]asically . . . stole money from individuals." The district court considered the need for the sentence "to reflect the seriousness of the offense, to promote respect for the law and to provide just punishment for the offense" to be an "extremely important" factor. The court sought "to deter other people from scamming not one community but several communities throughout 26 states." The court further found "[t]his particular defendant has shown no remorse and really doesn't care that he wrecked the lives of many people by defrauding them of some of their savings." The court found no need for educational or vocational training, medical care, or other corrective treatment. The district court also said,
Based on all the factors of this case, the tremendous problems that it caused to the individuals, all the testimony that was presented in court, the fraud and the complexity of the fraud, the number of states and the number of individuals, and where these people were sought to in fact contribute to this scheme unwittingly. The only one who knew that this was a scheme were the ones putting this scheme together, and the lead person in that entire scheme was Mr. Williams.
The district court sentenced Williams as follows:


     Count 29           172 months
     Counts 1 to 28     60 months
     Counts 30 to 47    172 months
     Counts 53 to 55    120 months

These sentences are to be served concurrently. The district court also ordered restitution in the amount of $2,995,645.20, and three years of supervised release for each count, to run concurrently.
We note that the 172-month sentence is below a statutory maximum sentence of 20 years, which was authorized for Count 29[62] as well as for each of Counts 30 to 47.[63] The maximum statutory penalty for each of the offenses enumerated in Counts 1 to 28 was five years,[64] and for each offense enumerated in Counts 53 to 55, the maximum penalty was ten years.[65]
For the reasons explained in Gall and Kimbrough, we give considerable deference to the district court's imposition of the 172-month sentence.[66] The district court saw and heard the evidence, made credibility determinations, had full knowledge of the facts, and gained insights not conveyed by the record.[67] The district court had access to Williams and had "`greater familiarity with'" this case and Williams "than the Commission or" this *813 court.[68] While we may not have imposed the same sentence, that is not the test. The district court considered the factors in 18 U.S.C. § 3553(a) and articulated the reasons for arriving at the sentence. In light of the record and the district court's findings, we cannot say that the district court abused its discretion in concluding that a 172-month sentence was reasonably necessary to achieve the objectives of 18 U.S.C. § 3553(a).[69]

* * *
We AFFIRM the sentence imposed by the district court.
NOTES
[1]  United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005).
[2]  United States v. Williams, 101 Fed.Appx. 435, 436 (5th Cir.2004).
[3]  See U.S.S.G. § 2S1.1(a)(1) (1998).
[4]  See id. § 3D1.2 (1998).
[5]  See id. § 3C1.1 (1998).
[6]  See id. § 5K2.0 (1998).
[7]  See Williams, 101 Fed.Appx. at 437-38.
[8]  See id. at 438-39.
[9]  U.S.S.G. § 5K2.0 (1998).
[10]  See Williams, 101 Fed.Appx. at 438-39 (citing United States v. Hemmingson, 157 F.3d 347, 363 (5th Cir. 1998) and United States v. Tansley, 986 F.2d 880 (5th Cir. 1993)).
[11]  543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005).
[12]  Id. at 244, 125 S.Ct. 738.
[13]  Id. at 245-46, 125 S.Ct. 738.
[14]  Id.
[15]  United States v. Pineiro, 470 F.3d 200, 204 (5th Cir.2006).
[16]  United States v. Matthews, 312 F.3d 652, 657 (5th Cir.2002) (quoting Tollett v. City of Kemah, 285 F.3d 357, 363 (5th Cir.2002)).
[17]  United States v. Becerra, 155 F.3d 740, 752-53 (5th Cir.1998) (quoting N. Miss. Commc'ns, Inc. v. Jones, 951 F.2d 652, 656 (5th Cir. 1992)), abrogated on other grounds by Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621, as recognized by United States v. Farias, 481 F.3d 289 (5th Cir.2007).
[18]  See Becerra, 155 F.3d at 753.
[19]  101 Fed.Appx. at 439 (emphasis added).
[20]  Id. at 438-39.
[21]  See Booker, 543 U.S. at 245, 125 S.Ct. 738.
[22]  See United States v. Bad Marriage, 439 F.3d 534, 538 (9th Cir.2006) ("If [the earlier opinion in this case] is read to establish the law of the case under a mandatory Sentencing Guidelines regime, Booker, which leaves Guidelines as advisory only, is intervening controlling authority displacing prior law of case.").
[23]  Gall v. United States, ___ U.S. ___, 128 S.Ct. 586, 591, 169 L.Ed.2d 445 (2007).
[24]  Id. at 597.
[25]  Id.
[26]  Id.
[27]  U.S.S.G. § 3C1.1 (1998).
[28]  United States v. Alonzo, 435 F.3d 551, 553 (5th Cir.2006).
[29]  18 U.S.C. § 3742(f)(1).
[30]  Williams v. United States, 503 U.S. 193, 203, 112 S.Ct. 1112, 117 L.Ed.2d 341 (1992).
[31]  Gall, 128 S.Ct. at 597.
[32]  Id.
[33]  Id.
[34]  Id.
[35]  United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005).
[36]  ___ U.S. ___, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007).
[37]  ___ U.S. ___, 128 S.Ct. 558, 169 L.Ed.2d 481 (2007).
[38]  Gall, 128 S.Ct. at 596-97.
[39]  Id. at 597.
[40]  Kimbrough, 128 S.Ct. at 564 (quoting 18 U.S.C. § 3553(a)).
[41]  ___ U.S. ___, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007).
[42]  Kimbrough, 128 S.Ct. at 570 (alteration in original) (citing Rita, 127 S.Ct. at 2465 for the proposition that "a district court may consider arguments that `the Guidelines sentence itself fails properly to reflect § 3553(a) considerations.'").
[43]  Gall, 128 S.Ct. at 592-93.
[44]  Id. at 601-02 n. 11 ("Specifically, probation is not recommended under the Guidelines when the applicable Guidelines range is outside Zone A of the sentencing table as it is here. USSG § 5B1.1.").
[45]  Id. at 601-02.
[46]  Id. at 602.
[47]  Id. ("[T]he Guidelines are only one of the factors to consider when imposing sentence. . . ."); Kimbrough, 128 S.Ct. at 564 ("[T]he Guidelines, formerly mandatory, now serve as one factor among several courts must consider in determining an appropriate sentence.").
[48]  Gall, 128 S.Ct. at 596; see also Kimbrough, 128 S.Ct. at 574 ("[D]istrict courts must treat the Guidelines as the `starting point and the initial benchmark.'") (quoting Gall).
[49]  Kimbrough, 128 S.Ct. at 574 (quoting Rita, 127 S.Ct. at 2465).
[50]  Gall, 128 S.Ct. at 596 ("[T]he district judge should then consider all of the § 3553(a) factors to determine whether they support the sentence requested by a party."); id. at 597 ("[An appellate court] may consider the extent of the deviation, but must give due deference to the district court's decision that the § 3553(a) factors, on [the] whole, justify the extent of the variance.").
[51]  Kimbrough, 128 S.Ct. at 574 (quoting Rita, 127 S.Ct. at 2469 and Gall, 128 S.Ct. at 586).
[52]  Kimbrough, 128 S.Ct. at 574-75 (quoting Rita, 127 S.Ct. at 2465).
[53]  Id. at 575 (quoting Rita, 127 S.Ct. at 2465).
[54]  See U.S.S.G. §§ 2S1.1, 2B1.1 (2005).
[55]  See, e.g., United States v. Walters, 490 F.3d 371, 374 (5th Cir.2007) (invalidating an above-Guidelines sentence because the district court relied upon factors already incorporated by the Guidelines); United States v. Perrin, 478 F.3d 672, 678 (5th Cir.2007) (invalidating a below-Guidelines sentence in part because the district court relied upon factors already incorporated by the Guidelines); cf. United States v. Sanchez-Ramirez, 497 F.3d 531, 535-36 (5th Cir.2007) (affirming the district court's decision to impose an above-Guidelines sentence because the circumstances were egregious compared to normal cases of the same type).
[56]  Gall, 128 S.Ct. at 595 ("We reject, however, an appellate rule that requires `extraordinary' circumstances to justify a sentence outside the Guidelines range.").
[57]  Id.
[58]  Id.
[59]  Gall, 128 S.Ct. at 596.
[60]  Id. at 595-96 (The Supreme Court stressed, "[m]ost importantly, both the exceptional circumstances requirement and the rigid mathematical formulation reflect a practicecommon among courts that have adopted `proportional review'of applying a heightened standard of review to sentences outside the Guidelines range. This is inconsistent with the rule that the abuse-of-discretion standard of review applies to appellate review of all sentencing decisionwhether inside or outside the Guidelines range.").
[61]  Id. at 594-95.
[62]  See 18 U.S.C. § 1956(h).
[63]  See id. § 1956(a)(1).
[64]  See id. §§ 371, 1341-43.
[65]  See id. § 1957(a).
[66]  Gall, 128 S.Ct. at 597-98; Kimbrough, 128 S.Ct. at 574-75.
[67]  See Gall, 128 S.Ct. at 597.
[68]  Id. at 597-98.
[69]  See Kimbrough, 128 S.Ct. at 576 ("The ultimate question . . . is `whether the sentence was reasonablei.e., whether the District Judge abused his discretion in determining that the § 3553(a) factors supported a sentence of [15 years] and justified a substantial deviation from the Guidelines range.'") (quoting Gall, 128 S.Ct. at 600).
