
    UNITED STATES of America, Plaintiff—Appellee, v. Carlos VALLE-MARTINEZ, also known as Carlos Martinez, Defendant—Appellant.
    No. 07-1248.
    United States Court of Appeals, Tenth Circuit.
    Aug. 26, 2008.
    
      Robert M. Brown, Michael C. Johnson, Office of the United States Attorney, Denver, CO, for Plaintiff-Appellee.
    Edward R. Harris, Office of the Federal Public Defender, Raymond P. Moore, Federal Public Defender, Office of the Federal Public Defender, Denver, CO, for Defendant-Appellant.
    Before HENRY, Chief Judge, TYMKOYICH, and HOLMES, Circuit Judges.
   ORDER AND JUDGMENT

JEROME A. HOLMES, Circuit Judge.

Defendant-Appellant Carlos Valle-Mar-tinez pleaded guilty to one count of reentering the United States after being previously deported following a conviction for an aggravated felony, in violation of 8 U.S.C. § 1326(a)(1) and (2) and 8 U.S.C. § 1326(b)(2). The district court varied downward twelve months from the bottom of the advisory Guidelines range of forty-six to fifty-seven months, imposing a sentence of thirty-four months’ imprisonment. Mr. Valle-Martinez appeals arguing that his sentence is procedurally unreasonable. Exercising jurisdiction pursuant to 28 U.S.C. § 1291, we AFFIRM.

I. BACKGROUND

Mr. Valle-Martinez was indicted on one count of unlawful reentry of a deported alien after a conviction for an aggravated felony. He executed a plea agreement, and pleaded guilty. Subsequently, the probation office prepared a Presentence Investigation Report (hereinafter “PSR”). The PSR calculated a total offense level of 17, which included a three-level reduction for acceptance of responsibility. The offense level, together with a criminal history category of V, resulted in an advisory Guidelines range of forty-six to fifty-seven months’ imprisonment.

Mr. Valle-Martinez filed a motion for a downward variance pursuant to 18 U.S.C. § 3553(a) arguing that, to avoid unwarranted sentencing disparities, he was entitled to credit for the twenty-nine months he spent under a federal immigration de-tainer, after federal officials were aware of his illegal presence in the United States until they brought him into federal custody. The government did not object to a variance, but argued that Mr. Valle-Mar-tinez should receive a twelve-month rather than a twenty-nine-month variance.

At sentencing, the district court noted that under Tenth Circuit precedent the greater the deviation of the requested variance from the Guidelines range, the more weighty the justifications for the variance must be. In other words, there was a proportional relationship between the extent that a requested variance deviated from the Guidelines range and the magnitude of the reasons necessary to justify it. Additionally, the district court expressed its view that it could not justify more than a fifty percent variance from the bottom of the advisory Guidelines range based on a single § 3553(a) factor. After carefully weighing the § 3553(a) factors, the district court adopted the factual statements and Guidelines calculations in the PSR. The court concluded “that in consideration of all of the factors set forth in 18 U.S.C. Section 3553(a), including proportionality and the justness of the sentence, that a variant sentence is appropriate in this case.” R., Vol. II, Tr. at 16 (Sentencing Hearing Transcript, dated May 24, 2007).

The court imposed a sentence of thirty-four months’ imprisonment, “a sentence [the court found] and eonclude[d] is sufficient but not greater than necessary to comply with the purposes set forth in paragraph (2) of 18 U.S.C. Section 3553(a).” Id. at 17. The district court entered final judgment, and Mr. Valle-Martinez timely appealed.

II. DISCUSSION

Mr. Valle-Martinez challenges his sentence, asserting that the district court erred: (1) in concluding that it could not vary more than fifty percent from the low end of the advisory Guidelines range based solely on a single § 3553(a) factor; and (2) by engaging in a proportionality analysis in ruling on his variance request.

“We review [a] sentence for reasonableness, giving deference to the district court under the familiar abuse-of-discretion standard.” United States v. A.B., 529 F.3d 1275, 1277 (10th Cir.2008) (internal quotation marks omitted). There are procedural and substantive components of reasonableness. See, e.g., United States v. Atencio, 476 F.3d 1099, 1102 (10th Cir. 2007), overruled in part on other grounds by Irizarry v. United States, — U.S. -, 128 S.Ct. 2198, 2201 n. 1, 2203-04, 171 L.Ed.2d 28 (2008).

In Gall v. United States, — U.S. -, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007), the Court described instances of “significant procedural error, such as fading to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the § 3553(a) factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentence — including an explanation for any deviation from the Guidelines range.” Id. at 597 (emphasis added); see also United States v. Huckins, 529 F.3d 1312, 1317 (10th Cir.2008). As the Gall Court’s use of the phrase “such as” reflects, “[tjhis list of potential procedural errors is not exhaustive, and other procedural errors may be considered, as well.” United States v. Azure, 536 F.3d 922, 930 (8th Cir.2008).

The substantive component relates to the length of the sentence. See United States v. Hamilton, 510 F.3d 1209,1217-18 (10th Cir.2007), cert. denied, — U.S. -, 128 S.Ct. 1922, 170 L.Ed.2d 782 (2008) (“In evaluating the substantive reasonableness of a sentence, we ask whether the length of the sentence is reasonable considering the statutory factors delineated in 18 U.S.C. § 3553(a).”); Atencio, 476 F.3d at 1102 (“A substantively reasonable sentence ultimately reflects the gravity of the crime and the § 3553(a) factors as applied to the case.”).

Mr. Valle-Martinez emphatically disclaims any intention of challenging the substantive reasonableness of his sentence. See Aplt. Op. Br. at 17 n. 2 (“Mr. Valle-Martinez is not challenging the substantive reasonableness of his sentence.”); Aplt. Reply Br. at 7 (“Mr. Valle-Martinez does not argue that his sentence was substantively unreasonable----[He] is only arguing that the manner in which the sentence was arrived at involved error.”). We agree that Mr. Valle-Martinez’s contentions of error, which relate to the allegedly improper constraints that the district court imposed upon its sentencing discretion, are properly reviewed under the rubric of procedural reasonableness. Cf. United States v. Conlan, 500 F.3d 1167, 1169 (10th Cir. 2007) (recognizing so-called Begay error, a district court’s erroneous decision to limit its sentencing discretion by a presumption of reasonableness applied to the Guidelines range, as an instance of procedural error).

Because Mr. Valle-Martinez did not object at sentencing to the district court’s alleged procedural errors, we review for plain error. To secure relief under this demanding standard, he “must show: (1) an error, (2) that is plain, which means clear or obvious under current law, and (3) that affects substantial rights. If he satisfies these criteria, this Court may exercise discretion to correct the error if it seriously affects the fairness, integrity, or public reputation of judicial proceedings.” United States v. Goode, 483 F.3d 676, 681 (10th Cir.2007) (internal quotation marks omitted) (quoting United States v. Kimler, 335 F.3d 1132, 1141 (10th Cir.2003)).

We turn to Mr. Valle-Martinez’s first argument. After Gall, we do not employ a proportionality analysis in considering the propriety of variances. More specifically, “[w]e no longer require that ‘extraordinary’ circumstances justify a sentence outside the Guidelines range nor do we mathematically calculate the percentage variance from the Guidelines and use that percentage ‘as the standard for determining the strength of the justifications required.’ ” Huckins, 529 F.3d at 1317-18 (quoting Gall, 128 S.Ct. at 595). Thus, United States v. Garcia-Lara, 499 F.3d 1133, 1138-39 (10th Cir.2007), petition fin-cert. granted and judgment vacated by, — U.S. -, 128 S.Ct. 2089, 170 L.Ed.2d 814 (2008), and like pre-Gall variance cases from our circuit no longer apply. See United States v. Smart, 518 F.3d 800, 806-07 (10th Cir.2008). “[Ajlthough a district court must provide reasoning sufficient to support the chosen variance, it need not necessarily provide ‘extraordinary’ facts to justify any statutorily permissible sentencing variance, even one as large as [ ] 100%.... ” Id. at 807.

Nonetheless, the extent of the variance remains a consideration post-Gall. The district court’s justification for a variance must be “sufficiently compelling to support the degree of the variance.” Id. (quoting Gall, 128 S.Ct. at 597). Accordingly, the district court must “includ[e] an explanation for any deviation from the Guidelines range.” United States v. Muñoz-Nava, 524 F.3d 1137, 1147 (10th Cir.2008) (quoting Gall, 128 S.Ct. at 597). However, when considering a deviation from the Guidelines range, we “must give due deference to the district court’s decision that the § 3553(a) factors, on a whole, justify the extent of the variance.” Gall, 128 S.Ct. at 597.

Even assuming that our pre-Gall cases intimated that a sentencing court cannot reasonably base a sentence varying more than fifty percent from the low end of the Guidelines range on just one § 3553(a) factor, Gall dictates otherwise. In Gall, the Court noted that “[t]he District Court quite reasonably attached great weight to Gall’s self-motivated rehabilitation,” a single sentencing factor. Id. at 602. See also United States v. Williams, 526 F.3d 1312, 1322 (11th Cir.2008) (relying on Gall, stating: “A district court’s unjustified reliance on a single § 3553(a) factor may be a symptom of an unreasonable sentence. However, such a sentence is not necessarily unreasonable.” (emphasis added and citation and internal quotation marks omitted)); United States v. Pauley, 511 F.3d 468, 476 (4th Cir.2007) (disclaiming its pri- or case law in light of Gall “to the extent that our language ... suggests that a court cannot reasonably accord significant weight to a single sentencing factor in fashioning its sentence”).

Applying this precedent, we conclude that the district court committed procedural error, and that the error was clear and obvious under current law. Specifically, the district court erred in requiring more than one § 3553(a) factor to justify a variance more than fifty percent below the bottom of the advisory Guidelines range. Accordingly, Mr. Valle-Martinez has satisfied the first two prongs of the plain error test.

Moving to the third prong of plain error review, Mr. Valle-Martinez must demonstrate that the error affected his substantial rights. An error does not affect substantial rights unless it is prejudicial, meaning that there is “a reasonable probability that, but for the error claimed, the result of the proceeding would have been different.” United States v. Gonzalez-Huerta, 403 F.3d 727, 733 (10th Cir. 2005). More specifically, in the sentencing context, a defendant “can make this showing by demonstrating a reasonable probability that had the district court applied the [proper] sentencing framework, he would have received a lesser sentence.” United States v. Trujillo-Terrazas, 405 F.3d 814, 819 (10th Cir.2005).

Our review of the record does suggest that the sentencing court felt that its discretion to grant a variance was limited by our pre-Gall case law’s admonition to mathematically define the magnitude of the variance. And, when it determined that the requested variance fell nearer the “exceptional” end of the numerical, proportionality continuum, the court perceived itself to be further constrained to limit the scope of the variance, because only one § 3553(a) factor supported it. However, we need not definitively determine whether Mr. Valle-Martinez has satisfied the third prong of the plain error test. Even if we assume that he has carried his burden under this prong, Mr. Valle-Martinez cannot satisfy the fourth prong. See United States v. Nguyen, 413 F.3d 1170, 1184 (10th Cir.2005) (“[Assuming the [district court’s] comments satisfied the third prong, which we need not reach here — we conclude they do not support our requirements to notice plain error under the fourth prong.”); United States v. Soderst-rand, 412 F.3d 1146, 1155-56 (10th Cir. 2005) (“assuming” that defendant “could show that the sentencing below affected his substantial rights” but concluding that defendant failed to establish the fourth plain error prong).

“[C]ourts have held that sentencing error meets the fourth prong of plain-error review only in those rare cases in which core notions of justice are offended.” Gonzalez-Huerta, 403 F.3d at 739; see also United States v. Sierra-Castillo, 405 F.3d 932, 941-42 (10th Cir.2005) (“Gonzalez-Huerta establishes the principle that failing to correct non-Sixth Amendment Booker error when the defendant has failed to preserve the error in the district court will rarely be found to [have] seriously affected the fairness, integrity, or public reputation of judicial proceedings.”). The application of fourth-prong standards in post-Booker cases like Gonzalez-Huerta is particularly germane here because those cases addressed a situation that is analogous to the one alleged by Mr. Valle-Martinez — that is, one in which the district court erroneously (under the law at the time of appeal) viewed its sentencing discretion as being mandatorily constrained by the Guidelines. In one such case, we stated well the very rigorous nature of the defendant’s undertaking on plain error review:

Our analysis under this fourth prong when an error is non-constitutional is not flippant or perfunctory; the standard is formidable, as we will only exercise our discretion when an error is particularly egregious and the failure to remand for correction would produce a miscarriage of justice. A plain error affecting substantial rights cannot, without more, satisfy the fourth prong.

Trujillo-Terrazas, 405 F.3d at 820 (citations, internal quotation marks, and footnote omitted) (quoting Gonzalez-Huerta, 403 F.3d at 736, and United States v. Olano, 507 U.S. 725, 737, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993)). Mr. Valle-Martinez’s allegations of error do not raise constitutional issues. Accordingly these plain error principles are not applied under a “relaxed standard.” United States v. Dazey, 403 F.3d 1147, 1178 (10th Cir.2005); see United States v. Clark, 415 F.3d 1234, 1242 (10th Cir.2005) (“Because this case involves constitutional Booker error, we apply the fourth prong standard less rigidly”)-

Consequently, we have noted that in “a run of the mill case with non-constitutional Booker error .... [e]ven if a defendant can demonstrate that the district court felt particular sympathy for him, and might impose a lesser sentence on remand, failing to correct this type of plain error would not impugn the fairness, integrity, and public reputation of judicial proceedings.” Trujillo-Terrazas, 405 F.3d at 821 (emphasis added). In contrast, “[w]e have repeatedly held that where a defendant demonstrates a strong possibility of receiving a significantly lower sentence, the fourth prong is met.” United States v. Andrews, 447 F.3d 806, 813 (10th Cir.2006) (emphasis added); see also Clark, 415 F.3d at 1243 (reversing under plain error and noting “[w]e are not prepared to say that an unconstitutionally imposed sentence leading to three years’ additional incarceration is fair”). Cf. United States v. Brown, 316 F.3d 1151, 1161 (10th Cir.2003) (“A review of federal appellate decisions considering whether to correct unobjected-to sentencing errors reveals that the key concern has been whether correct application of the sentencing laws would likely significantly reduce the length of the sentence.” (emphasis added)).

Mr. Valle-Martinez makes two principal arguments in an attempt to carry his formidable burden. First, he claims that the error affected the fairness of his sentencing because it increased his burden of proving an entitlement to the requested twenty-nine month variance. Second, he asserts that the district court’s articulation of an incorrect ground for not granting the requested variance adversely impacts the integrity of the judicial system.

While these arguments are not without substance, we cannot conclude that they “implicate core notions of justice” or “the kind of fundamental fairness issues necessary to satisfy the fourth plain-error prong.” Sierrar-Castillo, 405 F.3d at 942. Even in the more aggravated context of non-constitutional Booker error — where the problem a defendant faced was not an erroneous, higher burden of proof to achieve a given sentence, but rather the district court’s erroneous view that the Guidelines put certain sentences off limits altogether — we have required more than a generalized claim of unfairness based on the difficulty of the defense’s forensic task. Cf. Andrews, 447 F.3d at 813 (noting, in the Booker context, “several non-exclusive factors” of a more concrete sort that are relevant to the fourth prong inquiry). Furthermore, it surely cannot be enough to satisfy the fourth prong of the plain error test for an appellant to establish that the district court articulated an invalid legal basis for its action. To be sure, such an articulation would likely provide the basis for satisfying the first two prongs of the test (i.e., that the error was clear and obvious). But it would not (without more) do anything to implicate core notions of justice associated with the fourth prong. See Trujillo-Terrazas, 405 F.3d at 820 (“A plain error affecting substantial rights cannot, without more, satisfy the fourth prong.” (internal quotation marks omitted)). Accordingly, Mr. Valle-Martinez’s arguments are unavailing.

In any event, Mr. Valle-Martinez cannot successfully carry his burden under the fourth prong because, even if we assume that the district court would be inclined to impose a lesser sentence on remand, Mr. Valle-Martinez cannot establish that the district court would likely impose a significantly lesser sentence.

The district court indicated its “rough satisfaction with [Mr. Valle-Martinez’s] sentence [which] weighs against noticing plain error under the fourth prong.” United States v. Johnson, 414 F.3d 1260, 1265 (10th Cir.2005). The district court carefully balanced the § 3553(a) factors, considering the nature and circumstances of the offense, and Mr. Valle-Martinez’s history and characteristics — including the fact that, unlike other similarly situated immigrants who have lived law-abiding lives, Mr. Valle-Martinez had committed multiple felonies. Furthermore, working to Mr. Valle-Martinez’s benefit, the district court gave salience in its § 3553(a) analysis to the possibility that had the government immediately taken him into federal custody, Mr. Valle-Martinez could have served his federal and state sentences concurrently. More specifically, the district court stated:

It’s a very difficult decision. I think in light of what I’ve just reviewed a variance of 24 months cannot be justified as reasonable. To render the sentence a just one I think — and this is I think peripherally related to proportionality, some relief is warranted because the federal government really waited 28, 29 months before bringing the case to this Court, precluding any consideration for concurrent sentencing. Whether or not a judge would have sentenced concurrently, partially concurrently, or not, is frankly an open question.
What the result however is, is that there has been no opportunity tb make the case for some form of concurrent sentencing, and to close that door, so that the result at this point in time, given solely the advice of these Sentencing Guidelines, which takes into consideration these other factors, would be a sentence of 46 months on top of the time he’s already served in state court, without any credit that could be afforded by the Bureau of Prisons on the sentence to be imposed in this case. So to be a just sentence some relief I think is appropriate.
I find ... and conclude that in consideration of all of the factors set forth in 18 U.S.C. Section 3553(a), including proportionality and the justness of the sentence, that a variant sentence is appropriate in this case.

R., Vol. II, Tr. at 15-16.

The district court concluded that a sentence of thirty-four months was “sufficient but not greater than necessary to comply with the purposes ... of 18 U.S.C. Section 3553(a).” Id. at 17. This is significant evidence that the district court would not be inclined to impose a significantly lesser sentence were we to remand for resentenc-ing. See Johnson, 414 F.3d at 1265.

Furthermore, because this case does not involve “obvious calculation errors,” which “[o]ur case law shows ... will be noticed more freely on plain error review,” we cannot say with any precision the extent of any adverse sentencing impact Mr. Valle-Martinez suffered because of the district court’s erroneous view regarding the scope of its sentencing discretion. Id. Cf. United States v. Hill, 239 Fed.Appx. 460, 463 (10th Cir.2007) (unpublished) (“exercis[ing] our discretion to correct” an error resulting in a sentence at least twenty-two months above the Guidelines maximum); United States v. Herrera, 286 Fed.Appx. 546, 560 (10th Cir.2008) (unpublished) (“Defendant-Appellant’s base offense level was substantially increased”; thus, “there is a reasonable likelihood that were this court to vacate the sentence and remand, a significantly lower sentence would result.”).

Accordingly, under the foregoing rationale, we conclude that Mr. Valle-Martinez has failed to satisfy the fourth prong of the plain error test.

As for his second argument that the district court erred by applying our pre-Gall proportionality analysis in assessing his variance request, as discussed above, under current law the district court did indeed err in performing its variance analysis and the error is clear and obvious. However, Mr. Valle-Martinez has acknowledged that he advanced this argument preGall merely “to preserve the issue for further review.” Aplt. Op. Br. at 18. Significantly, he has not articulated a discrete plain error analysis as to this second argument. In particular, apart from his contentions concerning the first argument, Mr. Valle-Martinez had not attempted to “explain how this error meets” the third and fourth prongs of the plain error test. Muñoz-Nava, 524 F.3d at 1147. Thus, Mr. Valle-Martinez “has not met his burden and we cannot conclude the district court plainly erred.” Id.

Finally, Mr. Valle-Martinez argues that the aggregation of the two sentencing errors warrants reversal under the cumulative error doctrine. “The [] point of [cumulative error] review, is to examine all the actual errors which are individually harmless to determine if together they render” the sentencing unfair. Hamilton v. Mullin, 436 F.3d 1181, 1196 (10th Cir. 2006). “The harmlessness of cumulative error is determined by conducting the same inquiry as for individual errors— courts look to see whether the defendant’s substantial rights were affected.” United States v. Sarracino, 340 F.3d 1148, 1169 (10th Cir.2003) (internal quotation marks omitted) (quoting United States v. Rivera, 900 F.2d 1462, 1470 (10th Cir.1990) (en banc)). We conclude that in the aggregate the two unrecognized plain errors identified by Mr. Valle-Martinez did not affect his substantial rights. Mr. Valle-Martinez is simply unable to establish that the district court would impose a significantly lighter sentence on remand. We thus conclude that reversal is not warranted.

Because we conclude that any procedural error by the district court should not be recognized under plain error review, we AFFIRM Mr. Valle-Martinez’s sentence. 
      
       This Order and Judgment is not binding precedent, except under the doctrines of law of the case, res judicata, and collateral estoppel. It may be cited, however, for its persuasive value consistent with Fed. R.App. P. 32.1 and 10th Cir. R. 32.1. After examining the briefs and the appellate record, this three-judge panel has determined unanimously that oral argument would not be of material assistance in the determination of this appeal. See Fed. R.App. P. 34(a); 10th Cir. R. 34.1(G). The case is therefore ordered submitted without oral argument.
     
      
      . Specifically, after asking counsel the length of the requested variance, the district court engaged in the following dialogue with him:
      [THE COURT:] This case I think has to be viewed in light of Tenth Circuit authority, which looks at variant sentences as to levels of how variant they may be — exceptional, I suppose modest, and then there is some range in between.... The further you vary from [the bottom of the Guidelines] range, the more exceptional the circumstances have to be.
      And the Tenth Circuit has said I think most recently that reliance upon one of the statutory factors alone is inadequate to justify a variance.... Reliance on one statutory factor alone, in this case the proffered statutory factor is that of disparity, is inadequate reason to justify the variance.
      ... [T]he latest case seems to say to me that if I were to vary more than 50 percent simply on the one factor of disparity, it would not be a reasonable sentence.
      [DEFENSE COUNSEL:] I mean certainly it says that if you’re going to vary to an exceptional degree that it should be based on more than one factor or that it can’t be based on one factor. But I mean to the extent it doesn't line out what an exceptional degree is and set forth—
      THE COURT: More than 50 percent is approaching that.
      R., Vol. II, Tr. at 3-6.
     
      
      . In his opening brief which was filed prior to the Supreme Court’s opinion in Gall v. United States, - U.S. -, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007), Mr. Valle-Martinez further argued that the district court erred by characterizing his requested variance as “exceptional,” thus requiring extraordinary circumstances to justify it. The nomenclature of proportionality analysis upon which this argument is premised, however, does not survive Gall. Id. at 594. Therefore, we need not address the argument. Mr. Valle-Martinez acknowledges this. See Aplt. Reply Br. at 7 n. 1 (“Because Gall eliminated such appellate court labeling of non-Guideline sentences, this Court need not decide whether the district court was correct that this Court would view the request as ‘exceptional.’ ”).
     
      
      . See generally United States v. Begay, 470 F.3d 964, 975-76 (10th Cir.2006), rev’d on other grounds, - U.S. -, 128 S.Ct. 1581, 1588, 170 L.Ed.2d 490 (2008).
     
      
      . See generally United States v. Booker, 543 U.S. 220, 259-60, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005).
     
      
      . The court observed that seven years earlier Mr. Valle-Martinez had committed his first drug felony, at the age of nineteen. Moreover, after he was convicted and deported, he illegally re-entered the United States and later committed two more drug felonies prosecuted by the State of Colorado.
     
      
      . The government notes that ”[t]he district court apparently meant 29 months, the full amount of the variance requested by Mr. Valle-Martinez.” Aplee. Br. at 15 n. 3. The government may be correct; however, the matter is immaterial to our resolution of this appeal, so we need not express a definitive view on the subject.
     