
647 F.3d 1021 (2011)
UNITED STATES of America, Plaintiff-Appellee,
v.
Camille Suzanne LENTE, Defendant-Appellant.
No. 10-2194.
United States Court of Appeals, Tenth Circuit.
July 29, 2011.
*1023 Benjamin A. Gonzales, Assistant Federal Public Defender, Albuquerque, NM, for Appellant.
Andrea W. Hattan, Assistant United States Attorney (Kenneth J. Gonzales, United States Attorney with her on the brief), Las Cruces, NM, for Appellee.
Before GORSUCH, HOLLOWAY, and MATHESON, Circuit Judges.
MATHESON, Circuit Judge.
Camille Suzanne Lente challenges her sentence as procedurally and substantively unreasonable. Ms. Lente killed three young men and seriously injured a young woman in a car accident that occurred when she was driving while intoxicated. She entered a guilty plea to three counts of involuntary manslaughter and one count of assault resulting in serious bodily injury.[1] She was originally sentenced to 216 months (18 years) in prison, a significant upward variance from her proposed Guidelines range of 46 to 57 months' imprisonment. A divided panel of this court vacated her sentence and remanded for resentencing in a per curiam, unpublished decision with no majority opinion. See United States v. Lente, 323 Fed.Appx. 698, 699 (10th Cir.2009).[2] On resentencing, a *1024 different district court judge sentenced Ms. Lente to 192 months (16 years) in prison. She now appeals from her resentencing. We conclude the district court's failure to address Ms. Lente's argument about the need to avoid unwarranted sentencing disparities constitutes reversible procedural error. Exercising our jurisdiction pursuant to 28 U.S.C. § 1291 and 18 U.S.C. § 3742(a)(3), we reverse and remand.

I. BACKGROUND

A. Factual Background

The following factual background is taken from Judge Holmes's opinion in Ms. Lente's first appeal.
On the night of December 2, 2005, after consuming between 13 and 19 beers, Ms. Lente drove her mother's Chevrolet Suburban on the Isleta Indian Reservation, which is located in New Mexico. At approximately 10:40 p.m., her Suburban, which was northbound, crossed the center line of the highway into the southbound traffic lane, causing a head-on collision with a Ford Ranger truck, driven by Jessica Murillo. Ms. Lente's passenger in the Suburban, Anthony Tewahaftewa, and the two passengers in the Ford Ranger, Andres Murillo and Joshua Romero, were declared dead at the scene. Ms. Murillo survived, but sustained fractures to her right femur, right shoulder, and right ankle, and received numerous facial lacerations. Ms. Lente suffered two broken ankles and a dislocated hip. Ms. Murillo and Ms. Lente were transported to a hospital. . . . Two hours after the accident, a blood sample was taken from Ms. Lente. Ms. Lente's blood alcohol level ("BAL") was 0.21-over two times the New Mexico legal limit of .08-and marijuana was present in her system.
Lente, 323 Fed.Appx. at 699-700 (Holmes, J., concurring). Ms. Lente was twenty-two years old on the night of the accident.
At her resentencing, Ms. Lente introduced the following undisputed evidence about the circumstances leading up to the accident. According to interviews taken after the accident, Ms. Lente and Mr. Tewahaftewa had been drinking together that day. They ended up at the home of Elaine Jojola where she and Ms. Lente's mother, Nancy Abeita, had been drinking. According to Ms. Jojola, Mr. Tewahaftewa was trying to kiss and hug her and was boisterous and talking about gangs. She disliked his behavior. She called his sister to come for him, but the sister refused. Ms. Jojola told Mr. Tewahaftewa to leave, but he refused. Ms. Abeita gave Ms. Lente the keys to her car and told her daughter to drive Mr. Tewahaftewa home.

B. Procedural Background

We present the procedural history in some detail as a necessary predicate to the analysis of procedural error.
Ms. Lente was charged with three counts of involuntary manslaughter in violation of 18 U.S.C. §§ 13, 1153, and 1112, and one count of assault resulting in serious bodily injury in violation of 18 U.S.C. §§ 1153 and 113(a)(6). She entered into a plea agreement and pleaded guilty to all four counts in the indictment. The government stipulated that Ms. Lente had accepted responsibility, which entitled her to a three-level reduction in her base offense level.


*1025 1. The First Sentencing

The Presentence Report ("PSR") computed an advisory Guidelines range of 46 to 57 months. For each of the three involuntary manslaughter convictions, the PSR assigned a base offense level of 22 under U.S.S.G. § 2A1.4. Twenty-two is the highest base offense level under that provision and is reserved for those instances in which "the offense involved the reckless operation of a means of transportation." U.S.S.G. § 2A1.4(a)(2)(B). The assault carried a base level of 14, which was adjusted by six levels to a level of 20 based on the severity of Ms. Murillo's injuries. There were no further adjustments.
The PSR then assessed an additional four-level adjustment for Ms. Lente's multiple victims. See U.S.S.G. § 3D1.4. The Guidelines instruct that this four-level adjustment is added on to the highest offense level (22 in this case), which resulted in an offense level of 26. The PSR computed a three-level reduction for acceptance of responsibility, resulting in a total offense level of 23. The PSR placed Ms. Lente in a criminal history Category I. Ms. Lente's Guidelines range was 46 to 57 months.
The PSR found no grounds for a departure, stating: "After assessing the defendant's criminal history and social history, she does not appear to have any circumstances that would take her away from the heartland of cases of similarly situated defendants." R. Vol. 2 at 29 ¶ 101. The PSR did, however, recommend an upward variance. A Guidelines sentence, it stated, would not reflect the seriousness of Ms. Lente's crimes, provide just punishment, promote respect for the law, or deter Ms. Lente from committing further criminal acts.
The government filed a pre-sentencing motion for an upward departure or an upward variance, concurring with the PSR's recommendations. The district court sentenced Ms. Lente to three consecutive 72-month sentences for the three counts of involuntary manslaughter, which was the maximum sentence Ms. Lente could receive for these counts. The court also imposed a concurrent term of 120 months for the assault count. The final sentence was 216 months' imprisonment (18 years). Ms. Lente appealed. This court, with no majority opinion, vacated her sentence and remanded for resentencing by a different district court judge.

2. Briefs on Remand

Ms. Lente renewed and supplemented her objections to the PSR and asked for a sentence within the Guidelines range. She argued that "[t]he need to avoid unwarranted sentencing disparities among defendants with similar records convicted of similar crimes, a required consideration under 18 U.S.C. § 3553(a)(6), supports a sentence within the guideline range." R. Vol. 1 at 151. She summarized her review of federal sentencing practices in manslaughter cases from 2001 to 2009. Ms. Lente noted that her "previous sentence of 216 months was grossly above other manslaughter sentences," based on examining other above-Guidelines sentences for manslaughter during the nine-year period. Id. at 152. Ms. Lente also reviewed sentences from other cases with similar offenders and similar offenses, noting that all of the defendants in those cases received sentences much lower than her sentence. When there was an upward departure or variance, it was moderate compared to the increase urged in her case. She concluded by arguing that the
history and pattern of sentencing for manslaughter offenses support a conclusion that the Sentencing Commission formulated reasonable guidelines for the offense that satisfy the § 3553 goals in the overwhelming majority of cases. *1026 Thus, sentencing within those guidelines meets the need to avoid unwarranted sentencing disparities among defendants with similar records and convicted of similar offenses.
Id. at 155-56.
The government argued that the § 3553(a) factors "[o]verwhelmingly [w]arrant [a]n [u]pward [v]ariance." Id. at 207. The government analyzed all of the § 3553(a) factors, but focused primarily on the nature and circumstances of the offense, see § 3553(a)(1), emphasizing that Ms. Lente consumed an excessive amount of alcohol, drove without a driver's license, had a high blood alcohol content ("BAC") of .21, and killed three people, including a twelve-year-old boy.
With respect to § 3553(a)(6) and the need to avoid unwarranted sentencing disparities, the government argued that Ms. Lente's conduct "caused so much destruction and was so outrageous that [her] case simply does not compare to other drunk-driving related fatalities." Id. at 213. The government reiterated that Ms. Lente had a high BAC and that she killed three people, which is "much more than the `typical' involuntary manslaughter case." Id. at 214. The government concluded that "to sentence [Ms. Lente] significantly above the guideline range and instead up towards the statutory maximum allowable by law poses little risk of a disparity with other like-criminals, as [Ms. Lente] is wholly in a category of her own." Id.

3. Re-sentencing Hearing

On July 22, 2010, the court heard further testimony and argument by the parties. The government said it did not want to "rehash all of the argument that both sides have already presented," but it did want to "provide [the court] with some additional points and . . . tools [to] use in crafting the appropriate decision in this case." R. Vol. 3 at 91. It started by highlighting the § 3553(a)(6) sentencing-disparity issue, noting that it was "one particular factor that [the court] must consider," and asserting that the cases presented by Ms. Lente were distinguishable because they were "pre-Booker"[3] cases. Id. at 91-92. The government compared Ms. Lente's case to Pettigrew, a "post-Booker" case in which the district court departed upward from the Guidelines range of 70 to 87 months to impose a sentence of 126 months for one count of involuntary manslaughter, two counts of assault resulting in serious bodily injury, and one count of misdemeanor assault.[4] The government argued that the "discrepancy" between the ten years in Pettigrew and the eighteen years it was requesting in this case "doesn't seem like much when here we have two additional people who lost their lives due to Ms. Lente's conduct." Id. at 94.
Ms. Lente also opened her argument with the sentencing-disparity issue. Counsel began by reading a letter from the director of the Office of Policy and Legislation for the U.S. Department of Justice, Criminal Division to Judge Sessions, the head of the United States Sentencing Commission:
In our consideration of federal sentencing policy, we begin from the principle that offenders who commit similar offenses and have similar criminal histories should be sentenced similarly. This was the foundational principle of the Sentencing Reform Act of 1984. We are concerned that our sentencing system *1027 may be meeting this principle of sentencing reform less and less.
Id. at 168-69. Counsel explained that "this principle is what the debate today is all about." Id. at 169. He claimed that, in this case, the government was inviting the district court "to move away from Congress's goal of sentencing uniformitythat goal being avoiding unwarranted disparities among defendants with similar records found guilty of similar conduct." Id. at 172.
Ms. Lente argued that the government was ignoring the facts of comparable casesWolfe, Jones, and Whiteskunk.[5] She asserted that other similarly situated defendants did not receive sentences significantly outside the Guidelines for their offenses, yet the government was asking the court to impose a sentence that was almost twice what the defendant in Pettigrew received, noting that "he got the highest sentence of all, and he had almost the worst criminal history of all." Id. at 193. She concluded by arguing that "under all the circumstances, a sentence of 57 months in this case is sufficient but not greater than necessary, and it is not in disparity with people who have committed similar crimes like this who have similar criminal histories and backgrounds." Id. at 194.

4. Second Sentencing Decision

At the close of the sentencing hearing, the district court took the matter under advisement. The court subsequently issued a written decision. The first half of the decision recounts the factual and procedural background. See R. Vol. 1 at 425-435. The court noted that it was "resentencing on a clean slate" because there was no consensus on the Tenth Circuit panel as to the reasons for remand. Id. at 437. Agreeing with the government's request to vary upward, the court concluded that the Guidelines range of 46 to 57 months was "woefully inadequate to accomplish the goals of sentencing in this case," because "the Guidelines do not appropriately capture the seriousness of [Ms.] Lente's offense." Id. at 440.[6] The court stated that "after carefully considering all the statutory factors set forth in 18 U.S.C. § 3553(a), I find that a sentence of 192 months is sufficient, but not greater than necessary to accomplish the goals of sentencing." Id. The court then explained its reasoning.

a. Underrepresented criminal history

First, the court found that the Guidelines did not adequately represent Ms. Lente's criminal history because she did not receive any criminal history points for her five prior tribal convictions. The court noted that four of the five convictions involved the use of alcohol and all involved violent and/or reckless behavior. It concluded that "[t]hese prior convictions show a pattern of alcohol abuse and reckless behaviora pattern that led to [Ms.] Lente's decision to drink 13 to 19 beers on December 2, 2005 and drive on State Road 47." Id. at 441.
Because three of the five convictions occurred when Ms. Lente was a juvenile, the court did not rely on them to enhance Ms. Lente's sentence. But the court found *1028 it "entirely appropriate to enhance Lente's sentence on the basis of her two adult tribal convictionsone for assault and battery and one for disorderly conduct." Id. The court noted further that if the convictions had occurred in state or municipal court, her Guidelines range would have increased to 57 to 71 months. The court concluded it would be "highly unjust" for Ms. Lente "to avoid[ ] the consequence[s] of these prior convictions merely because they occurred in tribal court." Id.

b. Failure of Guidelines to account adequately for each additional victim

Second, the court found that the Guidelines did not adequately account for Ms. Lente's offense causing multiple deaths. Under the Guidelines' grouping rules, Ms. Lente was assessed four units for her four convictions (three involuntary manslaughter and one assault resulting in serious bodily injury), which resulted in a four-level increase to her Guidelines range. See U.S.S.G. § 3D1.4. The district court noted that "[i]n accordance with these rules, the bottom end of Lente's sentencing range was increased by 5-6 months for each of her four victims." R. Vol. 1 at 442. The court concluded that 5 or 6 months did not adequately represent the value of each of these young lives.
The court stressed it was not finding the Guidelines are categorically inadequate at accounting for the value of the victims' lives. It explained that the Guidelines may be adequate when there is one victim or when the victim or victims shared some minor culpability (e.g., the victims themselves were intoxicated or willfully rode in a car with an intoxicated driver). But here, where the victims are "entirely blameless," the court concluded that "the Guidelines do not sufficiently enhance a defendant's sentence for these additional victims." Id. at 443.
Finally, the court noted that the government had proffered data showing the rarity of drunk driving offenses that result in three deathsin 2005, the average number of fatalities per drunk-driving related crash was 1.16. Ms. Lente killed almost three times as many people as the average and seriously injured another. The court stated that "[t]hese statistics help show the tragic nature of this particular crash. . . [and] they help illustrate why the 5-6 month enhancement provided by the Guidelines for each victim insufficiently represents the unusual violence of this crime." Id.

c. Presence of additional factors demonstrating extreme recklessness

Third, the court said there were additional factors that demonstrate Ms. Lente's "extraordinary recklessness and show why this case is outside the `heartland' of cases contemplated by the Guidelines." Id. The court gave three examples: (1) Ms. Lente's excessively high BAC; (2) driving without a valid New Mexico driver's license; and (3) driving on State Road (SR) 47, a well-traveled road just outside of Albuquerque.
The court first noted Ms. Lente's .21 BAC measured two hours after the crashover two-and-a-half times the New Mexico legal limit of 0.8. The court further noted that Ms. Lente's BAC was "significantly over the statewide average" in drunk driving cases, citing to 2005 statistics showing that .16 was the mean BAC for drunk drivers in New Mexico. Id. at 444.
Second, the court observed that Ms. Lente had never held a valid New Mexico driver's license. "While I acknowledge that the lack of a driver's license does not *1029 necessarily correlate with a lack of driving experience, it certainly suggests that [Ms.] Lente has never had any formal driving training." Id. The court also said that Ms. Lente's decision to drive without a valid driver's license "demonstrates [her] further disregard for the law." Id.
Finally, the court noted that SR 47 is well-traveled and the crash occurred in the Isleta Pueblo, just twelve miles outside of the city of Albuquerque. The court said Ms. Lente must have been aware of these road characteristics because she had lived in this area her whole life and yet "still chose to drive while highly intoxicated on this well-traveled road." Id. at 445.

d. Sentencing goals

Finally, the court found that the Guidelines sentence of 46 to 57 months does not achieve the sentencing goals set forth in 18 U.S.C. § 3553 because it does not reflect the seriousness of the offense, and it would not adequately deter Ms. Lente from future criminal conduct nor protect the public from Ms. Lente. The court noted that Ms. Lente's "criminal history shows a repeated willingness to drink to excess and engage in reckless behavior, often endangering the safety of others. Despite multiple terms of imprisonment by tribal authorities[7] and five separate terms of probation, [Ms.] Lente has continued to engage in such reckless behavior." Id. Accordingly, the court found that a "substantial sentence is necessary to deter Lente from future offenses and to protect the public." Id. at 446.

5. The Sentence

To arrive at the sentence of 192 months, the district court imposed a term of 72 months for each of the involuntary manslaughter counts (72 months is the statutory maximum for involuntary manslaughter). Two of the 72-month terms, for Joshua Romero and Andres Murillo (the passengers in the other car), were set to run consecutively.[8] The other 72-month term, which related to Anthony Tewahaftewa (the passenger in Ms. Lente's car), was split so that 48 months was set to run consecutively, while the remaining 24 months was set to run concurrently. The court explained that it was running the sentence related to Mr. Tewahaftewa partially concurrent because, although Mr. Tewahaftewa had been the victim of involuntary manslaughter, he had engaged in risky behavior by consuming alcohol with Ms. Lente and then choosing to ride in the car with her. In contrast, "[t]he other three victims . . . did not engage in any risky behavior whatsoever and, tragically, just happened to be at the wrong place at the wrong time." Id. at 446 n. 9. The court also imposed a term of 120 months for the assault on Jessica Murillo (the driver of the other car) resulting in serious bodily injury. That 120-month term was set to run concurrently.

6. Objections to the Sentence

Ms. Lente filed written objections to the district court's sentencing decision. She lodged various procedural objections, including the court's reliance upon the frequency of traffic on SR 47 and other features regarding the location of the accident, *1030 failure to address mitigating circumstances leading to the accident, and "failure to address 18 U.S.C. § 3553(a)(6), the need to avoid unwarranted sentencing disparities among defendants with similar records," noting that "[s]he ha[d] made extensive argument to the court on this point." R. Vol. 1 at 362.
The court held a hearing on the objections. The main focus was on SR 47 as an aggravating factor. Ms. Lente claimed she had no notice it would be used to support an upward variance. She further complained the court improperly inferred that the road was well-traveled at the time of the accident and that she was aware of that fact. After the hearing, the court entered a written order sustaining in part and overruling in part Ms. Lente's objections. The court issued an amended decision to reflect slight modifications or deletions to four statements. The sentence remained the same. Ms. Lente appealed.

II. DISCUSSION
Ms. Lente argues that the district court imposed a procedurally and substantively unreasonable sentence. We review the district court's sentencing decision under an abuse of discretion standard. Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007). Our review proceeds in two steps. First, we must "ensure that the district court committed no significant procedural error." Id. If the district court's decision is "procedurally sound," we move on to the second step and "consider the substantive reasonableness of the sentence imposed." Id. Because we do not reach the substantive reasonableness of a sentence if there is reversible procedural error, we will address Ms. Lente's procedural challenges first. See United States v. Cerno, 529 F.3d 926, 937 (10th Cir.2008), cert. denied ___ U.S. ___, 129 S.Ct. 1905, 173 L.Ed.2d 1061 (2009) ("Only if the district court follows sound procedure may we then consider whether the resulting sentence is reasonable in substance."); id. at 940 ("[B]ecause [defendant] must be sentenced anew, we do not reach his challenge to the substantive reasonableness of his present sentence.").
In general, a procedural challenge relates to the "method by which the sentence is calculated." United States v. Wittig, 528 F.3d 1280, 1284 (10th Cir.2008), cert. denied, ___ U.S. ___, 129 S.Ct. 1985, 173 L.Ed.2d 1083 (2009). The Supreme Court has identified the following procedural errors: "failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the § 3553(a) factors, [and] selecting a sentence based on clearly erroneous facts." Gall, 552 U.S. at 51, 128 S.Ct. 586. A procedural challenge is also proper when the district court has "fail[ed] to adequately explain the chosen sentenceincluding an explanation for any deviation from the Guidelines range." Id. "[A] major departure should be supported by a more significant justification than a minor one." Id. at 50, 128 S.Ct. 586. A substantive challenge concerns the reasonableness of the sentence's length and focuses on the district court's consideration of the § 3553(a) factors and the sufficiency of the justifications used to support the sentence. See Wittig, 528 F.3d at 1284-85.

A. Identifying Procedural Challenges

With this framework in mind, we turn to what Ms. Lente argues are procedural errors: (1) increasing her sentence based on features of SR 47; (2) increasing her sentence because the offense was unusually reckless, and failing to address circumstances of the accident that mitigated the level of her recklessness; (3) increasing the sentence because three people died; (4) failing to address the impact of Ms. *1031 Lente's disadvantaged background on her criminal history and failing to explain how her history bore the weight of the variance; (5) failing to address the disparity between the court's sentence and those of similar offenses and offenders; (6) failing to explain the court's rejection of uncontradicted evidence of Ms. Lente's positive potential for rehabilitation.
Although Ms. Lente characterizes all of these issues as affecting the procedural reasonableness of her sentence, some of them are actually substantive reasonableness challenges. Our preliminary task is to identify the procedural challenges.
(1) Ms. Lente argues that the district court violated her procedural due process rights by "basing its sentence on irrelevant facts and unproven assumptions that on the night and place of the accident, the road was busy and [she] knew it was, and by not allowing her to challenge meaningfully the bases for the court's assumptions." Aplt. Br. at 23. This is a proper procedural argument because it challenges the district court's method of fact-finding on a fact that it used to increase her sentence.
(2) Ms. Lente argues that the court erred by (a) increasing her sentence based on her "extraordinary recklessness" due to her high BAC of .21 and her driving without a license and (b) failing to address her argument that the circumstances leading to the accident mitigated against a finding of extraordinary recklessness. The second part is a proper procedural challenge to the court's failure to adequately explain her sentence by not addressing her material, non-frivolous argument. See United States v. Pinson, 542 F.3d 822, 833-834 (10th Cir.2008).
The first part of her argument, however, challenges the substantive reasonableness of her sentence. Although she argues it is procedural error to rely on an irrelevant factor, her BAC and lack of a driver's license are not irrelevant factors and concern the circumstances of her offense. See 18 U.S.C. § 3553(a)(1). Her true objection is to the weight that the court placed on these factors to support its "extraordinary recklessness" determination. A challenge to the sufficiency of the justifications for the sentence is a substantive reasonableness challenge. See Wittig, 528 F.3d at 1284-85.
(3) Ms. Lente argues that the district court erred in increasing her sentence because three people died. She contends it was procedural error for the court to give inadequate explanation of its policy disagreement with the Guidelines. Although the absence of explanation could constitute procedural error, see, e.g., United States v. Merced, 603 F.3d 203, 217-219 (3d Cir.2010), the court did give a procedurally adequate explanation for why it disagreed with the Guidelines. Ms. Lente's true complaint is with the substance of that explanation, i.e., whether the district court presented a persuasive reason for disagreeing with the Guidelines. This challenge speaks to substantive reasonableness.
(4) Ms. Lente argues that the district court failed to address the impact of her disadvantaged background on her criminal history. But she admits that the district court summarized Dr. Rapoport's testimony about her upbringing, and that the court concluded her abusive background did not support mitigating her sentence. See Aplt. Br. at 35 (citing R. Vol. 1 at 434-35; id. at 440 n. 5). The court's statement that "the testimony of Dr. Rapoport. . . did not give me any reason to mitigate [Ms. Lente's] sentence," R. Vol. 1 at 440 n. 5, indicates no procedural shortcoming. Ms. Lente's true challenge appears *1032 to be to the district court's balancing of her background characteristics and her criminal history and the weight the court gave to those factors. This is a substantive, not procedural, challenge. See, e.g., Pinson, 542 F.3d at 835-36 ("[T]he weight the district court places on certain factors is reviewed for substantive unreasonableness.").
(5) Ms. Lente asserts that the district court failed to address her § 3553(a)(6) argument about the disparity between her sentence and those of similar offenses and offenders. This is a proper procedural challenge that we will address at some length below.
(6) Ms. Lente argues that the district court failed to explain its rejection of uncontradicted evidence of her potential for rehabilitation, citing to testimony from Dr. Rapoport that, in his opinion, her depression could be successfully treated through medication.
The court gave somewhat inconsistent statements about Dr. Rapoport's testimony. Compare R. Vol. 1 at 440 n. 5 (acknowledging Dr. Rapoport's opinion that Ms. Lente could be treated successfully and stating that the court had "no reason to doubt Dr. Rapoport's assessment") with id. (stating that the court had "no credible evidence suggesting that Lente is particularly amenable to treatment"). But the court adequately explained that Dr. Rapoport's assessment that Ms. Lente's "depression (and, accordingly, her alcoholism) could be treated successfully" did not "lessen[] [her] culpability for her crimes nor does it detract from the horrific nature of her crimes." Id. And the district court acted consistently with Dr. Rapoport's assessment by recommending Ms. Lente for mental health treatment. See id. ("[G]iven Dr. Rapoport's assessment, I have recommended to the Bureau of Prisons that [Ms.] Lente undergo mental health treatment while she serves her sentence.").
There is no procedural issue here. Rather, Ms. Lente's true complaint is that the district court should have given more weight to her amenability to treatment when considering § 3553(a)(2). See Aplt. Br. at 39. But that argument speaks to the substantive reasonableness of her sentence, not to procedural error.

B. Procedural Error Analysis

The Supreme Court has instructed appellate courts to "ensure that the district court committed no significant procedural error." Gall, 552 U.S. at 51, 128 S.Ct. 586. Having sorted through Ms. Lente's arguments, we are left with three procedural challenges: improper fact-finding about SR 47, failure to address mitigating circumstances on recklessness, and failure to address the need to avoid unwarranted sentencing disparities. We address them in order of significance.

1. Failure to address the § 3553(a)(6) sentencing-disparity argument

Ms. Lente argues the district court committed procedural error when it failed to address her argument that the government's proposed variant sentence of 18 years would create unwarranted sentencing disparities with sentences of similar offenses and offenders. This was Ms. Lente's main argument for a within-Guidelines sentence. The parties devoted substantial briefing and oral argument to this issue before the district court. See, e.g. R. Vol. 1 at 131-132, 138, 141, 151-56 (Ms. Lente's Objections to the PSR); id. at 213-214 (Government's Memorandum in Response to the PSR); id. Vol. 3 at 91-94, 202, 207-210 (Government's argument at sentencing hearing); id. at 168, 172-73, 191-93, 211 (Ms. Lente's argument at sentencing *1033 hearing); id. Vol. 1 at 351-52, 358, 362 (Ms. Lente's Sentencing Objections).
Ms. Lente submitted Sentencing Commission data to the district court on manslaughter sentences from 2001 to 2009. The data aggregate sentences for both involuntary and voluntary manslaughter, so the sentences themselves are probably higher than they would be if only involuntary manslaughter were the data set. To put Ms. Lente's sentence in context, the year with the highest median percentage increase over the maximum end of the Guidelines range was 2004 at 68.6 percent. Ms. Lente's sentence was 237 percent above the end of the range. The year with the highest median number of months above the maximum end of the range was 2009 at 49.05 months. Ms. Lente's sentence was 135 months above the end of the range. The highest average sentence was 65.8 months in 2009. Ms. Lente's sentence was 192 months.
The data on manslaughter non-departure upward-variance sentences after Booker from 2005 to 2009 add further perspective. The average portion of such cases per year was eight percent. The average median percentage increase was 43.1 percent (237 percent for Ms. Lente). The average median number of additional months was 24 (135 for Ms. Lente). Over the past five years, an upward variance that exceeded 43 percent occurred in only four percent of all manslaughter cases, and an increase of over 24 months above the Guidelines occurred in only four percent of such cases.
In addition, Ms. Lente presented to the district court comparative involuntary manslaughter cases and argued that the defendants in these cases with more serious criminal histories received much lower sentences than Ms. Lente received in her first sentencing. See United States v. Pettigrew, 468 F.3d 626 (10th Cir.2006) (126 months for involuntary manslaughter, two assaults causing serious injury, and misdemeanor assault from DUI accident; criminal history included second degree murder); United States v. Jones, 332 F.3d 1294 (10th Cir.2003) (71 months for three counts of involuntary manslaughter from DUI accident; criminal history included five prior DUI convictions); United States v. Whiteskunk, 162 F.3d 1244 (10th Cir. 1998) (24 months for involuntary manslaughter; criminal history included prior DUI).
Ms. Lente also cited to United States v. Wolfe, 435 F.3d 1289, 1294 (10th Cir.2006), as a comparable case where the defendant was convicted of two counts of involuntary manslaughter from a DUI accident, and, like Ms. Lente, had no criminal history points. In Wolfe, the district court initially departed upward and imposed a 41-month sentence. We reversed and remanded for resentencing because "the district court departed upward to an extraordinary degree without sufficient explanation." See id. at 1305. The defendant in Wolfe was sentenced to 20 months on resentencing. See United States v. Wolfe, D.N.M. Case No. 03-cr-02056, R.Doc. 36 (Judgment entered April 5, 2006).
Finally, Ms. Lente presented cases from outside the circuit to demonstrate that the variance recommended by the PSR and the government was "far afield" of the punishment for similar offenses and offenders. R. Vol. 1 at 153-154. For example, she cited to United States v. Kathman, 490 F.3d 520, 521-22 (6th Cir.2007), where a twenty-two year-old first offender killed two people in a DUI accident. The Sixth Circuit affirmed a sentence of 20 months for two counts of DUI involuntary manslaughter, which was a downward departure from the proposed Guidelines range of 41 to 51 months. Id. at 526.
*1034 The government presented counterarguments to a few of these cases and responded with one case of its own, an unpublished decision from the Western District of Oklahoma, United States v. Leonard, W.D.Okla. Case No. 03-cr-203, R.Doc. 118 (Judgment entered October 26, 2004). The government argued that this case, which it characterized as a "pre-Booker" case, demonstrated the problem with considering pre-Booker sentencing cases for comparative purposes. See R. Vol. 3 at 92-93. The government explained that in Leonard the court imposed an 87-month sentence for two counts of involuntary manslaughter and one count of serious bodily injury from a DUI accident, but the court also indicated in the alternative that it would impose a 120-month sentence if the Guidelines were determined to be unconstitutional. See id.
We do not attempt to resolve which side had stronger comparative case examples or arguments. That is for the district court to resolve in the first instance and for this court to consider on substantive reasonableness review. The point here is to show that Ms. Lente presented to the district court a material, non-frivolous argument based on sentencing data and comparative cases on the need to avoid unwarranted sentencing disparities. The district court did not mention any of these cases or the sentencing data, and it did not address this sentencing factor after Ms. Lente devoted much of her briefing and argument to this issue.
Even if Ms. Lente had not raised a specific argument on the sentencing-disparity issue, a sentencing court must consider the seven § 3553(a) factors, see Gall, 552 U.S. at 49-50, 128 S.Ct. 586, and "[o]ne factor that a district court must consider in imposing an appropriate sentence is `the need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct. . . .'" United States v. Martinez, 610 F.3d 1216, 1228 (10th Cir.), cert. denied, ___ U.S. ___, 131 S.Ct. 543, 178 L.Ed.2d 399 (2010) (quoting 18 U.S.C. § 3553(a)(6)). Although the district court stated at the sentencing hearing that it took "into account extensively the sentencing factors of 18 U.S.C. 3553(a)(1) through (7)," R. Vol. 3 at 223, and stated in its sentencing decision that it "carefully consider[ed] all the statutory factors set forth in 18 U.S.C. § 3553(a)," R. Vol. 1 at 440, there is no express mention of § 3553(a)(6) or any discussion of the apparent disparity between Ms. Lente's sentence and the sentences of other offenders, especially similar offenders.
The government acknowledges that the district court did not "expressly consider 18 U.S.C. § 3553(a)(6) and its directive that sentences avoid unwarranted sentence disparities," Aplee. Br. at 49, but contends that this does not constitute procedural error because the court was not required to expressly consider this or any other factor on the record, see id. at 49-52. We disagree.
The government relies primarily on United States v. Ruiz-Terrazas, 477 F.3d 1196 (10th Cir.2007), and United States v. Martinez-Barragan, 545 F.3d 894, 898 (10th Cir.2008). Both, however, were appeals of within-Guidelines sentences after the defendants had requested a below-Guidelines sentence. See Martinez-Barragan, 545 F.3d at 898, 902; Ruiz-Terrazas, 477 F.3d at 1198. When a district court imposes a within-Guidelines sentence, "the court must provide only a general statement of its reasons, and need not explicitly refer to either the § 3553(a) factors or respond to every argument for leniency that it rejects in arriving at a reasonable sentence." Martinez-Barragan, 545 F.3d at 903 (quotation and citation *1035 omitted). This precedent is inapplicable here because Ms. Lente's sentence is 135 months above the applicable Guidelines range.
We have explained that, "[u]nder 18 U.S.C. § 3553(a), the court must state . . . the reasons for its imposition of the particular sentence, and, if the sentence is . . . outside the [guidelines] range, . . . the specific reason for the imposition of a sentence different from that described, which reasons must also be stated with specificity in the written order of judgment and commitment." United States v. Pinson, 542 F.3d 822, 833 (10th Cir.2008) (quotations omitted). We further instructed that "[t]he court must also address, in its statement of reasons, the material, non-frivolous arguments made by the defendant." Id.; see also United States v. Ausburn, 502 F.3d 313, 329 (3d Cir.2007) ("[W]e have stated at least one concrete requirement to establish that the sentencing court gave meaningful consideration to the relevant § 3553(a) factors: the court must acknowledge and respond to any properly presented sentencing argument which has colorable legal merit and a factual basis.").
Beyond the district court's saying at the sentencing hearing and in its written decision that it had considered all of the § 3553(a) factors, there is no further indication that the district court considered Ms. Lente's material, non-frivolous § 3553(a)(6) sentencing-disparity argument, which she supported with sentencing data and case examples. Our precedent does not allow us to presume that it did so. See Pinson, 542 F.3d at 833 ("The district court is not required to recite any magic words to demonstrate that it has considered all of the relevant arguments, but we will not presume the district court weighed a party's arguments in light of the 3553(a) factors where the record provides no indication that it did so." (quotations omitted)); see also United States v. Harris, 567 F.3d 846, 854 (7th Cir.), cert. denied, ___ U.S. ___, 130 S.Ct. 1032, 175 L.Ed.2d 632 (2009) ("[W]hen a court has passed over in silence the principal argument made by the defendant even though the argument is not so weak as not to merit discussion, we do not have the assurance we need to satisfy ourselves that the defendant's individual circumstances have been thoroughly considered." (quotation omitted)).
For us to conduct "meaningful appellate review," of the district court's significant upward-variant sentence, the district court must expressly consider § 3553(a)(6) and address Ms. Lente's argument that her sentence would create unwarranted sentencing disparities. See Gall, 552 U.S. at 50, 128 S.Ct. 586; Rita v. United States, 551 U.S. 338, 356, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007) ("The sentencing judge should set forth enough to satisfy the appellate court that he has considered the parties' arguments and has a reasoned basis for exercising his own legal decisionmaking authority."); see also United States v. Merced, 603 F.3d 203, 215 (3d Cir.2010) ("[I]t is not enough for the district court to carefully analyze the sentencing factors. A separate and equally important procedural requirement is demonstrating that it has done so.").
Because the district court failed to address Ms. Lente's material, non-frivolous § 3553(a)(6) sentencing-disparity argument, we conclude that the court committed procedural error.[9]See Pinson, 542 *1036 F.3d at 833 ("The court must also address, in its statement of reasons, the material, non-frivolous arguments made by the defendant.").

2. Failure to address mitigating circumstances

Ms. Lente argues that the district court erred when it failed to address her argument that the circumstances leading up to the accident mitigated against a finding that she was acting with more than normal recklessness. She introduced undisputed evidence about pre-accident developments, including that her mother gave her the keys to her mother's car and told her to drive Mr. Tewahaftewa home because he was drunk and acting inappropriately. She argued these circumstances mitigated against a finding that she acted with excessive recklessness. See R. Vol. 1 at 132-133 (Objections to the PSR); id. Vol. 3 at 190-191 (Sentencing hearing), id. Vol. 1 at 362 (Objections to the Sentencing Decision).
The district court identified three aggravating factors to support a finding of "extraordinary recklessness." But it did not address Ms. Lente's undisputed evidence about Mr. Tewahaftewa's drunken behavior just before the accident, her mother's and Ms. Jojola's attempts to convince Mr. Tewahaftewa to leave Ms. Jojola's home on his own, Ms. Jojola's asking his sister to come get him, and Ms. Lente's mother's decision to give Ms. Lente the keys to her car and tell Ms. Lente to drive him home.
The government argues that the district court was not required to "to respond to every argument for leniency that it reject[ed] in arriving at a reasonable sentence." Aplee. Br. at 44 (quoting Martinez-Barragan, 545 F.3d at 898). The government's reliance on Martinez-Barragan is again misplaced because the defendant there was arguing for a downward variance from a within-Guidelines sentence. As we explained in Pinson, when a court imposes a sentence outside of the Guidelines range, it must address the material, non-frivolous arguments made by the defendant. 542 F.3d at 833. Ms. Lente's contention that the circumstances immediately preceding the crash mitigated against a finding that she was acting with excessive recklessness is a material, non-frivolous argument in response to the PSR and government's recommendation for a significant upward-variant sentence.
The government also contends that the district court's "written opinion demonstrates that the court carefully considered Lente's mitigation argument" because "the court explained that two years of Lente's sentence for count 3 would run concurrent because Mr. Tewahaftewa, unlike Lente's *1037 other victims, engaged in risky behavior." Aplee. Br. at 44. But this part of the district court's decision did not respond to Ms. Lente's mitigating-circumstances argument about her behavior leading up to the accident. It was based instead on the district court's conclusion that Mr. Tewahaftewa engaged in risky behavior by choosing to ride with Ms. Lente after he had consumed alcohol with her, as compared to the other victims who "just happened to be at the wrong place at the wrong time." R. Vol. 1 at 446 n. 9. The district court's decision did not address Ms. Lente's argument that her mother influenced her decision to drive by giving her the keys to her car and instructing her to drive Mr. Tewahaftewa home. This fact mitigated against a finding that Ms. Lente was acting with excessive recklessness.
When it imposed a 135-month upward variance based in part on Ms. Lente's excessive recklessness, the district court should have addressed Ms. Lente's mitigating-circumstances argument. Cf. United States v. Vrdolyak, 593 F.3d 676, 682 (7th Cir.), cert. denied, ___ U.S. ___, 131 S.Ct. 200, 178 L.Ed.2d 244 (2010) (concluding that district court erred in granting a downward variance when it gave "without adequate articulated consideration, enormous weight to letters urging leniency for the defendant, while virtually ignoring the evidence that tugged the other way."). The court's failure to do so constitutes procedural error.

3. State Road 47

The district court took judicial notice of SR 47's location and characteristics to infer that a longtime local resident such as Ms. Lente would know it is a "well-traveled road." R. Vol. 1 at 445. The court relied on this inference to support its finding that Ms. Lente was excessively reckless when she drove on SR 47 after a day of heavy drinking. Id. Ms. Lente complains that the court made assumptions about traffic conditions on SR 47 at the specific time and place of the accident and that she was not provided sufficient notice or opportunity to be heard on this issue.
The court did not, as Ms. Lente suggests, do anything more than find SR 47 to be a well-traveled road and that Ms. Lente knew it to be so. These findings combined with a drunk driver's choosing to drive on SR 47 are relevant to recklessness and relate to the nature and circumstances of the offense. See § 3553(a)(1). Although more specific information about traffic congestion at the time and place of the accident may have been more probative, we find no procedural error in the court's considering the general nature of the road in its recklessness analysis. If Ms. Lente objects to the weight of this factor in determining recklessness, that is a substantive reasonableness argument, which we do not address here.
As for Ms. Lente's procedural due process argument, although she received late notice about the SR 47 issue, the court afforded her a hearing on this subject. We do not discern a significant procedural error. Even if we did, we do not think its correction would have affected the sentence, and it is therefore harmless. We turn next to harmless error on the other procedural matters.

C. Harmless Error Analysis

The government asserts that, even if the district court committed procedural error, any such error was harmless. "Harmlessness must be proven by a preponderance of the evidence, and the burden of making this showing falls on the beneficiary of the errorin this case, the government." Cerno, 529 F.3d at 939. A harmless error "is that which did not affect the district court's selection of the *1038 sentence imposed." United States v. Kaufman, 546 F.3d 1242, 1270 (10th Cir. 2008), cert. denied, ___ U.S. ___, 130 S.Ct. 1013, 175 L.Ed.2d 621 (2009).
The government states that "[t]he record makes clear that the court carefully considered 18 U.S.C. 3553(a)'s sentencing factors and believed they warranted a significant upward variance." Aplee. Br. at 52 (citing R. Vol. 1 at 440; id. Vol. 3 at 223).[10] The government contends that "[r]emanding the case to the district court for further elaboration on why the court concluded sixteen years was warranted is highly unlikely to change the result." Aplee. Br. at 52.
Although the procedural error regarding the district court's failure to address Ms. Lente's mitigating-circumstances argument may have been harmless, we cannot reach that conclusion about the district court's failure to address Ms. Lente's § 3553(a)(6) sentencing-disparity argument. We conclude that this error requires reversal for two reasons.
First, the district court's express consideration of Ms. Lente's § 3553(a)(6) sentencing-disparity argument might have convinced the court to reach a different sentence. See United States v. Lynn, 592 F.3d 572, 582 (4th Cir.2010) (concluding that procedural failure to adequately explain sentence was not harmless error because "the district court's explicit consideration of [defendant's] arguments for a lower sentence might have convinced the court to impose such a sentence"). The government bears the burden to show that the error did not affect the sentence. Its argument consists of assertions that the district court considered the § 3553(a) factors and that a different sentence on remand is "highly unlikely." That is not enough.
Second, the district court's failure to address this significant, material, and non-frivolous argument prevents us from conducting meaningful appellate review of the substantive reasonableness of the sentence. See Gall, 552 U.S. at 50, 128 S.Ct. 586 (explaining that district court "must adequately explain the chosen sentence to allow for meaningful appellate review and to promote the perception of fair sentencing"); Rita, 551 U.S. at 356, 127 S.Ct. 2456 ("The sentencing judge should set forth enough to satisfy the appellate court that he has considered the parties' arguments and has a reasoned basis for exercising his own legal decisionmaking authority."); Merced, 603 F.3d at 225 (reversing for procedural error for failing to address § 3553(a)(6) argument and explaining that insistence that sentencing courts follow the requisite procedures allows the court to fulfill its important role of exercising effective appellate oversight).
Ms. Lente and the government devoted extensive briefing and oral argument to the unwarranted disparity issue. They no doubt decided it was incumbent on them to do so in view of § 3553(a)(6) and the significantly variant sentence proposed in the PSR and imposed in the first sentencing proceeding. Ms. Lente marshaled sentencing data and comparative case sentencing decisions for the court's consideration. Whether or not the court considered Ms. Lente's arguments, its opinion's avoidance of a response to them leaves us without understanding the role of a critical sentencing factor in shaping the sentence *1039 in this case. Perhaps the government is right that the district court will reach the same outcome after it fills in this gap, but the government has not convinced us by a preponderance. We cannot fulfill our appellate role, however deferential, in assessing the substantive reasonableness of the sentence without the gap having been filled. See United States v. Pena-Hermosillo, 522 F.3d 1108, 1116 (10th Cir.2008) (reversing for procedural error for failure to adequately explain a sentence because it was not clear from the record why the district court denied an enhancement); Cerno, 529 F.3d at 937 ("Only if the district court follows sound procedure may we then consider whether the resulting sentence is reasonable in substance."); see also United States v. Gapinski, 561 F.3d 467, 469 (6th Cir.2009) (reversing sentence as procedurally unreasonable because "the record [did] not show that the district court considered and explained its reasons for rejecting [defendant's] non-frivolous argument for a lower sentence").
The need to avoid unwarranted disparities is a critical sentencing factor. Equal justice is a core goal of our constitutional system. We require courts to justify sentences to meet that goal. When justification is not forthcoming, the credibility of the sentence suffers. Whether the sentence is five years, ten years, or sixteen years, we insist on the procedural safeguard of explanation to assure us that justice has been done. We make no judgment about the proper length of Ms. Lente's sentence. We remand for proper procedural foundation.

III. CONCLUSION
For the foregoing reasons, we conclude that Ms. Lente's sentence is procedurally unreasonable. Accordingly, we REVERSE and REMAND for resentencing consistent with this opinion.
NOTES
[1]  These offenses fall under federal jurisdiction because they were major crimes committed by an Indian within Indian country. See 18 U.S.C. § 1153.
[2]  Judge Hartz and Judge Holmes voted to vacate the sentence and remand for resentencing but for different reasons. Judge Hartz concluded that remand was necessary because the government had breached its plea agreement. Judge Holmes determined that remand was necessary because Ms. Lente's sentence was substantively unreasonable. Judge McWilliams in dissent voted to affirm the sentence.
[3]  United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005).
[4]  United States v. Pettigrew, 468 F.3d 626, 633 (10th Cir.2006).
[5]  United States v. Wolfe, 435 F.3d 1289 (10th Cir.2006); United States v. Jones, 332 F.3d 1294 (10th Cir.2003); United States v. Whiteskunk, 162 F.3d 1244 (10th Cir.1998).
[6]  Before discussing its reasons for the upward variance, the court indicated that upward departures might have been available under U.S.S.G. § 4A1.3 and § 5K2.1, but the court stated it would "not go out of its way to impose an upward departure where the PSR has not recommended one and the United States has not requested one." R. Vol. 1 at 438-39.
[7]  According to the PSR, Ms. Lente spent time in tribal jail twiceonce for ten days and once for thirty days.
[8]  See 18 U.S.C. § 3584(a) ("Multiple terms of imprisonment imposed at the same time run concurrently, unless the court orders . . . that the terms are to run consecutively."); United States v. Rodriguez-Quintanilla, 442 F.3d 1254, 1256 (10th Cir.2006) ("[A] district court has the discretion to impose consecutive or concurrent sentences.").
[9]  Our conclusion is consistent with United States v. Merced, 603 F.3d 203, 213, 216 (3d Cir.2010). In Merced, the district court granted a significant downward variance. The government argued on appeal that the district court committed procedural error by ignoring the government's § 3553(a)(6) sentencing-disparity argument. The Third Circuit agreed, explaining that "[o]ne factor the court must consider is the need to avoid unwarranted sentencing disparities," and that the court's "failure to do so in the face of a colorable argument that an outside-the-Guidelines sentence will create a risk of such disparities constitutes procedural error." Merced, 603 F.3d at 222 (quotation omitted). The court noted further that "[t]his is especially true if the sentence falls outside of the Guidelines, or where . . . a party specifically raises a concern about disparities with the district court and that argument is ignored." Id. at 224. The decision explained that "the government voiced unmistakable concern that granting [defendant] a significant variance could create unwarranted sentencing disparities." Id. Because the government raised a colorable legal argument with a factual basis in the record, "the District Court should have addressed it as part of its meaningful consideration of the sentencing factors." Id. The court ultimately concluded that "[b]efore the District Court granted such a large variance [(128 months from similarly situated offenders)], it should have explained why that variance would not contribute to unwarranted sentencing disparities pursuant to § 3553(a)(6)," and "[i]ts failure to do so was procedural error." Id. at 225.
[10]  These record citations are to the court's statements that it "carefully consider[ed] all the statutory factors set forth in 18 U.S.C. 3553(a)," R. Vol. 1 at 440, and had "taken into account extensively the sentencing factors of 18 U.S.C. 3553(a)(1) through (7)," id. Vol. 3 at 223.
