TYMKOVICH, Chief Judge.
This is the second appeal arising from crimes committed by two corrections officers, Raymond Barnes and Christopher Brown, while employed at the Muskogee County Jail. The government argues the sentences the district court imposed after we remanded for resentencing are substantively unreasonable. Because we find the district court did not abuse its discretion in granting a downward variance from the United States Sentencing Guidelines, we affirm.
I. Background
Barnes and Brown both held administrative roles at the Muskogee County Jail. Barnes served as the Jail Superintendent and Brown worked alongside him as the Assistant Jail Superintendent. Our previous opinion extensively recounted the abuse both Barnes and Brown perpetrated on the jail's inmates. See United States v. Brown , 654 Fed.Appx. 896, 900-902 (10th Cir. 2016) (unpublished). In short, both defendants physically abused prisoners in a variety of ways, engaged in excessive force against inmates, and intimidated other jail employees to conceal their illicit activities.
Authorities charged Barnes and Brown with three counts of assaulting or conspiring to assault prisoners at the jail. In 2014, a jury convicted both of various charges. The jury convicted Barnes of one count of conspiracy to violate constitutional rights and two counts of deprivation of rights under color of law. See 18 U.S.C. §§ 241, 242. The jury found Brown, on the other hand, guilty of one count of conspiracy to violate constitutional rights, one count of deprivation of rights under color of law, and one count of making a false statement to a federal agent. See 18 U.S.C. § 1001. The district court sentenced Barnes to twelve months' imprisonment followed by twenty-four months of supervised release. Brown received a sentence of six months' imprisonment followed by thirty-six months of supervised release.
In the first appeal, Barnes and Brown challenged their convictions. The government cross-appealed, arguing both sentences were procedurally and substantively unreasonable. We affirmed the convictions, but vacated the sentences as procedurally unreasonable because the district court had not adequately explained the basis for the sentences imposed.
*915Brown , 654 Fed.Appx. at 900. Since we resolved the case on procedural unreasonableness, we declined to reach the government's argument that the sentences were substantively unreasonable.
On remand, the district court held a hearing, took additional testimony from witnesses, and heard arguments about the appropriateness of a variance. The court concluded it would not apply the advisory guidelines range of 70 to 87 months and granted a variance to each defendant. Accordingly, the court resentenced Barnes to twenty-four months of imprisonment followed by twenty-four months of supervised release. The court also gave Brown a new sentence of twelve months' imprisonment followed by thirty-six months of supervised release. All told, the district court doubled each of their terms of imprisonment.
The government again appeals, arguing the new sentences are substantively unreasonable. We affirm. The district court did not abuse its discretion in applying the relevant sentencing factors as reflected in its explanation of the sentences based on defendant-specific facts and circumstances.
II. Analysis
The government contends the district court abused its sentencing discretion by imposing too lenient a sentence on both defendants. The government urges us to find the sentences substantively unreasonable.
A. Substantive Reasonableness
We review a district court's sentencing determination for substantive unreasonableness by considering whether the sentence "is unreasonable given the totality of the circumstances in light of the 18 U.S.C. § 3553(a) factors." United States v. Caiba-Antele , 705 F.3d 1162, 1165 (10th Cir. 2012). We review a sentence's length for abuse of discretion. United States v. Walker , 844 F.3d 1253, 1255 (10th Cir. 2017). A district court abuses its sentencing discretion only if the sentence " 'exceeded the bounds of permissible choice.' " United States v. McComb , 519 F.3d 1049, 1053 (10th Cir. 2007) (quoting United States v. Ortiz , 804 F.2d 1161, 1164 n.2 (10th Cir. 1986) ). We "will reverse only if the sentence imposed was 'arbitrary, capricious, whimsical, or manifestly unreasonable.' " United States v. DeRusse , 859 F.3d 1232, 1236 (10th Cir. 2017) (quoting United States v. Gantt , 679 F.3d 1240, 1249 (10th Cir. 2012) ).
When determining a sentence, a court must consider the seven statutory factors set forth in § 3553(a). The factors include:
1. The nature and circumstances of the offense and the history and characteristics of the defendant;
2. the need for a sentence to reflect the seriousness of the crime, deter future criminal conduct, prevent the defendant from committing more crimes, and provide rehabilitation;
3. the sentences that are legally available;
4. the Sentencing Guidelines;
5. the Sentencing Commission's policy statements;
6. the need to avoid unwarranted sentence disparities; and
7. the need for restitution.
See 18 U.S.C. § 3553(a) (1-7).
We give substantial deference to the district court's weighing of these factors. "The sentencing judge is in a superior position to find facts and judge their import under § 3553(a) in the individual case." Gall v. United States , 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007). "The judge sees and hears the evidence, makes credibility determinations, has full knowledge of the facts and gains insights *916not conveyed by the record." Id. "It has been uniform and constant in the federal judicial tradition for the sentencing judge to consider every convicted person as an individual and every case as a unique study in the human failings that sometimes mitigate, sometimes magnify, the crime and the punishment to ensue." Id. at 52, 128 S.Ct. 586. In short, "the uniqueness of the individual case ... does not change the deferential abuse-of-discretion standard of review that applies to all sentencing decisions." Id.
And when we review a downward variance from the recommended guidelines range, as we do here, even more solicitude to the sentencing court is appropriate. A "downward variance is based simply on the district court's discretionary authority to consider 'the nature and circumstances of the offense' " and select " 'a sentence sufficient, but not greater than necessary,' to comply with all of the purposes of sentencing." See DeRusse , 859 F.3d at 1237 (quoting 18 U.S.C. § 3553(a) ) (emphasis added).
In addition, our review must acknowledge that sentencing courts can and should "engage in a holistic inquiry of the § 3553(a) factors." See United States v. Lente , 759 F.3d 1149, 1174 (10th Cir. 2014) (quoting United States v. Lopez-Macias , 661 F.3d 485, 492 (10th Cir. 2011) ). A district court properly engages in this inquiry when it bases its decision on specific, articulable facts supporting the variance and does not employ an impermissible methodology or rely on facts that would make the decision out of bounds. DeRusse , 859 F.3d at 1236.
For these reasons, we uphold even substantial variances when the district court properly weighs the § 3553(a) factors and offers valid reasons for the chosen sentence.
Consider, for example, DeRusse , where, we upheld a substantial variance from a 108-135 months guidelines range down to 70 days already served. In so holding, we rejected the government's suggestion that a "variance based on the district court's discretionary authority should be constrained by ... the specific requirements listed in [the] guideline...." Id. at 1237. "A variance," we explained, "can be imposed without compliance with the rigorous requirements for departures." Id. (quoting Gantt , 679 F.3d at 1247 ).
Rather than looking to compliance with the Guidelines, we looked instead to whether the district court properly weighed all the § 3553(a) factors. We concluded it had, ultimately agreeing with the district court that the crime represented "aberrational" behavior that was partially attributable to mental health issues for which the defendant was receiving treatment. Id. at 1240. Although we would likely not have "reached the same sentencing decision in the first instance," we concluded the court did not abuse its substantial discretion in choosing the sentence. Id. at 1241.
In short, then, the adequacy of the court's consideration and explanation of the § 3553(a) factors is the keystone of our analysis. We look to the record to determine whether the district court satisfactorily engaged and examined the factors in a holistic fashion. But the court need not rely on every single factor-no algorithm exists that instructs the district judge how to combine the factors or what weight to put on each one.
The distinction between procedural and substantive reasonableness is a significant but not necessarily sharp one, especially as it concerns a sentencing court's explanation for the sentence. That explanation *917serves both procedural and substantive functions.
First, just as a court's consideration of the § 3553(a) factors is a procedural requirement, so is its explanation of how those factors apply. In fact, the explanation is the procedural step that shows the factors have been considered. In Gall , the Supreme Court said "failing to adequately explain the chosen sentence" can be "a significant procedural error." 552 U.S. at 51, 128 S.Ct. 586. In this appeal, the government does not challenge the sentences' procedural reasonableness. Aple. Reply Br. at 3 ("To be clear, the United States is not arguing that the district court failed to adequately explain its reasons-i.e. , that it made procedural errors....").
Second, the content of the district court's explanation is relevant to whether the length of the sentence is substantively reasonable. To determine substantive reasonableness, Gall instructs that 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." 552 U.S. at 51, 128 S.Ct. 586. Part of that deference extends to the court's analysis of the § 3553(a) factors. See United States v. Smart , 518 F.3d 800, 808 (10th Cir. 2008) (holding appellate courts must grant deference "not only to a district court's factual findings but also to its determinations of the weight to be afforded to such findings."). A sentence is more likely to be within the bounds of reasonable choice when the court has provided a cogent and reasonable explanation for it.
This dual purpose of the court's sentencing explanation is one reason the line between procedural and substantive reasonableness is blurred. See United States v. Reyes-Santiago , 804 F.3d 453, 468 n.19 (1st Cir. 2015) ("The line between procedural and substantive sentencing issues is often blurred. ... [and] 'the lack of an adequate explanation can be characterized as either a procedural error or a challenge to the substantive reasonableness of the sentence.' ") (quoting United States v. Crespo-Ríos , 787 F.3d 34, 37 n.3 (1st Cir. 2015) (internal quotation marks and brackets omitted)); see also United States v. Liou , 491 F.3d 334, 337 (6th Cir. 2007) ("[T]he border between factors properly considered 'substantive' and those properly considered 'procedural' is blurry if not porous....").
Below, we consider the explanation given for the challenged sentences to assist us in determining whether the district court abused its discretion in weighing the § 3553(a) factors-and thus whether the sentences are substantively reasonable. See United States v. Rentz , 696 Fed.Appx. 348, 352 (10th Cir. 2017) (unpublished) ("[B]oth the record and the district court's stated reasoning provide us an adequate basis to assess the substantive reasonableness of the sentence imposed."). The dissent argues that in considering the district court's explanation, we rely "on a rationale that instead fits the inquiry for procedural reasonableness." Dissent at 924. But while courts should avoid unduly blurring the line between substantive and procedural reasonableness, there is nevertheless some unavoidable overlap. See United States v. Jeter , 721 F.3d 746, 756 (6th Cir. 2013) ("[C]laims of substantive and procedural reasonableness overlap in that they both concern whether the district court properly considered certain § 3553(a) factors.").
With these considerations in mind, we turn to the district court's sentencing analysis in this case.
1. Barnes
The district court properly addressed each of the § 3553(a) factors in sentencing Barnes.
*918First, the court based its sentence on the trial record itself, witness testimony at the resentencing hearing, and statements and other submissions from members of Barnes's family, co-workers, and friends. The court then walked through the sentencing factors contained in § 3553(a), observing that despite the stressful environment where Barnes worked, "there [was] no justification for the actions which resulted in [his] conviction." App. 609. Even so, the district court considered Barnes to be a poor candidate for a guidelines sentence. He was age 46 at sentencing, and married with three children. In addition, he was raising four nieces and nephews he took custody of after his sister died (the father, who is in the country illegally, was unable to care for them). At the time of resentencing, his natural children were aged 14, 20, and 21, and the other children were 11, 15, 16, and 17. The record reflects that his sister's children were performing better in school and socially since Barnes and his wife took custody.
Barnes was also fighting tongue cancer and had other health problems which required "14 medications daily." Id . at 610-611. Prior to sentencing, Barnes had led "a stable lifestyle and appear[ed] active in his community." Id . The court concluded Barnes's risk of recidivism would be "low to nonexistent and he posed no apparent threat to the community." Id. at 611. Barnes had not been convicted of previous crimes, and the district court considered its two-year prison sentence "significant time"-especially coupled with supervisory release.
Considering the seriousness of the crime and deterrence, the court adequately reviewed the significant impact the sentence would have on Barnes's career and family as well as on similarly situated officers. Overall, the court determined "the sentence imposed will provide specific and general deterrence to any future anti-social behavior of this defendant and others, especially those in law enforcement." Id. at 611-612. The court reached this conclusion after a thorough discussion of the defendant's specific situation-he would no longer be able to work in law enforcement, and, we note, would face all the ancillary consequences attending a felony conviction. The court further reasoned the sentence would properly deter similarly-situated "Law Enforcement Officers or Corrections Officers who learn of the facts surrounding this case and may be tempted to engage in similar conduct."Id. at 612.
In sum, the district court thoroughly supported its variance with an analysis of the § 3553(a) factors. The court had "taken notice of the advisory guideline range" and could not "find that a sentence within that advisory range is necessary to comport with the factors identified in United States Code Section 3553(a) and to achieve the overall goal of sentencing." Id. After considering the guidelines factors as a whole, the court decided to vary downward from the guidelines range to comport with the broader goals of sentencing. In view of its careful discussion, we find that the court did not abuse its discretion in considering and justifying a variance based on the § 3553(a) factors.
2. Brown
The district court also properly addressed each of the § 3553(a) factors for Brown.
First, the court considered the trial testimony concerning Brown's culpability and took additional testimony at the sentencing hearing. The court then noted that Brown was not the ringleader of the assaults. In fact, "the majority of witnesses [at trial] testified that they did not observe Brown assault any inmates, nor did they hear him give orders to any other staff instructing *919them to assault or mistreat the inmates." Id . at 652. Reviewing Brown's personal characteristics, the court observed that Brown has no criminal record, "maintains a stable lifestyle with no documented substance abuse or other anti-social behavior," has "five minor children," and exhibits a "low to nonexistent" risk of recidivism. Id. The court thus explicitly detailed why Brown's personal attributes and dependent-heavy family structure might mitigate the need for a standard guidelines sentence.
Recognizing the seriousness of the crime and the need for deterrence, the court noted that it was imposing "a significant portion of imprisonment followed by a period of Supervised Release"; Brown would no longer be able to work in law enforcement; and his family had already been and "[would] continue to be significantly impacted." Id. at 652-653. The court found "[n]othing in the defendant's background ... suggest[ing] that a sentence within the advisory guideline range is needed to deter him from any further law violations or misconduct." Id. at 653. The court was also confident the selected sentence would deter Brown from future crime and other officers from "similar misconduct." Id.
In discussing the remaining § 3553(a) factors and "the sentencing options available for this defendant," the court could not "find that a sentence within that advisory range is necessary to comport with the factors identified in [the guidelines] and to achieve the overall goal of sentencing." Id. at 653-654. The court thought the combination of prison time and supervised release, along with the mitigating circumstances in Brown's personal history, warranted a sentence of 12 months' incarceration and three years of supervised release.
As in its analysis of Barnes's sentence, then, the court holistically considered the § 3553(a) factors and supported its analysis with facts specific to Brown's situation. The court did not rely on impermissible factors or rely exclusively on one factor. We thus find the court did not abuse its discretion in justifying its variance in Brown's sentence as well.
B. The Government's Arguments
The government points to several cases where we have found low sentences to be substantively unreasonable: United States v. Friedman , 554 F.3d 1301 (10th Cir. 2009), United States v. Walker , 844 F.3d 1253 (10th Cir. 2017), and United States v. Morgan , 635 Fed.Appx. 423 (10th Cir. 2015) (unpublished). The government argues these cases control the outcome of this case. We are not persuaded these cases compel reversal of the sentences here.
In Friedman , the defendant pleaded guilty to bank robbery, and his guidelines range was 151 to 188 months. 554 F.3d at 1302, 1308. The district court varied downward to a sentence of 57 months. We concluded the sentence was substantively unreasonable because "(1) the defendant had an extensive history of recidivism and lacked remorse and (2) the 57-month sentence created unwarranted sentence disparities." Walker , 844 F.3d at 1259 (summarizing Friedman , 554 F.3d at 1307-14 ). Friedman admitted to committing eight bank robberies, and at least two of the "robberies involved weapons or the threat of weapons." Friedman , 554 F.3d at 1309. Friedman himself acknowledged he had "only been able to remain free of prison for twenty months out of the twenty-seven years of his adult life." Id. Nothing in Friedman's record of consistent reversion to crime suggested that he would not again return to a life of crime.
Yet in the face of these strong indications of a propensity to recidivate, the district court provided no specific facts to *920support its conclusion that the defendant would not be prone to recidivism. Instead, the judge cited only "a feeling about [him] that [he] can make it and [he's] going to." Friedman , 554 F.3d at 1307. Because the court did not cite to any specific facts supporting its conclusion, we concluded the sentence was arbitrary and capricious.
Here, in contrast, the district court set forth concrete reasons why it would vary below the Guidelines. Since the court rooted its decision in specific, permissible facts particular to each defendant, Friedman does not compel a contrary conclusion.
Similarly, Walker considered a sentence for two counts of bank robbery that had been reduced from a range of 151-188 months to 33 days of time-served in pretrial detention. We found the sentence substantively unreasonable because the district court failed to weigh the § 3553(a) factors holistically, instead relying "almost exclusively" on one factor-Walker's "newfound sobriety"-to justify the sentence. Walker , 844 F.3d at 1259.
That is far from the case before us now. Here, the court carefully addressed each factor and concluded its assessment of all of the factors counseled a downward variance for each defendant. While it is doubtful we would have weighed or applied the factors the same way in this case given the seriousness of the crimes, on balance, the court did not impose sentences outside permissible choice.1
Finally, in Morgan , we reversed a downward variance from a range of 41-51 months to five years of probation for a politician convicted of bribery. "[T]he court's decision to vary downward to probation was based on the following: (1) seriousness of the offense, (2) the letters of support, and (3) deterrence." 635 Fed.Appx. at 448. We found the district court "paid only lip service to the seriousness of the offense" because it explained its "fair sentence" could be "reached by first calculating the guideline sentence based on the crime of conviction (Count 63) and then dividing it by 63, the total number of counts, including the mistried and acquitted counts...." Id. By proffering this rationalization, the district court mitigated the seriousness of the convicted offense with the mistried and acquitted counts, which should not have made the convicted count any less blameworthy. This sentencing methodology was arbitrary and considered impermissible factors, making the sentencing substantively unreasonable. The court similarly placed undue emphasis on supporting letters while overly discounting the need for deterrence.
In sum, we found the court's sentence substantively unreasonable in Morgan because the court considered impermissible factors and failed to consider an important factor: general deterrence. In the present *921case, however, the district court did not rely on impermissible factors, nor did it fail to consider any important factors.
Thus, none of the cases the government cites calls into question our conclusion here.
The government further suggests the district court could not justify a variance by relying on facts that the Guidelines already took into account. But that suggestion is mistaken. "[U]nder current precedent '[d]istrict courts have broad discretion to consider particular facts in fashioning a sentence under 18 U.S.C. § 3553(a), even when those facts are already accounted for in the advisory guidelines range.' " Lente , 759 F.3d at 1169 (quoting United States v. Yanez-Rodriguez , 555 F.3d 931, 946 (10th Cir. 2009) ).
We make one final note on the dissent's thoughtful but overly complex approach in reaching a contrary conclusion. The dissent maps sentences for convictions under §§ 241 and 242 onto a histogram in order to show that the sentences for Barnes and Brown were too low for the otherwise prototypical nature of their offenses. But there is no "mathematical formula that uses the percentage of a departure as the standard for determining the strength of the justifications required for a specific sentence." Gall , 552 U.S. at 47, 128 S.Ct. 586. "Our sentencing scheme 'seeks to eliminate not all sentencing disparities, but only unwarranted disparities.' " Lente , 759 F.3d at 1169 (quoting United States v. Contreras , 180 F.3d 1204, 1210 (10th Cir. 1999) ). We are confident that district courts can responsibly examine general sentencing trends for a particular crime without losing sight of the individual characteristics of the defendants before it.
And in any event, the court here "reviewed its sentences in prior deprivation of rights cases" and was "satisfied that the sentence" would "be consistent and avoid unwarranted disparities." App. 735. Even if the disparities factor weighs in favor of a higher sentence, the district court considered it alongside other factors and the facts of this case and did not abuse its discretion in imposing the sentences it did.
III. Conclusion
Sentencing is both art and science, and it may be the hardest job our district judges undertake. While we are confident we would have imposed higher sentences based on the record in this case, we cannot say the district judge exceeded the bounds of permissible choice. We rely on the discretionary authority of our district courts as a powerful tool to ensure individualized consideration of each defendant's particular circumstances and characteristics.
After careful examination, we conclude that authority was not exceeded here. The dissent thoughtfully considers the district court's analysis of each of the individual § 3553(a) factors and ultimately concludes that the sentences are too lenient. We have no substantial quarrel with any particular point in its analysis, but our application of the standard of review leads us to uphold the sentences on remand. We therefore AFFIRM .