Dennis Jacobs, Circuit Judge:

*123Jesse Sawyer, having pled guilty to sexual exploitation of children and receipt of child pornography, was originally sentenced primarily to 30 years in prison and a lifetime of supervised release. We ruled that that sentence was shockingly high given Sawyer's harrowing upbringing and comparatively low danger to the community, and remanded to the district court for resentencing. The district court disagreed with our analysis but found that Sawyer's exemplary record as an inmate justified a reduction to 25 years. Sawyer returned the matter to our docket, challenging his new sentence on both reasonableness and law-of-the-case grounds. By order of July 30, 2018, we affirmed Sawyer's new sentence. We now explain that we did so because the district court effectively complied with our instruction to significantly reduce Sawyer's sentence and because that sentence is now within the realm of reasonableness.

BACKGROUND

In 2014, defendant Jesse Sawyer pled guilty to two counts of sexual exploitation of children in violation of 18 U.S.C. § 2251(a) and one count of receipt of child pornography in violation of 18 U.S.C. §§ 2252A(a)(2)(A) and 2256(8)(A). The sexual exploitation charges arose out of approximately 30 cellphone photos taken by Sawyer of two girls, aged 4 and 6. The girls had close relationships with Sawyer. The photos depicted the children's genitals. Sawyer kept the photos and there was no evidence that he took any steps to distribute them to third parties. The count of receipt of child pornography concerned images that Sawyer downloaded from the Internet.

Each sexual exploitation charge carried a fifteen-year mandatory minimum sentence and a maximum of 30 years. See 18 U.S.C. § 2251(e). The receipt of child pornography count carried a mandatory minimum sentence of five years and a maximum of 20 years. See 18 U.S.C. § 2252A(b)(1). The guideline range for the three sentences was the combined maximum of 80 years. See United States Sentencing Guidelines Manual ("USSG") § 5G1.1(a) ("Where the statutorily authorized maximum sentence is less than the minimum of the applicable guideline range, the statutorily authorized maximum sentence shall be the guideline sentence."). In the absence of these statutory limitations, the guidelines would have called for a life sentence. See USSG §§ 2G2.1, 2G2.2, 4B1.5.

The presentence report and the defendant's sentencing memorandum described Sawyer's personal history of abuse as a child. By age seven, he was repeatedly subjected to sexual abuse, including rape, with the approval and even encouragement of his parents and other family members.

*124By age 10, he was introduced to drugs and alcohol. He and his siblings were never shielded from their adult relatives' sexual promiscuity and frequent drug use; they were, in fact, encouraged to participate. As well, Sawyer's father beat him, at one point with such ferocity that Sawyer lost control of his bowels.

At the original sentencing, the judge described the defendant's childhood as "a childhood that never was," "horrid [and] nightmarish," and marked by "incredible sadness." Transcript of Sentencing, July 7, 2015, at 30-31. The judge noted that a psychologist retained by the defense described Sawyer as a moderate to high risk to reoffend. She found that he presented a significant danger to the community because he had "an inadequate and distorted perception of rape and child molestation." Id. at 32. She expressed great concern for the violation of trust and victimization of the two girls. She stated, "I can't excuse what you did. I take into consideration your life but I can't excuse that darkness in your heart and soul that made you prey upon two innocent children." Id. at 35.

The original sentence was primarily 30 years imprisonment--15 years on each sexual exploitation of children count, to run consecutively, and five years on the receipt of child pornography count, to run concurrently--and supervised release for the rest of his life thereafter. He appealed that sentence to us in 2016, contending that it was both procedurally and substantively unreasonable. We rejected the claims of procedural unreasonableness. United States v. Sawyer, 672 F. App'x 63, 64-65 (2d Cir. 2016) (summary order). We concluded, however, that the 30-year sentence was substantively unreasonable. Id. at 65-67. It was insufficiently justified by concerns of public protection because Sawyer had no history of sexual assault with these victims or other children, and there was no specific evidence of such future risk. While Sawyer violated both children by exposing them to the camera and touching them in the process, there was no evidence--and the government does not suggest--that he engaged in penetrative sexual assault in any form. A 30-year sentence would have been appropriate for "extreme and heinous criminal behavior," and the conduct in this case did not rise to such a level. Id. at 66.

In remanding the case for resentencing, we also identified a specific shortcoming in the district court's consideration of the sentencing factors set out at 18 U.S.C. § 3553(a). We noted that "the district court clearly failed to give appropriate weight to a factor listed in Section 3553(a) that should have mitigated the sentence substantially: the history and characteristics of the defendant." Sawyer, 672 F. App'x at 67 (internal quotation marks omitted). "Particularly given Sawyer's scant criminal history (he was scored within the Criminal History Category of I), the deplorable conditions of his childhood should have militated in favor of a sentence less severe than the one imposed." Id. We concluded that the defendant's own extraordinary history of childhood abuse and the expert testimony that the unresolved and untreated trauma therefrom contributed to the commission of the offense would justify "not just a departure from the Guidelines, but a significant one indeed." Id. We vacated the sentence and remanded to the district court using the procedure described in United States v. Jacobson, 15 F.3d 19 (2d Cir. 1994).

At the July 7, 2017 resentencing hearing, the district judge expressed in detail her disagreement with our decision: "surely ... anyone reviewing the sentence would conclude, as I did, that it was substantively reasonable." App'x at 235. She had not thought she "was doing anything that could be considered shockingly high."

*125Id. at 237. In particular, she noted that nothing in our decision convinced her to revisit her conclusions regarding the relevance of Sawyer's childhood or his likely danger to the community. In sum, she remained of the view that "that sentence was an appropriate one and is sufficient but not greater than necessary to meet the goals of sentencing." Id. at 264. All that said, the judge nevertheless reduced Sawyer's sentence by five years to account for his "extraordinary post-sentencing rehabilitative efforts." Id.

Sawyer returned this case to our docket by a letter of July 14, 2017.

DISCUSSION

Sawyer's primary challenge to his new sentence is that it fails to comply with our previous mandate. We disagree.

The mandate rule, a component of the law of the case doctrine, requires district courts to comply with our holdings regarding that case. See Burrell v. United States, 467 F.3d 160, 165 (2d Cir. 2006). Issues implicitly or explicitly decided on appeal are not open for contrary ruling on remand. Id. The district court retains authority over issues not addressed on appeal, but where an appellate court has resolved an issue, the district court is not empowered to ignore or reject the appellate court's disposition of the issue. Id.

Our previous review of Sawyer's sentence ruled that a 30-year term of imprisonment was "shockingly high," see United States v. Broxmeyer, 699 F.3d 265, 289 (2d Cir. 2012), in light of Sawyer's circumstances, and thus substantively unreasonable. The law of this case is thus that a 30-year term of imprisonment is substantively unreasonable, and the mandate required a substantial reduction. The sentencing judge reduced Sawyer's prescribed term of imprisonment by five years--one-sixth--which is undoubtedly substantial.

At the resentencing hearing, the district court expressly rejected our reasoning, which was odd and regrettable. But our mandate did not bar her from doing so. The scope of our mandate must be understood in terms of the scope of our authority to review a district court's decisions. In reviewing sentences for substantive reasonableness, we are "particularly deferential." United States v. Thavaraja, 740 F.3d 253, 259 (2d Cir. 2014) (internal quotation marks omitted). We only "patrol the boundaries of reasonableness," United States v. Cavera, 550 F.3d 180, 191 (2d Cir. 2008), taking care not to "substitut[e] our own judgment for that of district courts" by undertaking our own rebalancing of sentencing factors, Broxmeyer, 699 F.3d at 289. Our mandate did not require the district judge to weigh the sentencing factors in the way we would have done, so long as she brought the sentence within the (elastic) bounds of reasonableness.

It is not unheard of for a district judge to disagree with an appellate ruling. But it is not necessary that a district judge should endorse our decisions. The mandate rule only "compels compliance." United States v. Ben Zvi, 242 F.3d 89, 95 (2d Cir. 2001) (internal quotation marks omitted). The district judge in this matter may have complied under protest, but she complied nevertheless. It was doubted, but it was done.

On this second appeal, Sawyer continues to protest the reasonableness of his sentence, but we cannot bring ourselves to call it shocking under governing law. He faced a mandatory minimum of fifteen years. Regrettably, twenty-five years is no great departure from sentences routinely imposed in federal courts for comparable offenses. See, e.g., *126United States v. Smith, 697 F. App'x 31, 31-32 (2d Cir. 2017) (summary order); United States v. Rafferty, 529 F. App'x 10, 12-14 (2d Cir. 2013) (summary order); United States v. Ketcham, 507 F. App'x 42, 43-45 (2d Cir. 2013) (summary order); United States v. Levy, 385 F. App'x 20, 21, 24-25 (2d Cir. 2010) (summary order). "In 2010--the most recent year for which data is available--the average sentence for production of child pornography was 267.1 months, or approximately 22 years." United States v. Brown, 843 F.3d 74, 92 (2d Cir. 2016) (Pooler, J., dissenting). The sentence is barbaric without being all that unusual.2

CONCLUSION

For the foregoing reasons, the judgment of the district court is AFFIRMED .

I agree in every respect with the majority's description of the facts in the case and the reasoning that led the panel to declare the original 30-year sentence to be substantively unreasonable. The majority accurately identifies the deficiencies in the original sentence which led to reversal. These were insufficient justification for such a long sentence by concerns of public protection and the sentencing court's failure to give appropriate weight to the defendant's history and characteristics. These are among the factors commonly considered by sentencing courts in reaching sentencing decisions under 18 U.S.C. § 3553. The panel ruled that the district court failed to give sufficient weight to these factors. The case was remanded for resentencing in a manner consistent with our decision.

On resentencing, the district court declined to give any additional weight to either of the factors we identified. The majority accurately describes the district court's rejection of the appeals court ruling. I intend no criticism of the trial judge. She was candid about the reasons for her decision and recommended that the case be referred to another judge if we were to conclude that she erred in rejecting our first ruling. That was an appropriate course of action, and we can ask no more of a judge who cannot in good conscience follow an appellate ruling.

What we cannot do-and where I part company with the majority-is to fail to enforce our original ruling. Had the district court resentenced the defendant to the same 30-year sentence, I have no doubt that the other panel members would have joined me in reversing and referring the case to another district judge for a second resentencing. It is not necessary to agree with an appellate ruling, but under any system of the rule of law it is necessary to follow it.

On resentencing in this case, the district court merely changed the subject. After rejecting our decision, the court found another, previously unavailable reason to impose a reduced sentence. In the district court's view, the defendant's two years of model conduct within the prison system after his original sentencing justified a five-year reduction of sentence. This new factor led the court to impose a 25-year sentence in place of the original 30 years.

The majority is prepared to accept the new sentence as reasonable in length and, in effect, call it a day. I am not. The new sentence still fails to take into proper consideration the two § 3553(a) factors we singled out as the basis for reversal. That the defendant has since demonstrated other reasons for a reduced sentence is an entirely separate development that fails to *127justify the district court's refusal to follow the original mandate. At this time, we still do not know how a district court which followed the mandate-by giving significant downward weight to the two § 3553(a) factors we identified-would sentence this defendant. What all three members of this panel unanimously identified as significant substantive errors in the original sentencing decision remain uncorrected. These errors continue to form the primary basis for the new sentence.

The issue that separates us is not trivial or confined to the facts of this case. It goes directly to our authority to supervise the sentencing process. In the years between adoption of the federal sentencing guidelines in 1987 and the decision of the Supreme Court in United States v. Booker , 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), review for substantive unreasonability was available principally for considering the scope and extent of a departure from the guidelines. Id. at 261, 125 S.Ct. 738. With the arrival of the current regime of advisory guidelines, the Supreme Court expanded the reach of substantive unreasonability review to cover all sentences. Id. at 260, 125 S.Ct. 738.

As Booker and subsequent cases make clear, substantive unreasonability is the vehicle through which we review the district court's performance in addressing and weighing the sentencing factors identified in 18 U.S.C. § 3553(a). The district court must identify the relevant factors and weigh and balance them appropriately. The judge "must adequately explain the chosen sentence to allow for meaningful appellate review and to promote the perception of fair sentencing." Gall v. United States , 552 U.S. 38, 50, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007). In reviewing this decision, the appeals court applies an abuse of discretion standard.

The process of review is carefully described in United States v. Cavera, 550 F.3d 180 (2d Cir. 2008). It has two parts. We look first at the reasons given by the district court to explain its decision. Giving reasons is mandatory. "Most obviously, the requirement helps to ensure that district courts actually consider the statutory factors and reach reasoned decisions." Id . at 193. Requiring a statement of the courts' reasoning encourages public confidence in federal courts and the fair administration of justice. Id. ; Rita v. United States , 551 U.S. 338, 356, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007) ("Confidence in a judge's use of reason underlies the public's trust in the judicial institution."). Moreover, in the absence of reasons, appellate review of the basis of the decision is severely hampered. "We cannot uphold a discretionary decision unless we have confidence that the district court exercised its discretion and did so on the basis of reasons that survive our limited review. Without a sufficient explanation of how the court below reached the result it did, appellate review of the reasonableness of that judgment may well be impossible." Cavera, 550 F.3d at 193.

We then consider whether the § 3553(a) factors, on the whole, justify the sentence. After Booker , it is a constitutional necessity that the sentencing court make its own determination, informed but not constrained by the sentencing guidelines, about the appropriate length of the sentence. Under an abuse of discretion standard, we defer to the district court and affirm all sentences except those falling outside of the "broad range" warranted by the totality of the circumstances. United States v. Jones , 531 F.3d 163, 174 (2d Cir. 2008). We may not substitute our preferred sentence for the district court's. "The fact that the appellate court might reasonably have concluded that a different sentence was appropriate is insufficient to justify reversal of the district court."

*128Gall , 552 U.S. at 51, 128 S.Ct. 586. Deference to the district court makes reversal on grounds of substantive unreasonability relatively rare, but it does not eliminate meaningful review of the reasons for a sentence.

Applying these general statements to the facts in this case reveals that the sentencing process went awry following the first appeal. At the first sentencing, the district court identified three § 3553(a) factors which guided the sentencing decision: the defendant's history of extreme childhood abuse, the future danger he posed to children, and the serious harm which results from downloading images of child pornography. In the district court's view, these factors supported a sentence of 30 years. In particular, the district court gave minimal weight to the defendant's lengthy history of childhood abuse. The district court concluded, "I can't excuse what you did. I take into consideration your life but I can't excuse that darkness in your heart and soul that made you prey upon two innocent children." Joint Appendix ("J.A.") 167. The court imposed a 30-year sentence, which represented a variance down from the 80-year guideline range.1

We disagreed with the weight the district court assigned to the defendant's personal history and his future dangerousness. We followed Cavera in "consider[ing] whether the [ § 3553(a) factors], as explained by the district court, can bear the weight assigned [them] under the totality of circumstances in the case." United States v. Sawyer , 672 F. App'x 63, 65 (2d Cir. 2016) (quoting Cavera , 550 F.3d at 191 ). Applying an abuse-of-discretion standard, we determined that the § 3553(a) factors the district court addressed did not "appear remotely sufficient to support imposing such a sentence on a person who shared no images with others, possessed fewer images than defendants in typical cases, and did not have sex with the victims or any other underage persons." Id. at 65-66.

Our original ruling set no parameters on the length of the second sentence. It did not propose an alternative sentence. It did not presume to instruct the district court as to the relative significance of the § 3553(a) factors. It required only that the district court reconsider its overreliance on future danger to the community and the insufficient weight given to the defendant's history and personal characteristics. In the panel's view, these factors should have resulted in significant down weight in the sentencing decision. In remanding the case for resentencing, we identified these issues explicitly: "In light of the district court's overreliance on Sawyer's danger to the community, and its failure to afford sufficient weight to Sawyer's history and personal characteristics, settled law dictates that the sentence be vacated on grounds of substantive unreasonableness." Sawyer , 672 F. App'x at 67.

On resentencing, the district court declined to follow this clear mandate. The district court addressed both factors and found no reason to change its mind. In addressing the defendant's history as a victim of abuse, the court stated, "On the mandate, the issue, failure to afford sufficient weight to the way you were raised in determining your sentence, looking at the fact that I departed by 50 years from the [80 year] guideline range, I still can't say in good conscience that my sentence at *129that time was substantively unreasonable." J.A. 258.

Turning to the question of danger to the community, the district court stated, "I felt that there was a lot of evidence in the record, and I still feel that way, to convince me that you continue to be a danger to the community." J.A. 258. The court noted that there were two victims and that the defendant had fled to Florida following discovery of the crime. The court also referred to his arrest at ages 19 and 23 for misdemeanor charges of endangering the welfare of a child.2 The court pointed to the report of the defense psychologist, who described the defendant's risk of re-offense as moderate to high and further described him as being aroused by young children and failing to respect the boundaries which protect children from sexual abuse. In sum, the judge announced that she had not changed her views since the original sentencing:

Although the Court of Appeals disagreed, I did feel that I fully considered a multitude of factors in imposing the prior sentence of 30 years. I still believe that sentence was an appropriate one and is sufficient but not greater than necessary to meet the goals of sentencing.

J.A. 264.

This case poses a fundamental question of court governance. Following an appellate court's determination that a sentence is substantively unreasonable because it fails to give weight to specific § 3553(a) factors, is the district court free on remand to take a second look and decline to change its original position? The only answer consistent with the mandate rule is that the decision of the panel must be followed. Briggs v. Pennsylvania R. Co. , 334 U.S. 304, 306, 68 S.Ct. 1039, 92 L.Ed. 1403 (1948) ("In its earliest days this Court consistently held that an inferior court has no power or authority to deviate from the mandate issued by an appellate court. The rule of these cases has been uniformly followed in later days ...." (citations omitted) ); In re Ivan F. Boesky Sec. Lit. , 957 F.2d 65, 69 (2d Cir. 1992). How much to change the sentence based on the factors identified in the mandate lies within the sentencing discretion accorded to the district courts. But that discretion does not extend to the outright rejection of the mandate which occurred in this case.

The remaining question is whether finding some other basis for a reduced sentence prevents a second reversal. Such a rule would tend to reduce the role of the appellate court to passing on the length of the sentence only. That limitation is inconsistent with Booker , Gall , and Cavera , which identify the role of the appeals court in reviewing the reasons for the sentence, especially those derived from § 3553(a), and determining whether these reasons, considered as a whole, support the sentence. Cf. Gall , 552 U.S. at 47, 128 S.Ct. 586 (rejecting a "rigid mathematical formula" for reasonableness that compared the length of the sentence to the Guidelines because the relative weight of factors cannot be quantified as a percentage of the term). In this regard, the majority's determination that a one-sixth reduction of the original sentence is sufficient to render the *130sentence reasonable is unpersuasive. The consideration of qualitative reasons for the sentence - not the specific term of years - lies at the heart of the process of review of sentencing decisions for substantive unreasonability.

This panel's prior mandate was that the two primary factors that the district court relied upon in fashioning the original sentence did not receive the proper weight. That error placed the sentence beyond the broad scope of discretion accorded to district courts. On remand, the district court declined to follow this decision by according some weight to these factors. The district court's actions mean that these factors still have not received consideration in a manner consistent with the mandate. The district court enjoys wide discretion in deciding how much weight to assign to the two factors. It would thus be difficult to quarrel with a decision following remand that the factors changed the sentence only a little. But the fact that our ruling did not alter the manner in which the district court viewed these factors at all is a glaring indication that its consideration of them remains unchanged and out of balance.

At the risk of repetition, I return to the directive in Cavera to examine the reasons given by the district court for a sentence. The critical issue is not whether the term of years is too long or too short. It is whether the reasons given by the sentencing judge can reasonably support the sentence. Here, we have already considered the principal reasons offered at both sentencings and found them to be insufficient to support the original sentence. That sentence has been re-imposed-reduced only by an unrelated factor not previously available. By failing to enforce its original mandate, the majority denies the defendant a sentence that fairly addresses the reasons which we previously identified as critical to a just sentence.

For these reasons, I respectfully dissent.