Geoffrey W. Crawford, District Judge:
*560This case returns on a second appeal following resentencing. Because we conclude that the district court did not follow this panel's prior mandate, we vacate the sentence for the second time and order resentencing before a different judge.
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 young girls, aged 4 and 6 at the time of the offenses. 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 which Sawyer downloaded from the Internet.
Each of the sexual exploitation charges 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.
The Original Sentencing
The presentence report and the defendant's sentencing memorandum described Sawyer's personal history as a victim himself of childhood sexual abuse. He was subjected to severe abuse, including rape, as a small boy at the hands of men and women. At the first sentencing, the judge described the defendant's childhood as "horrid [and] nightmarish" and marked by "a childhood that never was" and "incredible sadness." Transcript of Sentencing, July 7, 2015, at 30-31. By the age of 7, he had been victimized sexually. He witnessed prostitution and drug use in his home. Before the age of 10, he was introduced to drugs and alcohol. 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 *561the 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 15 years, consecutive, on each of the child exploitation counts and five years, concurrent, on the receipt of child pornography count, for a total effective sentence of 30 years of imprisonment.
The First Appeal
On appeal, Sawyer contended that his sentence 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 65-66. It was not 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 a risk of such behavior in the future. 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 .... 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." Sawyer , 672 F. App'x at 67. We concluded that the defendant's own extraordinary history of childhood abuse and the expert testimony that it contributed to the commission of the offense justified "not just a departure from the Guidelines, but a significant one indeed." Id. We vacated the sentence and remanded for "imposition of a new sentence that comports with this opinion." Id.
The Second Sentence
The district court held a de novo sentencing hearing on July 7, 2017, and reduced the total sentence from 30 to 25 years.1 The judge's sentencing remarks identify Sawyer's good conduct in prison following the first sentencing as the basis for the five year reduction. The judge did not alter her sentence to reflect the direction in this panel's mandate. She 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 that time was substantively unreasonable. I would be surrendering the conviction of what I did.
Transcript of Sentencing, July 7, 2017 ("Resentencing Tr.") at 34. The judge explained that she remained persuaded, in light of Sawyer's childhood abuse and the findings of the defense psychologist, that *562"because of the way you were raised, you do continue to be a clear and present threat to society and specifically to children." Id. at 37. She reviewed at length the basis for her original sentence. She stated, "[a]lthough 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." Id. at 40. In closing, the judge indicated that if a further remand became necessary, for reasons of judicial economy, the case would be best sent to a different judge.
Scope of Review
"In sentencing, as in other areas, district judges at times make mistakes that are substantive. At times, they will impose sentences that are unreasonable. Circuit courts exist to correct such mistakes when they occur." Rita v. United States , 551 U.S. 338, 354, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007). As a reviewing court, we accord great latitude to the experience and judgment of the sentencing court, but we retain authority to vacate sentences which are unreasonable in length or in some other way fail to meet the requirements of 18 U.S.C. § 3553.
The mandate rule, a component of the law of the case doctrine, requires district courts to comply with circuit court mandates in proceedings on remand. 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. 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.
Discussion
When we first heard this case on appeal, we ruled that a 30-year sentence was substantively unreasonable in light of the circumstances of the case. See Sawyer , 672 F. App'x at 67. The substance of our prior ruling is not at issue in this appeal, and we need not recapitulate our earlier summary order in full detail here. It suffices to restate in brief the two related shortcomings we identified in the first sentence: (1) the district court's failure to give sufficient downward weight to the effect of the severe sexual abuse Sawyer endured at home throughout his childhood, and (2) the district court's overreliance on the factor of Sawyer's danger to the community.
An extraordinary history of familial sexual abuse during childhood has long been recognized as a potential basis for downward departure. See United States v. Brady , 417 F.3d 326, 333 (2d Cir. 2005) ("[I]n extraordinary circumstances a downward departure may be warranted on the ground that 'extreme childhood abuse caused mental and emotional conditions that contributed to the defendant's commission of the offense.' ") (quoting United States v. Rivera , 192 F.3d 81, 85 (2d Cir. 1999) ). Neither the district court nor this court had any difficulty recognizing the horrific and extraordinary nature of the childhood abuse Sawyer suffered. See Sawyer , 672 F. App'x at 67.
In imposing a 30-year sentence, the district court also misapprehended the danger posed to the community by Sawyer. Sawyer produced a comparatively small number of images, and there was no evidence at sentencing that he had disseminated child pornography to others or had sexual contact with any children beyond the touching of the inner thigh. The danger posed to the community by such an individual is assuredly less than that posed *563by someone who has actually sexually assaulted children. The 30-year sentence in this case flattened the real and meaningful distinction between Sawyer and other child abusers who have shown themselves to be greater threats. Id. at 66 ; see United States v. Dorvee , 616 F.3d 174, 187 (2d Cir. 2010) ; compare, e.g. , United States v. Irey , 612 F.3d 1160 (11th Cir. 2010) (en banc) (vacating a 210-month sentence and ordering the imposition of a 30-year sentence on a defendant who "raped, sodomized, and sexually tortured fifty or more little girls, some as young as four years of age, on many occasions over a four- or five-year period" and "scripted, cast, starred in, produced, and distributed worldwide some of the most graphic and disturbing child pornography that has ever turned up on the internet.").
Moreover, when the district court discussed the examining psychologist's mention of Sawyer's moderate to high risk to reoffend, Resentencing Tr. at 259, it failed to take note of that same psychologist's view that Sawyer's "risk would be reduced if he is able to complete a sex offender treatment program." App'x at 106. The psychologist noted that Sawyer had substantial untreated trauma and, given that he "never witnessed a healthy parenting experience," had his "psychological development arrested at an early age." Id. He "is motivated to stay drug and alcohol free" and is "remorseful, guilt ridden and self-loathing." Id. This all suggests that Sawyer's risk of reoffending depends largely on his access to treatment.
We vacated the sentence and remanded "for imposition of a new sentence that comports with this opinion." Sawyer , 672 F. App'x at 67. We directed the district court to impose a new sentence that included a significant downward departure reflecting Sawyer's childhood history. We also called for a reassessment of Sawyer's risk to the community.
The precise magnitude of the downward departures to be assessed on the basis of Sawyer's extraordinary history and risk to the community were left to be determined by the district court. But our mandate required some downward departure on the basis of Sawyer's history, and some downward departure based on a reassessment of the danger posed by Sawyer. These were issues we explicitly addressed on appeal, and the mandate rule compelled the district court to execute our directions.
On resentencing, the district court identified Sawyer's good conduct in prison since the original sentencing as a basis for a five-year reduction of the sentence, and imposed a sentence of 25 years of imprisonment. The district court ordered no downward departure on either of the grounds specifically identified in our summary order as grounds for significant downward departures. It thereby failed to comply with the mandate rule. Its sentence, imposed in violation of the mandate rule, cannot stand.
The reduction of the sentence from 30 years to 25 years for a reason not available at the time of the original sentencing did not satisfy our prior mandate. While the total sentence was shortened, the errors identified in our original summary order remained uncorrected. It may well be that Sawyer's good conduct in prison warrants an additional downward departure. Sawyer's good conduct might also support a conclusion that the risk to the community caused by his untreated trauma and the lack of moral guidance from his childhood can be significantly mitigated via rehabilitation. It was entirely appropriate for the district court to consider Sawyer's good conduct, and it could properly have done so in addition to, not instead of, addressing the errors we identified.
*564In reviewing the second sentencing, we do not question the good faith of the district judge in responding to a serious offense in a manner which she believed would best protect the victims and the community. Crimes involving the sexual abuse of children, especially very young children as in this case, are appropriately the subject of indignation and revulsion. But every federal sentence is potentially subject to review for reasonableness, including sentences for crimes which are deeply offensive. Where an appellate court determines that certain deficiencies render a sentence substantively unreasonable, a district court must correct those deficiencies on remand, even if the district court judge disagrees with the appellate court's determination.
"Three considerations ... are useful in deciding whether to reassign a case on remand: (1) whether the original judge would reasonably be expected upon remand to have substantial difficulty in putting out of his or her mind previously-expressed views or findings determined to be erroneous, (2) whether reassignment is advisable to preserve the appearance of justice, and (3) whether reassignment would entail waste and duplication out of proportion to any gain in preserving the appearance of fairness." United States v. DeMott , 513 F.3d 55, 59 (2d Cir. 2008) (quotation marks omitted). We have previously determined that "[h]aving reimposed an identical sentence after the first remand, the district judge may reasonably be expected to have substantial difficulty ignoring his previous views during a third sentencing proceeding." Id. The same reasoning favors reassignment in this case, where the district judge has noted on the record her continuing disagreement with this court and has informed us that "it would probably be better for judicial economy if another judge sentence for a third time." Resentencing Tr. at 53.
The sentence imposed on July 7, 2017 is VACATED , and this matter is REMANDED for resentencing. The clerk of the United States District Court for the Northern District of New York is respectfully directed to assign the matter to a different judge for resentencing.
The second sentence was 180 months each on Counts One and Two, consecutive for 120 months and concurrent for 60 for a total of 300 months or 25 years. Count Three remained a concurrent sentence of 60 months.