
523 F.3d 657 (2008)
Antoinette GIBSON, Plaintiff-Appellee/Cross-Appellant,
v.
David MOSKOWITZ, M.D., Defendant-Appellant/Cross-Appellee.
Nos. 07-1074, 07-1198.
United States Court of Appeals, Sixth Circuit.
Argued: March 11, 2008.
Decided and Filed: April 29, 2008.
*660 ARGUED: Marcy R. Matson, Hall Matson, East Lansing, Michigan, for Appellant. Heather A. Jefferson, Fieger, Fieger, Kenney, Johnson & Giroux, Southfield, Michigan, for Appellee. ON BRIEF: Marcy R. Matson, Hall Matson, East Lansing, Michigan, for Appellant. Heather A. Jefferson, Fieger, Fieger, Kenney, Johnson & Giroux, Southfield, Michigan, for Appellee.
Before: DAUGHTREY and SUTTON, Circuit Judges; POLSTER, District Judge.[*]

OPINION
SUTTON, Circuit Judge.
Ozy Vaughn, a mentally disabled inmate, died from severe dehydration after being held for several days in a 90 to 100 degree observation room. A jury determined that Dr. David Moskowitz's deliberate indifference and medical malpractice caused Vaughn's death and awarded his estate $2 million in compensatory damages (later reduced to $1.5 million) and $3 million in punitive damages. We affirm in part and reverse in part.

I.
On Friday, January 25, 2002, Vaughn, an inmate in the Riverside Correctional Facility in Ionia, Michigan, began acting strangely. Concerned about his behavior, prison officials moved him from his prison cell to an observation room in the Residential Treatment Program of the Ionia facility. Each inmate placed in an observation room is looked after by a "treatment team," which includes a psychiatrist, team of nurses and other trained personnel. For reasons that the record does not fully explain, the temperature in the observation room exceeded 90 degrees (even *661 though it was January in Michigan and even though heating a prison is not cheap, whether in 2002 or today).
After moving Vaughn to the observation room, prison officials placed Dr. David Moskowitz, a psychiatrist, on Vaughn's treatment team. That Friday, Moskowitz met with Vaughn, assessed his condition and proposed treatmentpsychiatric medication and observationto help Vaughn through the weekend.
When Moskowitz returned to work on Monday, he learned that Vaughn's condition had worsened. Although Moskowitz left open the possibility that Vaughn might have a "heat problem," JA 1256, his plan on Monday morning was to "keep observing Mr. Vaughn" and to give the medication "[a] little bit more time to work," JA 1302.
Vaughn's condition continued to deteriorate on Monday. At 12:30 p.m., Paul Foster, a prison guard, reported to the treatment team that Vaughn vomited in the bathroom after trying to drink a large amount of water from the bathroom sink. By Monday afternoon, Vaughn's room had reached 96 degrees. At the end of his Monday shift, Moskowitz concluded that "with cool temperature and more fluids [Vaughn] could be taken care of and . . . the dehydration could be prevented." JA 1308. Moskowitz's plan was to give the medication still more time to work, to transfer Vaughn to a cooler room and eventually to move Vaughn to a psychiatric hospital. Moskowitz "didn't feel that [Vaughn's] status was life threatening." Id.
He was wrong. Vaughn never reached the psychiatric hospital, and by the time he made it to a cooler room on Monday evening his condition had taken yet another turn for the worse. Vaughn began vomiting and dry-heaving, both of which continued into the night until he died from dehydration early Tuesday morning.
Antoinette Gibson, the representative of Vaughn's estate, filed this § 1983 action against Moskowitz and 22 other defendants, alleging deliberate indifference in violation of the Eighth (and Fourteenth) Amendment and raising several state law claims. Before trial, the district court dismissed seven defendants. The remaining defendants asserted qualified immunity, which the district court deniedsave for Nurse Jill Blankstrom, as to whom it granted qualified immunity on the deliberate indifference claims. The estate settled its claims against the remaining defendants, with the exception of Moskowitz, for $600,000. The estate took its claims against Moskowitz to trial, and the jury returned a verdict against Moskowitz on the § 1983 and the state law claims, awarding Gibson $2 million in compensatory damages, later reduced by $500,000 to account for settlements with the other defendants, and $3 million in punitive damages.

II.

A.
Moskowitz first challenges the sufficiency of the evidence, questioning whether it supports the jury's finding that he acted with deliberate indifference to Vaughn's serious medical needs and whether Vaughn's death was a reasonably foreseeable result of Moskowitz's conduct. An inmate may bring a § 1983 claim under the Eighth Amendment only where he can show that a state official acted with "deliberate indifference" to his "medical needs." Clark-Murphy v. Foreback, 439 F.3d 280, 286 (6th Cir.2006) (internal quotation marks omitted). "Deliberate indifference" requires more than mere mistreatment or negligence; it requires the plaintiff to show that the injury was "objectively" serious and that the defendant "subjectively" *662 ignored the inmate's medical needs. Id. (internal quotation marks omitted).
Was Vaughn's medical condition objectively serious? While Moskowitz concedes that Vaughn's medical needs had become serious by Monday, January 28, he argues that they were not serious on Friday, January 25when officials moved Vaughn to the observation room, when Moskowitz began treating Vaughn and when the jury ascribed initial liability to Moskowitz. But drawing all reasonable inferences in favor of the estate, as we must, Williams v. Nashville Network, 132 F.3d 1123, 1131 (6th Cir.1997), we disagree.
Here is what the jury was told about Vaughn's condition on January 25. At one point, he stood naked over his cellmate, holding his Bible and "talking about God." JA 1689. When he finished preaching, Vaughn "tore up all the pages from his Bible, threw the papers all over the floor" and claimed that "outside forces" were controlling his actions. JA 1693. Vaughn was confused, refused to eat or drink and had difficulty following directions. And his condition only deteriorated after officials moved him to the 90-plus degree observation room.
Several experts testified that Vaughn's medication and the hot observation room, in combination, created a serious medical risk, and Moskowitz himself admitted that he understood the potentially deadly combination. Dr. Gerald Shiener, the estate's psychiatric expert, explained to the jury that the drugs Moskowitz prescribed to treat Vaughn's schizophrenia "also affect the part of the brain that regulates temperature." JA 998. When patients on this type of medication are put into a hot environment, they develop a "positive feedback," which means they "keep getting hot and they can't convect the heat or get rid of the heat and their body heats up out of control"all of which leads to "a very dangerous situation." JA 999. Dr. Kathryn Burns, another expert for the estate and the former chief psychiatrist for the Department of Rehabilitation and Correction in Ohio, corroborated Shiener's testimony. "There is a condition among people who take psychotropic medication," Burns said, "where they can't deal with heat as well as other people can. It just impacts their . . . heat dissipation center in their brains." JA 1436.
Dr. Scott Jacobs, the estate's medical expert, bolstered these accounts. Jacobs "[a]bsolutely" believed that Vaughn's dehydration occurred over "a period of days," JA 1154, for three reasons: (1) Vaughn's "phenomenally high" sodium level of 182"to go from . . . a normal sodium [level] of 140 to sodium of 180 takes a long time. . . . It absolutely takes days and days," JA 1154-55; (2) Vaughn's blood-urea-nitrogen level, which measures the buildup of waste in the bloodstream and which was five times the normal level; and (3) "most profoundly," Vaughn's weight loss of 42 pounds over the several days leading to his death, which "could not have happened in one day, could not have happened in two days. It had to have happened over a several day period." JA 1155-56. A reasonable jury could find that Vaughn's medical needs were serious on Friday the 25th.
Did Moskowitz subjectively ignore Vaughn's medical needs? Moskowitz argues that he "did not believe that a serious medical need existed, and specifically did not feel that Mr. Vaughn was suffering from dehydration on January 28, 2002." Br. at 26. The question, however, is not just whether the state employee has admitted the inmate faced an excessive and imminent health risk; it is also whether circumstantial evidence, including "the very fact that the risk was obvious," Farmer v. Brennan, 511 U.S. 825, 842, 114 *663 S.Ct. 1970, 128 L.Ed.2d 811 (1994), shows the employee must have understood the nature of the risk. A reasonable jury could fairly conclude that Moskowitz "kn[ew] of and disregard[ed] an excessive risk to [Vaughn's] health or safety." Id. at 837, 114 S.Ct. 1970.
Moskowitz's own testimony goes part of the way to establishing the point. He knew Vaughn's observation room had heat problems, understood that the potential side effects of his prescribed medicine included "thermoregulation problems," JA 1243, and recognized that Vaughn "might be overheated," JA 1255. Nonetheless, he never asked that Vaughn's temperature be monitored over the weekend, and indeed it never was.
Testimony from other prison officials also supports the jury's finding. Whether through Vaughn's charts or through conversation with other staff members, Moskowitz knew that, over the weekend, Vaughn had stood in the same position for hours, had sweated profusely, had babbled nonsense, had been unable to operate a water cooler, had not slept more than "a couple of hours," JA 1256, had appeared to be in a catatonic state and had vomited, stared blankly and seemed completely out of touch with reality.
All of this was enough for Nurse Blankstrom to reach the conclusionwhich she initially shared with Moskowitz at noon on Mondaythat Vaughn was suffering from severe dehydration. When Vaughn vomited on Monday afternoon after trying to drink a large amount of water, Blankstrom told Moskowitz that she was "scared for Mr. Vaughn's safety and well being." JA 1568. She informed him that she had taken Vaughn's vitals, which were all abnormal. And she relayed her opinion that "the vomiting ultimately point[s] to [a] possibility [that] he was becoming dehydrated." JA 1562.
Blankstrom also asked Moskowitz to examine Vaughnwhich he did, concluding that the problem "was [not] the [medication] or symptoms or side effects from the [medication]," JA 1568and she arranged for Vaughn's medical team to meet to discuss Vaughn's treatment. Blankstrom told the team that Vaughn was exhibiting signs of dehydration and needed immediate medical help. And she asked Moskowitz to evaluate Vaughn one more time because Vaughn "was deteriorating greatly and might be dehydrated." JA 1567. Despite this request, Moskowitz never examined Vaughn again.
The testimony of the estate's experts also supports the verdict. Dr. Jacobs testified that Vaughn's deterioration "ha[d] to be apparent to really anyone" by Monday morning, JA 1173, because the physical manifestations of Vaughn's dehydration including weight loss of over 40 pounds in just a few dayswould have been "so prominent and so striking that you really couldn't miss it," JA 1174. Moskowitz "should have been shocked by [Vaughn's] appearance," Jacobs said. JA 1173. And Dr. Burns testified that Moskowitz should have recognized that Vaughn faced a substantial risk of harm. "[T]he only way," Burns continued, that all of Vaughn's symptomsthe "rapid respiratory rate. . . the confusion, the delirium . . . the [loss of] 40 pounds," JA 1456could have come about is dehydration. "[I]t's got to be water," Burns concluded. Id.
Does the evidence support the compensatory damages award? Even if sufficient evidence supported the jury's liability determination, Moskowitz argues that the evidence does not support the amount of compensatory damages, requiring a new trial on damages or a remittitur. We give abuse-of-discretion review to the denial of either motion. Skalka v. Fernald Envtl. *664 Restoration Mgmt. Corp., 178 F.3d 414, 424 (6th Cir.1999).
The district court did not abuse its discretion in letting this $1.5 million award stand. Vaughn's condition deteriorated over the course of several days, beginning late Thursday/early Friday and ending with his death early Tuesday morning. He suffered cramping, vomiting, confusion, delirium and disorientation during this time. He did not sleep, he sweated profusely and he looked physically ill. His vital signs were all abnormal, and he lost over 40 pounds from the onset of his dehydration until his death. Along with this physical pain, his experts testified, Vaughn would have suffered extreme mental anguish as well. While it is difficult to quantify in dollars what such extensive pain and suffering deserve, the district court did not abuse its discretion in concluding that the jury's award fell within a permissible range.
Does the evidence support the punitive damages award? Moskowitz argues that "no evidence" establishes "that [he] demonstrated reckless or callous disregard for Mr. Vaughn's rights." Br. at 44. That of course is a harder argument to make now that we have concluded that the estate presented sufficient evidence to support a finding of deliberate indifference. See Farmer, 511 U.S. at 839, 114 S.Ct. 1970 ("[W]e adopt [the subjective recklessness standard] as the test for `deliberate indifference' under the Eighth Amendment."). While we need not decide whether a finding of deliberate indifference "necessitate[s] a finding of callous indifference warranting punitive damages," Coleman v. Rahija, 114 F.3d 778, 787 (8th Cir.1997), it remains true that the two standards are "consistent," Farmer, 511 U.S. at 839-40, 114 S.Ct. 1970, and that much of the evidence bearing on the one question bears on the other. In particular, Moskowitz's failure to respond to Vaughn's deteriorating condition on Monday, when others testified that Vaughn's dire condition would have been "striking," "apparent" and "shocking," supports the award as do his appreciation of the heat-related side effects associated with the medications he prescribed and his inexplicably aloof response to the risk. On these facts, the trial court permissibly delegated the question of punitive damages to the jury.
Is the punitive damages award constitutionally excessive? Three considerations guide this inquiry: (1) the degree of reprehensibility of the conduct; (2) the disparity between the harm suffered by the plaintiff and the punitive damages award; and (3) the difference between the punitive damages and the civil penalty imposed in comparable cases. BMW of N. Am., Inc. v. Gore, 517 U.S. 559, 574-75, 116 S.Ct. 1589, 134 L.Ed.2d 809 (1996).
"Perhaps the most important indicium of the reasonableness of a punitive damages award is the degree of reprehensibility of the defendant's conduct." Id. at 575, 116 S.Ct. 1589. While there is no exchange rate for converting reprehensibility into dollars, an award at a minimum "should reflect the enormity of the offense," id. (internal quotation marks omitted), as shown by the permanence and severity of the injury together with the offender's degree of culpability, see id. at 575-76 & n. 24, 116 S.Ct. 1589. Vaughn's injury of course is the most permanent and severe possible, and the considerable evidence of Moskowitz's reckless conduct supports a substantial award.
The second considerationensuring "that exemplary damages . . . bear a `reasonable relationship' to compensatory damages""has a long pedigree." Id. at 580, 116 S.Ct. 1589. Nothing tells us exactly what ratios are reasonable, but the Supreme Court has said that the ratio normally will be no "more than 10 to 1." *665 Id. at 581, 116 S.Ct. 1589. Even giving Moskowitz the benefit of the doubt and comparing the punitive award with the portion of the compensatory damages for which he alone was responsible, the 2 to 1 ratio of punitive damages ($3 million) to compensatory damages ($1.5 million) falls well short of the high end of this range and indeed parallels the kind of relationship that the Court has said will often suffice. See State Farm Mut. Auto. Ins. Co. v. Campbell, 538 U.S. 408, 425, 123 S.Ct. 1513, 155 L.Ed.2d 585 (2003); Pac. Mut. Life Ins. v. Haslip, 499 U.S. 1, 23-24, 111 S.Ct. 1032, 113 L.Ed.2d 1 (1991).
Nor does the third considerationthe difference between the punitive damages award and the civil penalty authorized or imposed in comparable casesestablish that this award was excessive. Moskowitz points to four death-by-dehydration cases, but none involving a § 1983 claim or a punitive damages award. A sample of four cases, moreover, provides precious little guidance for establishing a norm. And the facts in these four cases, at any rate, differed considerably from the multi-day-wrenching facts in this onea man in the custody of the State who loses 40 pounds over four and a half days in the course of dying from dehydration. See JA 707-08 (describing $1 million medical malpractice award where 14-month-old child died the night after being treated and released from hospital); JA 706 (describing $1 million medical malpractice award (reduced to $500,000 based on comparative negligence) where 47-year-old man died of dehydration the day after being treated and released from hospital); JA 703-04 (describing $450,000 medical malpractice award for dehydration death of 5-month-old child); JA 704-05 (describing $605,523 nursing home negligence award where 77-year-old nursing home resident died, ten days after being transferred to a hospital, of pneumonia, complications from bedsores, uncontrolled blood sugars and dehydration). This small sample does not provide a basis for vacating the award.

B.
Moskowitz next argues that the trial court committed a number of evidentiary errors: (1) by admitting evidence concerning his discharge from the prison, (2) by admitting evidence of his treatment of patients other than Vaughn and (3) by refusing to admit evidence about Vaughn's criminal conviction. Abuse-of-discretion review applies to each argument. United States v. Humphrey, 279 F.3d 372, 376 (6th Cir.2002).
Moskowitz's discharge. At trial, Moskowitz testified that he "did everything within the standard of care and everything within [his] power to help this man." JA 1320. In response, the court permitted the estate to introduce evidence that the prison discharged him for violating medical-treatment rules. Moskowitz testified, the court reasoned, "that he did everything he could here. Now if there were rules he violated and that was a cause [of Moskowitz's termination] . . . then I think it needs to come in. . . . [T]he Court is going to allow it for impeachment purposes." JA 1336. Because the district court has "broad discretion" when weighing undue prejudice against probative value, United States v. Vance, 871 F.2d 572, 576 (6th Cir.1989) (internal quotation marks omitted), and because Moskowitz opened the door to this evidence, no abuse of discretion occurred.
Moskowitz's treatment of other patients. At trial, the estate asked Moskowitz whether he had ever "called [patients] derogatory names." JA 1214. When Moskowitz denied he had, the estate attempted to introduce evidence that Moskowitz used an offensive term to describe a patient in a medical chart. Moskowitz objected *666 unsuccessfullyon relevance grounds. Moskowitz now argues that the evidence should not have been admitted under Evidence Rules 402 and 403. Because the estate introduced the evidence only for impeachment purposes, because the evidence contradicted Moskowitz's testimony and because the district court limited the jury's access to the evidence (the court never revealed the offensive comment to the jury), the court did not abuse its discretion.
Vaughn's conviction. When the estate introduced evidence at trial that Vaughn was a "good guy," Moskowitz sought to introduce evidence about Vaughn's criminal conviction, namely that he had sexually assaulted a minor. No doubt, "good character" evidence often begets "bad character" evidence in response. See United States v. McGuire, 744 F.2d 1197, 1204 (6th Cir.1984). But the trial court still has a job to do in deciding what kind of rebuttal evidence is appropriate and in deciding when the risk of undue prejudice outweighs the probative force of admitting the evidence. See id. at 1205-06. The district court did not abuse its discretion in concluding that the limited nature of the "good character" evidence that Vaughn worked hard, behaved responsibly and helped others while in prisondid not warrant introducing evidence about his highly charged crime. The estate's evidence concerned Vaughn's behavior once he was in prison, not what he had done before he entered prison, and the court fairly could restrict any impeachment evidence to his conduct in jail.

C.
Moskowitz raises two other arguments about alleged procedural errors. First, Moskowitz argues that the trial court erred in applying Michigan's "high tier cap" on non-economic damages for medical malpractice. Br. at 57. Michigan law requires the presiding judge in a medical malpractice action to apply a cap on non-economic damages. Mich. Comp. Laws § 600.6098(1). The "low cap" of $382,800 limits a plaintiff's recovery for non-economic damages, unless the judge determines the damages fall within a statutory exception, in which case the "high cap" of $683,500 becomes the new limit. Id. § 600.1483(1), (4). The relevant exception here provides that if "as a result of the negligence of 1 or more of the defendants. . . [t]he plaintiff has permanently impaired cognitive capacity rendering him or her incapable of making independent, responsible life decisions and permanently incapable of independently performing the activities of normal, daily living," the "high cap" applies. Id. § 600.1483(1)(b); see also Shinholster v. Annapolis Hosp., 471 Mich. 540, 685 N.W.2d 275, 286-89 (Mich. 2004).
Because Vaughn already had a condition  schizophrenia  which "permanently impaired [his] cognitive capacity," Moskowitz argues that he could not satisfy the statutory exception. That Vaughn had an existing cognitive limitation, however, does not mean Moskowitz's care could not have impaired Vaughn's cognitive capacity in other waysas surely happened when Vaughn became increasingly dehydrated over the relevant four-and-a-half-day period. Indeed, his estate presented evidence that, although Vaughn suffered from schizophrenia, he had the cognitive capacity to act responsibly and independently and even to help others less able. The district court correctly rejected this argument.
Second, Moskowitz argues that the district court abused its discretion in allocating the compensatory damages award between the deliberate indifference and medical malpractice claims. In addition to determining whether the statutory "high *667 cap" applied to the estate's medical malpractice claim ($683,500), the court also had the duty to allocate the compensatory damages award between the two theories of reliefeither by asking the jury to make the allocation or by making the allocation itself. The court's instructions asked the jury to make a compensatory damages award (originally $2 million, later reduced by the court to $1.5 million) and to separate the damages "if you are able to do so." JA 490. While the jury was able to determine the amount of compensatory damages, it apparently was unable to allocate them and left this portion of the verdict blank.
That left the court with responsibility to make the allocation, a task often left to trial judges. See Passantino v. Johnson & Johnson Consumer Prods., Inc., 212 F.3d 493, 509 (9th Cir.2000) ("[T]he district court generally has discretion regarding how to allocate the damage award."); see also Viskase Corp. v. Am. Nat'l Can Co., 261 F.3d 1316, 1329 (Fed.Cir.2001) (after affirming a jury's finding of liability on one theory of relief and reversing its finding of liability on others, remanding so the district court "may determine whether the jury's assessment of damages," which did not allocate damages between theories of relief, "can be reconstructed from the accounting evidence"); Quezada v. Bernalillo, 944 F.2d 710, 722-23 (10th Cir. 1991), (vacating the unallocated damages award and instructing the district court on remand to allocate damages between state tort and § 1983 theories of relief where the appellate court affirmed the finding of state tort liability but set aside a judgment for the plaintiff on the § 1983 claim), overruled on other grounds by Saucier v. Katz, 533 U.S. 194, 121 S.Ct. 2151, 150 L.Ed.2d 272 (2001); cf. Johnson v. Howard, 24 Fed.Appx. 480, 485 (6th Cir. Dec.12, 2001) ("Although a double recovery may not be had, the jury is not prohibited from allocating a total damages award between different theories of recovery.").
In making this allocation, however, the court simply decided that the medical malpractice damages went to the top of the "high cap" ($683,500) and allocated the rest of the $1.5 million award to the deliberate indifference claim ($816,500). That allocation may well represent a permissible allocation of the damages between the two theories, but the court gave no explanation for its decision, leaving us guessing whether this exercise of discretion is a permissible one.
Nor is the allocation without consequence in this context. The trial court's division happens to be the best the estate could hope forallowing the medical malpractice damages to go precisely to the cap (and no higher), allocating the rest to deliberate indifference damages and effectively removing the cap as a limit on any damages in this case. The trial court's division also does not intuitively follow from the evidence. Because the deliberate-indifference standard requires the plaintiff to prove more in the way of culpability than the medical-malpractice standard requires her to prove, one might expect the damages attributable to medical malpractice to be higher than those attributable to deliberate indifference. But even if the trial court took the view that the damages should be allocated by halveswith 50% of the damages attributable to one theory and 50% attributable to the otherthat still would make a difference here. It would mean the estate would receive $750,000 in deliberate indifference damages and $683,500 (after the cap) in medical malpractice damagesor $1,433,500, which is to say $66,500 less than the court awarded.
The point is that the cap matters, and the district court's decision leaves it unclear whether it appreciated the potential *668 impact of the cap and, what is more, leaves it unclear why it allocated the damages the way it did. None of what we have said limits the district court's discretion on remand, and none of what we have said requires a new trial. We simply ask the district court to make an allocation, then explain why it has done so. In the final analysis, we cannot tell whether the district judge's allocation of damages falls within her discretion on this record. See DWG Corp. v. Granada Invs., Inc., 962 F.2d 1201, 1202 (6th Cir.1992); see also Bridgeport Music, Inc. v. Universal-MCA Music Publ'g, Inc., 481 F.3d 926, 930 (6th Cir.2007) (noting in the attorney-fee context that we "cannot know for sure" whether the court abused its discretion until and "unless such grounds are made explicit") (internal quotation marks omitted); id. ("[T]he court's silence prohibits us from examining the soundness of its discretionary judgment.") (internal quotation marks omitted); cf. Sprint/United Mgmt. Co. v. Mendelsohn, ___ U.S. ___, 128 S.Ct. 1140, 1146, 170 L.Ed.2d 1 (2008).

III.
For these reasons, we affirm in part and reverse in part.
NOTES
[*]  The Honorable Dan Aaron Polster, United States District Judge for the Northern District of Ohio, sitting by designation.
