Concurring opinion filed by Circuit Judge KAVANAUGH.
Opinion concurring in part and dissenting in part filed by Circuit Judge HENDERSON.
GRIFFITH, Circuit JudgeArmy Sergeant Juwan Johnson died in July 2005 after participating in a violent hazing ritual near Ramstein Air Force Base in Germany. A jury convicted appellant' Rico Williams of second-degree murder and witness tampering for his role in the hazing and in covering up information about Johnson’s death. We affirm Williams’s conviction for witness tampering, but we reverse his murder conviction.
I
Rico Williams was stationed at Ramstein Air Force Base as an Airman in the United States Air Force starting around 2001. He was discharged for medical reasons in May 2005 but remained at Ramstein as a dependent of his wife, Octavia, who was also an Airman. Williams was the leader, or “governor,” of a group that went by various names: “BOS,” “Brothers of the Struggle,” or “Gangster Disciples.” (For simplicity, this opinion will refer to the group as the BOS.) The BOS was made up of members of the U.S. Army and Air Force at Ramstein but was not affiliated with the military. Expert evidence at trial connected the BOS to the Gangster Disciples, an American gang with roots in Chicago and individual “sets,” or local groups, around the world. Although members of the BOS often got into fistfights, the government’s witnesses testified at trial that they did not engage in any other criminal activity.
The BOS did, however, regularly initiate hew members by beating them up in a ritual known as a “jump-in.” During a typical jump-in, approximately six members of the BOS hit the initiate for about six minutes. Blows were to be landed only between the neck and the waist, and the initiate was forbidden from defending himself in any way. During the jump-in, the initiates were asked repeatedly if they wanted to. proceed. If they said no, the initiation ended. After a jump-in, the new member would be hugged, kissed on the cheek, shown the BOS handshake, and taken out to celebrate. The BOS had performed around fifteen to eighteen jump-ins before Johnson’s; in none had a new member been hospitalized or killed.
Johnson’s jump-in took place on the night of July 3, 2005, at a brick-floored hut near the Ramstein base. Nicholas Sims, who was second in command to Williams in the BOS, testified for the government that nine people participated in Johnson’s jump-in — more than the usual six. Sims recalled that Williams asked Johnson whether he wanted to begin. Johnson responded: “Hell yeah.” Williams asked him again, and he again replied: “Hell yeah.” Then Williams punched Johnson in the face. Johnson fell immediately, but stood again. Asked if he wanted to continue, he repeated: “Hell yeah.” Williams again punched him in the face. The group then began hitting him below the neck and above the waist. After two or three minutes, the group stopped while Williams and *5Sims, as the top-ranking members of the BOS, continued to pummel Johnson for the next minute. The other members then joined in again on the beating.
Another government witness, Themetrious Saraglou, similarly testified that Williams asked Johnson before the beating began if “he was sure he wanted this,” and that Johnson said: “Hell yes.” Saraglou further testified that throughout the jump-in, when Johnson fell, he was asked: “Do you want this?” He “would reply and say, ‘yeah,’ or ‘hell yeah,’ or even ‘f*** yeah.’ ” Saraglou testified that by about halfway through the beating, Johnson wasn’t as “hyper” as he had been at the beginning; he began responding simply “yeah,” instead of “hell yeah.” At some point, Johnson was held up as members continued to hit him repeatedly. At another point, members kicked Johnson while he was on the ground. No kicking had occurred at prior jump-ins. "When the six minutes were up, the timekeeper had to yell “time” three times before the beating stopped. As a result, the jump-in lasted longer than usual.
Johnson never lost consciousness during the jump-in and though his mouth was bleeding, Johnson showed no other visible sign of serious injury when it ended. According to Sims, Johnson was exhausted and walking “like a drunk person, but by himself.” Saraglou testified that Johnson was walking slowly and said he was too sore to go out to celebrate with the others. Williams directed BOS members to take Johnson home and charged Florentino Charris with watching him overnight. Charris testified that around midnight, Johnson was slurring his speech and having trouble walking. Sometime later, Johnson asked to go to the hospital. Instead of taking him to the hospital, Charris relayed Johnson’s request to another BOS member, who called Williams. Williams said not to take him. Charris followed Williams’s direction, but told Johnson to let him know if he needed anything. Charris fell asleep in the room with Johnson. When he woke up in the morning, Johnson was dead.
An autopsy revealed injuries to Johnson’s brain and heart. These “blunt force injuries” inflicted during the initiation caused Johnson’s death, according to the government’s medical expert at trial. By contrast, the defense’s medical expert opined that the underlying cause of death was sickle-cell trait, a typically asymptomatic genetic condition, and that “superficial blunt impact injuries” were merely a “contributing” cause.
Two days following Johnson’s death, Williams moved back to the United States. He was arrested in Virginia in February 2009 and charged with four counts in relation to Johnson’s death, one of which the district court dismissed partway through trial. Of the remaining three, the first count was second-degree murder under the Military Extraterritorial Jurisdiction Act of 2000 (ME JA), which provides federal jurisdiction over crimes committed by a civilian accompanying the Armed Forces outside the United States. See 18 U.S.C. § 3261 et seq.
The two other counts charged that Williams had tampered with witnesses in violation of 18 U.S.C. § 1512(b)(3). One alleged that Williams made a threat to Sims and three other BOS members at a cookout the day after Johnson died. According to Sims, Williams told them that if questioned by the authorities, they were to say that Johnson died because “Turkish people jumped” him. Williams also threatened that they would be “basically done for” if they told the truth about Johnson’s death. Sims testified that he took this threat to mean Williams would kill anyone who told the truth. Trial Tr. 36-37 (Oct. 25, 2010). The other tampering count alleged that Williams called Saraglou from *6the United States later that month and told him to order Sims to cover up a tattoo that signaled gang membership.
In November 2010, a jury found Williams guilty of second-degree murder and one count of witness tampering based on his threat to Sims (but not to any others). The jury acquitted Williams of the tampering count related to Sims’s tattoo. In April 2012, Williams was sentenced to 22 years’ imprisonment on the murder conviction and a concurrent 10 years’ imprisonment for witness tampering. The court also ordered restitution of $756,000.
Williams moved for judgment of acquittal on the murder and witness-tampering counts. As for the murder count, he argued that the evidence was insufficient to establish that the requirements of MEJA were met or that he had the state of mind required for a murder conviction. The district court denied that motion. See United States v. Williams, 825 F.Supp.2d 117, 118-19 (D.D.C. 2011). Williams also moved for a new trial on the grounds that the government misstated the law during closing argument and that the district court made several incorrect evidentiary rulings. The district court denied these motions, too.
On appeal, Williams contends that the evidence was insufficient to convict him of murder. He also argues that a prosecutorial misstatement of law during closing argument substantially prejudiced his trial. He further challenges three evidentiary rulings by the district court and various other alleged prosecutorial errors. We have jurisdiction under 28 U.S.C. § 1291 and 18 U.S.C. § 3742(a).
II
We begin with Williams’s challenges to the sufficiency of the government’s evidence at trial.1 He maintains that the prosecution failed to prove that he was “residing with” a member of the U.S. military and that he was not a “national of or ordinarily resident in” Germany at the time the offense occurred, as required to establish federal jurisdiction- under MEJA. 18 U.S.C. § 3267(2). Further, he argues that the evidence was insufficient to find that he had the requisite state of mind for second-degree murder.
Our review is highly deferential: we must accept the jury’s verdict if “any rational trier of fact” could have found the elements of the crime beyond a reasonable doubt. United States v. Battle, 613 F.3d 258, 264 (D.C. Cir. 2010). We view the evidence in the light most favorable to the government, drawing no distinction between direct and circumstantial evidence, and “giving full play to the right of the jury to determine credibility, weigh the evidence and draw justifiable inferences of fact.” Id. Examined through this deferential lens, Williams’s sufficiency-of-the-evidence arguments fail.
A
At trial, the government was required to prove beyond a reasonable doubt that Williams met the elements of MEJA, *7which provides for federal jurisdiction over crimes committed by civilians accompanying a member of the Armed Forces abroad. See 18 U.S.C. §§ 3261, 3267(2). A defendant meets the statutory criteria for “accompanying” a military member if, at the time the crime occurred, he was: (1) a dependent of a member of the Armed Forces; (2) “residing with” that member outside the United States; and (3) “not a national of or ordinarily resident in the host nation.” Id. § 3267(2). Williams contends that the government failed to prove the second and third elements of MEJA.
Although the question is close, the evidence was sufficient for a rational juror to find beyond a reasonable doubt that Williams was “residing with” his wife Octavia, a member of the Air Force, when the crime occurred on July 3, 2005. Three of the government’s witnesses testified that Williams lived with Octavia. One of those witnesses, Charris, further testified that sometime after he joined the BOS in April or May 2005, he attended a meeting at Williams’s house and saw Octavia there. However, no witness said that Williams lived with Octavia at the time of Johnson’s death. Complicating matters, government witness Sims testified on cross examination that Williams was having marital problems in June 2005. Asked- whether Williams was “moving around and staying with” other people during this interval, Sims responded that he was. Trial Tr. 29 (Oct. 26, 2010). He did not identify where exactly Williams was staying but said that Williams was “all over the place.” Id. Williams left Germany and moved back to the United States on July 6, 2005.
This evidence meets the low bar required to defeat a sufficiency-of-the-evidence challenge. As the district court reasoned, a rational juror could have determined that Charris joined the group as late as the end of May 2005 and, therefore, that the meeting at. Williams’s house where Octavia was present took place in June or early July 2005. A juror could rationally infer from this evidence that Williams resided with his wife on July 3, 2005. Moreover, the government’s witnesses offered unqualified testimony that Williams- lived with Octavia. A rational juror could infer that one of the witnesses would have qualified his testimony had Williams moved out before the jump-in. Cf. United States v. Lamy, 521 F.3d 1257, 1268 (10th Cir. 2008) (holding that a jury may rationally infer from testimony that a house “is” within Indian country that the house was “within reservation boundaries at all times within the knowledge of the[ ] witnesses”). Taken together, this evidence was sufficient to permit a rational juror to find beyond a reasonable doubt that Williams resided with his wife at the time of Johnson’s death.
Sims’s statement that Williams was staying with other people in June 2005 may appear to cloud the picture. However, the jury was entitled to discredit that testimony. See United States v. Jenkins, 928 F.2d 1175, 1178 (D.C. Cir. 1991) (“Credibility determinations may rest on a witness’s demeanor and, for that reason, are for the jury, not us.”). And even those jurors who believed Sims could have inferred that Williams resided with Octavia at the time of Johnson’s death. Because MEJA does not define “residing,” we give the term its ordinary meaning. See Alabama v. North Carolina, 560 U.S. 330, 340, 130 S.Ct. 2295, 176 L.Ed.2d 1070 (2010). To “reside” is “[t]o dwell permanently or for a considerable time” or “to have one’s settled or usual home in or at a particular place.” OxfoRD English DictioNaey (2d ed. 1989) (emphasis omitted). A person can have more than one residence. See United States v. Venturella, 391 F.3d 120, 125 (2d Cir. 2004); Eastman v. Univ. of Mich., 30 F.3d 670, 673 (6th Cir. 1994). Thus, even jurors who *8credited Sims’s testimony that Williams was “staying” with other people in June 2005 could have determined that Williams still “resided” with his wife — either because he resided with her but was temporarily staying elsewhere, or because he resided in multiple places. Where the evidence can support “varying interpretations, at least one of which is consistent with” the jury’s verdict, we must defer to that verdict. United States v. Ayewoh, 627 F.3d 914, 919 (1st Cir. 2010) (emphasis omitted).
We similarly reject Williams’s argument that the evidence was insufficient to prove that he was not a “national of’ or “ordinarily resident in” Germany at the time of Johnson’s death. 18 U.S.C. § 3267(2)(C). As proof of nationality, the government introduced a questionnaire that Williams completed as part of a 1996 application for a national-security position. Williams checked the box indicating that he was a U.S. citizen or national by birth. He wrote “NA” in the section of the questionnaire that inquired about dual citizenship. Williams contends that the government’s evidence establishes only that he was not a German national in 1996. It says nothing about whether he was a “national of’ Germany on the date of Johnson’s death in 2005.
The evidence of Williams’s nationality is indeed dated. But as explained in a leading treatise on the law of evidence, “[wjhen the existence of an object, condition, quality, or tendency at a given time is in issue,” its “prior existence” can indicate that it “persisted] or continued] at a later period.” United States v. Stuart-Caballero, 686 F.2d 890, 893 (11th Cir. 1982) (per curiam) (quoting 2 Wigmoee, Evidence § 437(1) (Chadbourn rev. 1979)). The likelihood that a condition persists
depends on the chances of intervening circumstances having occurred to bring the existence to an end. The possibility of such circumstances will depend almost entirely on the nature of the specific thing whose existence is in issue and the particular circumstances affecting it in the case in hand. That a soap bubble was in existence half an hour ago affords no inference at all that it is in existence now; that Mt. Everest was in existence ten years ago is strong evidence that it exists yet[.]
Id. In our view, nationality falls closer to the Mount Everest end of the spectrum. An individual’s nationality, while not immutable, does not ordinarily change 'over the course of a nine-year period.2 Thus, knowing that Williams was not a German national in 1996, a juror could rationally infer that he was not one in 2005.
The evidence was also sufficient to prove that Williams was not “ordinarily resident in” Germany. Again giving this undefined term its ordinary meaning, we note that “ordinarily” means “usually.” OxFORD English Dictionary (2d ed. 1989). MEJA thus envisions that a person “accompanying the Armed Forces” in a host country resides in that country as a military dependent, but is not usually resident there. In other words, he lives there because of his connection to the military rather than because of other significant “local ties.” Daneshpayeh v. Dep’t of Air. Force, 17 F.3d 1444, at *2 (Fed. Cir. 1994) (unpublished) (approving an agency find*9ing that a civilian Air Force employee was “ordinarily resident in” Turkey because he had “profound local ties” there). This interpretation also accords with Congress’s intent in enacting MEJA, which was to permit the United States to try crimes committed by civilians connected to the military while simultaneously “recog-niz[ing] that the host nation has the predominant interest in exercising criminal jurisdiction over its citizens and other persons who make that country their home.” H.R. Rep. 106-778, pt. 1, at 21 (2000).
We further observe that before the passage of MEJA, the term “ordinarily resident” was used in Status of Forces agree-pients — treaties governing the duties and privileges of countries that station armed forces overseas. The military has interpreted the term in various publications. While the government does not ask us to defer to any of the military’s definitions, see United States v. Apel, — U.S. -, 134 S.Ct. 1144, 1151, 186 L.Ed.2d 75 (2014) (“[W]e have never held that the Government’s reading of a criminal statute is entitled to any deference.”), they confirm our interpretation that an individual must have at least some significant ties to the host nation, outside of his connection to the military, to qualify as “ordinarily resident.” 3
The government introduced evidence that Williams was stationed at Ramstein because of his military service from 2001 until he was discharged in May 2005. A rational jury could have readily inferred from this evidence that Williams was not “ordinarily resident in” Germany during this period. Cf. Collins v. Weinberger, 707 F.2d 1518, 1519 & n.7 (D.C. Cir. 1983) (explaining that the Status of Forces agreement for the North Atlantic Treaty Organization distinguishes military personnel — and accompanying civilian employees — stationed in a foreign nation from locals who are “ordinarily resident” there). A rational juror could also infer that Williams did not become an ordinary, or usual, resident of Germany in the interval between his discharge and Johnson’s death. For starters, this period was short, lasting no longer than two months. Further, evidence showed that Williams’s home was on base rather than in a private dwelling, and that he was married to an American servicemember rather than to a German national or ordinary resident. Evidence also revealed that Williams left Germany for the United States two days after Johnson’s death, on July 6, 2005, and never returned. See Daneshpayeh, 17 F.3d 1444, at *2 (employee who was “ordinarily resident” in Turkey lived there for almost 20 years, was married to a Turkish woman, and lived in an apartment building she owned). A jury could have rationally inferred from this evidence that Williams did not have significant local ties at the time of Johnson’s death but rather lived there because of his connection to the military.
Before leaving our discussion of MEJA, however, we observe that the government could have taken straightforward steps to “avoid the need for judicial consideration of what should be a non-problem.” United States v. Hall, 613 F.3d 249, 253 (D.C. Cir. *102010). With respect to Williams’s residency with his wife, for example, the government could have asked its witnesses where Williams lived at the time of Johnson’s death or introduced evidence of where Williams kept belongings or received mail. See United States v. Morris, 977 F.2d 617, 620 (D.C. Cir. 1992) (concluding that evidence that a defendant kept his possessions in an apartment could “support a reasonable inference that [he] lived [there]”). As we have in other close cases, we note that “[t]he sufficiency of evidence is always situational,” and that the government “should not find out the hard way what change in circumstances would be sufficient to render its inadequate performance on this issue fatal to a conviction.” Hall, 613 F.3d at 253.
B
Williams next argues that the evidence was insufficient for a rational juror to find beyond a reasonable doubt that he acted with the mental state required for murder. We reject this contention.4
Whether a defendant is convicted of second-degree murder, as opposed to involuntary manslaughter, depends on the presence of malice aforethought. Compare 18 U.S.C. § 1111(a) (murder), with id. § 1112(a) (manslaughter). Malice can be proven by showing that a defendant intended to kill or, as the government argued here, that he consciously disregarded an extreme risk of death or serious bodily injury. Williams contends that the government did not prove that his actions met the heightened standard of recklessness required for a murder conviction. He points to testimony that Johnson repeatedly said he wanted the jump-in to continue and did not appear seriously injured when it ended. Williams also argues that the evidence showed he told other BOS members to take Johnson to the hospital if necessary.
But the government presented ample evidence from which a rational juror could infer that Williams consciously disregarded an extreme risk of death or serious injury to Johnson. For example, testimony at trial suggested that Williams had a signature move called the “one-hitter quitter,” which knocked people out with one punch, and that he once refused to initiate the group’s female member via jump-in because it “would kill her.” Testimony also suggested that Johnson’s jump-in was more dangerous than prior hazings. Not only did it last longer and involve more people than usual, but Saraglou testified that Johnson was held up at one point while group members repeatedly punched him without asking if he wanted to continue the jump-in.. And Sims stated that at another point, Johnson curled up in a ball while he was kicked. According to Charris’s testimony, moreover, after the jump-in Williams told another BOS member over the phone not to take Johnson to the hospital. A rational juror could infer from this evidence that Williams was aware of his own strength, understood that jump-ins could lead to serious injury or death, and knew that Johnson’s jump-in presented a more extreme risk than most initiations. From this evi*11dence, .the jury was entitled to find that Williams behaved with conscious disregard of an extreme risk to human life. See United States v. Foster; 557 F.3d 650, 655 (D.C. Cir. 2009) (explaining that in a sufficieney-of-the-evidence challenge, the court must give “full play to the right of the jury to determine credibility, weigh the evidence and draw justifiable inferences of fact”).
Ill
Williams next argues that a prosecuto-rial misstatement of law during closing argument substantially prejudiced the outcome of his trial. We agree that the government misstated the law in its closing argument. Because the misstatement implicated a central issue — the state of mind with which Williams acted' — and was not sufficiently cured, it requires reversal of Williams’s murder conviction.
A
Before trial, the parties agreed on a jury instruction explaining that Johnson’s willing participation in the jump-in did not excuse or justify Williams’s conduct. The instruction read, in relevant part: “The defense of consent is not available for homicide or involuntary manslaughter, and therefore should not be considered.” Proposed Jury Instructions 46, No. l:09-cr-00026 (D.D.C. Oct. 19, 2010). After trial began, however, Williams asked the district court to add language to that instruction to clarify that the jury could consider Johnson’s consent to the jump-in “in determining whether the defendant had the necessary malice aforethought to establish the crime of second-degree murder.” Trial Tr. 57 (Nov. 5, 2010). He argued that the particular circumstances of the case required a more detailed instruction to clarify. that the jury could consider Johnson’s willing participation in the initiation when assessing whether Williams consciously disregarded ah extreme risk to human life. The district court denied this request because, in the court’s view, it was inaccurate to suggest that Johnson’s acquiescence could bear on Williams’s state of mind.
In closing argument, defense counsel emphasized that Johnson was excited about participation in the initiation and that every time he was asked if he wanted to continue with the beating, he said yes. Counsel went on to say:
[T]he Judge is going to tell you that consent is not a defense, and we understand that, but it has to factor in ... to whether [ ] Williams ... intended to kill [or] seriously injure [ ] Johnson, and had a reckless disregard for his life or serious injury. When [a] person ... is saying, yes, yes, yes, that’s got to affect something — it may not be a legal defense, but it’s got to affect the state of mind of the person who supposedly murdered him.
Trial Tr. 32 (Nov. 8, 2010). In its rebuttal, the government responded that defense counsel had inaccurately stated the law:
[Defense counsel] gave you some incorrect law because the judge is the one— he’s the final — he is the expert on the law, the judge. And you can’t take— Sergeant Johnson went in there thinking that he was going to' become a member of a brotherhood. He did not go in there willingly to get killed because consent is never ever a defense to murder. It is no defense to.second degree murder or involuntary manslaughter, and you know what, the judge is going to tell you— [defense counsel] told you to consider it; don’t even consider it because you can’t consider it. It is not a defense.... You can’t even consider it in his intent or anything else. You just cannot.
Id. at 100-01 (emphasis added). After the rebuttal concluded, defense counsel objected and asked the district court to give a “curative” instruction. The proposed language would have read:
*12During yesterday’s rebuttal argument, you heard [the government] tell you that you could not consider Juwan Johnson’s consent to the initiation ceremony when determining whether the government has proven beyond a reasonable doubt Mr. Williams’s intent to commit the offenses of second degree murder or involuntary manslaughter. As I will instruct you momentarily, consent is not a defense to these charges. However, under the law, you may consider Juwan Johnson’s consent to the initiation, among all the other evidence I have admitted, in determining whether the government has proven Mr. Williams’ intent to commit the crimes of second degree murder or involuntary manslaughter beyond a reasonable doubt.
Mr. Rico Williams’ Objection to Gov’t’s Improper Closing Arg. & Mot. for Curative Instruction 4-5, No. l:09-cr-00026 (D.D.C. Nov. 9, 2010).
The district court refused to read this proposed “curative” language to the jury, concluding again that it was inaccurate to suggest that the victim’s acquiescence had any impact on the defendant’s state of mind. However, the district court modified the first sentence of the consent instruction to read simply: “Consent is not a defense to second degree murder or involuntary manslaughter” — excising the language “and therefore should not be considered.” Trial Tr. 16-17, 46 (Nov. 9, 2010). The district court also offered to give the jury an additional instruction on proof of state of mind. It pointed to a standard criminal jury instruction that explains that someone’s state of mind “ordinarily cannot be proved directly,” but may be inferred from the defendant’s conduct and other “surrounding circumstances” that the jury finds relevant. Instruction No. 3.101 of the Criminal Jury Instructions for the District of Columbia (2014). The district court acknowledged, however, that this additional instruction would not satisfy the defense’s request for a curative instruction. The defense declined it, and the district court did not read it to the jury.
Williams argues that the government’s misstatement of law substantially prejudiced him. He agrees that consent is not an affirmative defense to homicide, but insists that Johnson’s consenting behavior — that is, his “continued, and enthusiastic, statements that he wanted the initiation. to continue” — suggested that Williams was not conscious of an extreme risk that Johnson might die or be seriously injured. Appellant’s Br. 63-65. According to Williams, the government’s rebuttal argument that consent cannot be considered “in [Williams’s] intent or anything else”— coupled with the district court’s instruction that “consent is not a defense”- — prevented the jury from considering crucial context when determining whether Williams acted with malice aforethought.
B
Williams asserts that the government’s closing argument improperly led the jury to believe that it could not consider crucial evidence of Williams’s state of mind, and that the jury instructions “supported” this misperception. Appellant’s Br. 65. In other words, he alleges that improper prosecutorial argument prejudiced his trial. When reviewing such challenges, we first examine whether the government’s statement was indeed error, keeping in mind that it need not have been deliberate or made in bad faith to be erroneous. See United States v. Watson, 171 F.3d 695, 700 (D.C. Cir. 1999). If the remark was error, we evaluate whether the error substantially prejudiced the defendant and therefore requires reversal. United States v. Straker, 800 F.3d 570, 628 (D.C. Cir. 2015). When considering prejudice, we examine, among other factors, the steps the district court took to cure the erroneous remark. See *13United States v. Gartmon, 146 F.3d 1015, 1026 (D.C. Cir. 1998).
i
The government misstated the law in its closing argument. When the government said that the jury could not consider Johnson’s consent in determining Williams’s “intent or anything else,” it inaccurately conflated two issues: (1) whether a victim’s consent can be a justification or excuse for the commission of a crime, and (2) whether it can bear on the presence or absence of an element of the crime.
This distinction is fundamental in criminal law. If an element of a crime is.missing, the charged culpable conduct has not occurred. Here, malice aforethought was an element of the crime with which Williams was charged; if he acted without this state of mind, he could not have been guilty of second-degree murder. By contrast, legally recognized justifications or excuses are “affirmative defenses” that eliminate criminal liability even though all of the elements of a crime are met. See 2 WayNe R. LaFave, Substantive CRIMINAL Law § 9.1 (2d ed. 2003). For example, a defendant who purposefully kills in self-defense satisfies the elements of murder: he has performed the required act (killing) with the required mental state (intent to kill). But he is not criminally liable because his actions are -deemed justified. Id. Similarly, a defendant who purposefully' kills but does not know that his conduct is wrong satisfies the elements of murder, but may be excused from.criminal liability because of insanity. Although his actions are not seen as justified, society excuses his conduct because he lacked responsibility for his actions through no fault of his own. Id.
An argument that a required element of a crime is missing is sometimes colloquially deemed a “defense.” For example, “the defense to a murder prosecution [might be] that the victim died accidentally.” 1 LaFave, supra, § 1.8 n.25. But this argument is “not really an ‘affirmative defense’ at all.” Id. Instead, it is “more correctly” viewed as an argument that the government has failed to prove an element of the crime. 2 LaFave, supra, § 9.1; see also United States v. Sandoval-Gonzalez, 642 F.3d 717, 723 (9th Cir. 2011) (distinguishing between “[cjlassic affirmative defenses,” such as justification or excuse, and “[o]ther ‘defenses’ ... advanced simply to negate an element of the crime”). At trial, Williams sought to make precisely this latter kind of argument: that Johnson died accidentally rather than as a result of Williams’s conscious disregard for human life. Properly understood, this contention is not an affirmative defense such as justification or excuse, but simply an assertion that a required element of the crime of murder — malice—was missing.
By contrast, the rule that consent cannot be a defense to homicide means simply that consent is not an affirmative defense in the vein of justification or excuse. See 40 Am. JüR. 2d HomiCide § 110 (“In application of the general principle that consent is not a defense to a crime if the activity that was consented to is against public policy, it is the rule that, in a prosecution for homicide, consent of the deceased is no excuse.” (emphasis added)); Vera Bergelson, Victims and Perpetrators: An Argument for Comparative Liability in Criminal Law, 8 Buff. Crim. L. Rev. 385, 399-400 (2005) (“[W]ith respect to some acts, society does not recognize even the possibility of valid consent.... The most prominent among them is homicide — the victim’s consent to be killed is never a complete justification for the perpetrator.” (emphasis added)). This rule does not foreclose a jury from considering all relevant facts and circumstances surrounding a homicide to determine whether the defendant consciously disregarded an extreme risk to human life, *14and therefore whether a necessary element of the crime had been proven.
To the contrary, such evidence is critical in determining whether a defendant is guilty of second-degree murder or the lesser crime of involuntary manslaughter. While second-degree murder requires at least a conscious disregard of an extreme risk of death or serious injury, involuntary manslaughter requires that a defendant engage in reckless conduct that created an extreme risk of death or serious injury of which he should have been aware, but was not. See Proposed Jury Instructions 40-42, No. 1:09-cr-00026 (D.D.C. Oct. 19, 2010). In other words, the difference between second-degree murder and manslaughter “lies in the quality of awareness of the risk.” United States v. Dixon, 419 F.2d 288, 293 (D.C. Cir. 1969) (Leventhal, J., concurring). The jury may infer that the defendant was aware of the risk from the surrounding circumstances. United States v. Cox, 509 F.2d 390, 392 (D.C. Cir. 1974). Here, Johnson’s repeated insistence that he wanted the jump-in to continue might have signaled to Williams that Johnson was in no serious danger. And if Williams believed that, Williams could not have been aware of an extreme risk to human life.
To illustrate, consider a counterfactual: what if, instead of repeatedly affirming that “yes,” he wanted to continue the initiation, Johnson had said “no,” or “stop”? Surely this evidence would point in favor of a finding that Williams consciously disregarded an extreme risk of death or injury. Johnson’s behavior was highly relevant — indeed, crucial — in determining whether Williams was guilty of murder or manslaughter. As such, Williams was entitled to have the jury consider that evidence. See Hopt v. People, 104 U.S. 631, 633-34, 26 L.Ed. 873 (1881); 5 ORField’s CRIMINAL PROCEDURE UNDER THE FEDERAL Rules § 30:23 (West 2016) (“Intent is a question of fact which must be submitted to the jury in the light of all relevant evidence.”).
But the government’s closing argument may well have led the jury to believe it could not consider this crucial evidence. In its closing, the defense focused the jury on Johnson’s enthusiastic participation in the jump-in, explaining that “[w]hen [a] person ... is saying, yes, yes, yes, that’s got to affect ... the state of mind of the person who supposedly murdered him.” In rebuttal, the government said the defense’s statement was “incorrect law.” The government then purported to interpret the jury instruction that consent is not a defense by explaining to the jury that “the judge is going to tell you” that “you can’t consider” Johnson’s consent when evaluating Williams’s “intent or anything else.” The dissent suggests that by “consent” the government only referred to the word’s legal meaning of subjective willingness, not manifestation of consent by behavior or words. But “[n]either courts nor juries parse extemporaneous remarks in closing argument as closely as sentences in carefully drafted legal documents,” and what matters is what the jury would “have understood the prosecutor to say.” United States v. Venable, 269 F.3d 1086, 1090 (D.C. Cir. 2001). Here, the government characterized as incorrect the defense’s statement that Johnson’s behavior — his “yeses” — was probative of Williams’s degree of recklessness, and further suggested to the jury that it could not consider this behavior for any purpose. This was error.
ii
A prosecutorial misstatement during closing argument is ground for reversal only if it substantially prejudiced the defendant. Straker, 800 F.3d at 628. “[Cjontext is key” in determining the ef-*15feet of the misstatement. Venable, 269 F.3d at 1090. If, considering the context of the full trial, we are “sure that the error did not influence the jury, or had but very slight effect, the verdict and the judgment should stand.” United States v. Fowler, 608 F.2d 2, 12 (D.C. Cir. 1979) (quoting Kotteakos v. United States, 328 U.S. 750, 764-65, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946)). But if we “cannot say, with fair assurance,” that “the judgment was not substantially swayed by the error, it is impossible to conclude that substantial rights were not affected.” Id. To determine whether the error substantially prejudiced the defendant, we consider the severity of the error, the centrality of the issue affected by the error, the closeness of the case, and the steps taken to cure the error. See Gartmon, 146 F.3d at 1026.
Looking first at severity, it is true that the problematic statement amounted to a small portion of closing argument. However, read “in context,” Venable, 269 F.3d at 1091, there is a very real chance that the statement led some jurors to believe they could not consider Johnson’s consenting behavior at all. The district court’s administration of the “consent is not a defense” instruction, after the government inaccurately interpreted it, may well have left jurors with the mistaken impression that they could not consider Johnson’s repeated statements that he wanted the initiation to continue. Because the statement was made by the government, it carried particular weight. See Spivey v. Head, 207 F.3d 1263, 1275 (11th Cir. 2000) (“Improper prosecutorial arguments, especially misstatements of law, must be considered carefully because ‘while wrapped in the cloak of state authority [they] have a heightened impact on the jury.’ ” (citation omitted)). And the remark’s potential for prejudice, was even more pronounced because it occurred during the government’s rebuttal — allowing the defense no opportunity to respond.
Further, any misunderstanding that this statement might have engendered implicated a central issue: Williams’s awareness of the risk to Johnson. To convict Williams of second-degree murder, the jury had to find that Williams was conscious of an extreme risk of death or serious injury to Johnson. If Williams was not conscious of this risk, but should have been, then the jury could convict him only of manslaughter. See Dixon, 419 F.2d at 293 (Leventhal, J., concurring).
As to the third factor in our analysis of substantial prejudice, the government acknowledged that the case was a close call on this very issue: Williams’s awareness of the risk. The district court agreed, explaining that “it was a close case between second degree murder and manslaughter” and that while “a reasonable jury could have reached the conclusion it reached, [ ] it would not have been irrational to conclude it was manslaughter instead.” Tr. of Proceedings 27 (June 3, 2011). To be sure, as described above (in II.B) and by the dissent, the evidence permitted the jury to find that Williams was aware of an extreme risk to human life. But other evidence suggested that Williams acted without a conscious disregard for human life— even if his behavior created an extreme risk that he should have known about. See United States v. Smart, 98 F.3d 1379, 1391 (D.C. Cir. 1996) (explaining that substantial prejudice is “not a mere suffieiency-of-the-evidence inquiry”). For example: no serious injuries had occurred in any of the fifteen to eighteen prior jump-ins the group had performed; members repeatedly asked Johnson if he wanted to continue with the initiation and testified that they would have stopped had he said no; Johnson had no unmistakable outward signs of major injuries after the jump-in; and some expert testimony suggested that trauma from the jump-in was not the primary cause of death — rather, Johnson’s undis*16closed, underlying medical trait was. The question of Williams’s awareness of the risk to Johnson was therefore close, and as we have explained, “the danger that an error will affect the jury’s verdict” increases significantly “in a case where the evidence at trial is conflicting.” Id. at 1392.
Finally, insufficient steps were taken to cure the error. To be sure, the district court’s general instructions informed the jury that the parties’ closing arguments were not evidence and that the jury should apply the law as instructed by the court. Such instructions can have an ameliorative effect. Venable, 269 F.3d at 1091. For example, where the government improperly suggested the defendant must prove his innocence, we have held that the court’s instruction on burden of proof cured the mistake because it clearly informed the jury of the relevant law. See id. at 1089, 1091. But “there are limits” to the efficacy of such general instructions when “the instructions d[o] not address the prosecutor’s error in closing argument, and the error affect[s] a central issue.” Watson, 171 F.3d at 702. For instance, in United States v. Hall, 610 F.3d 727 (D.C. Cir. 2010), we held that a closing argument’s “reference to [the court’s] forthcoming jury instructions could not alone remove the taint -of the error.” Id. at 742. In that case, cited by the defense as an example of a curative instruction, we found that the error was cured because the court’s instructions corrected the specific point of law that the government misstated. Id. at 742 & n.6.
Here, no instruction sufficiently corrected the potential confusion engendered by the government’s argument. While the district court instructed the jury on the state of mind required for murder and manslaughter, this instruction would not have corrected the misimpression that, under the separate “consent is not a defense to murder” instruction, Johnson’s statements and actions could not be considered in determining Williams’s consciousness of risk.5 Because the error went to a central and close issue in the case, and because it was insufficiently cured, we reverse Williams’s murder conviction.6
iii
On appeal, the government appears to concede that Johnson’s statements and behavior were important evidence of Williams’s state of mind, but it suggests that Williams’s use of the term “consent” in his proposed curative instruction invited confusion because it implied that Johnson’s subjective willingness to participate in the jump-in was pertinent in assessing Williams’s state of mind.
We agree that Williams might have been better served to use a term such as “consenting behavior” instead of “consent” to avoid any risk of misunderstanding. But the defense made sufficiently clear that it was using the term “consent” to refer to *17Johnson’s outward behavior- — not his subjective state of mind. For example, when requesting a curative instruction, defense counsel explained its argument this way: “[I]f someone is hitting somebody ... and they’re saying, Tes, I still want it, yes, I still want it,’ it would be reasonable — at least the defense would argue it would be reasonable to think that he’s not in ... physical jeopardy; that he can keep hitting him and he’s not going to kill him, that he’s going to keep hitting him and he’s not going to seriously injure him.” Trial Tr. 7 (Nov. 9, 2010). Counsel further argued that unless the government’s misstatement was “cured,” the jurors “are going to be saying: No, you can’t consider that he said, ‘hell yeah,’ whatever. You can’t consider that ... at all. The judge took that off limits for us.” Id. at 8. Looking at the record, we believe the district court understood counsel’s argument and simply rejected it. Tr. of Proceedings 25 (June 8, 2011) (“[Wjhatever the decedent may have said or done can in no way affect the mental state or mens rea of the defendant.” (emphasis added)).
We do not mean to suggest, however, that the district court was required to accept the precise curative language that Williams proposed. Of course, had it done so, Williams could not now complain that the instruction was improperly worded. See United States v. Wells, 519 U.S. 482, 488, 117 S.Ct. 921, 137 L.Ed.2d 107 (1997) (“[U]nder the invited error doetrine[,] a party may not complain on appeal of errors that he himself invited or provoked the district court to commit.” (alterations omitted)). Alternatively, had the court agreed with Williams’s concern but believed that his proposed instruction would confuse the jury, it could have rephrased the instruction to refer more directly to Johnson’s statements and behavior. Similarly, if the court was reluctant to highlight specific evidence favorable to Williams, as the dissent suggests, it could have rephrased the instruction to refer generally to the victim’s behavior (just as the model instruction that the district court offered, and the dissent approves, refers generally to “any statement made or acts [done by the defendant],” Instruction No. 3.101 of the Criminal Jury Instructions for the District of Columbia (2014)). Or the court could have recited evidence favorable to both sides, as the dissent proposes. Instead, it concluded that no curative instruction was needed. We disagree.
The government also points out that Williams declined the district court’s offer to read an additional instruction on proof of state of mind. If the government means to suggest that Williams invited error by refusing an instruction that would have cured the government’s misstatement, it presented this argument inadequately in its brief. City of Nephi v. FERC, 147 F.3d 929, 933 n.9 (D.C. Cir. 1998) (explaining that a party “fail[s] properly to raise [an] argument” on appeal when it “merely inform[s] the court” of the factual basis for a claim).
At any rate, the additional instruction suggested by the district court would not have cured the government’s misstatement. As described above, that instruction simply provided that a person’s state of mind “ordinarily cannot be proved directly,” but that the jury may infer state of mind “from the surrounding circumstances.” Instruction No. 3.101. The instruction further explained that the jury may consider the statements and acts of the defendant and “all other facts and circumstances received in evidence” that indicate his state of mind. Id. But the prejudice Williams identifies is that the jury might have believed that the consent instruction separately precluded it from considering the victim’s consenting behavior as one of these relevant “facts and circumstances.” The consent instruction is *18somewhat unusual in that it effectively forbids the jury from considering certain evidence, rather than merely telling the jury which elements it must find and how to weigh the evidence. Given this feature, and in light of the unique circumstances that developed at closing argument, the jury could readily have perceived the consent instruction as limiting any instructions on state of mind. The additional instruction therefore would not have cured the jury’s potential misunderstanding. Even had it been given to the jury, we would not be able to “say, with fair assurance,” that “the judgment was not substantially swayed by the error.” Fowler, 608 F.2d at 12 (quoting Kotteakos, 328 U.S. at 764-65, 66 S.Ct. 1239).
IV
In his remaining challenges, Williams points to three evidentiary errors and three instances of alleged misconduct by the government. Williams argues that these errors inflamed the jury and therefore require reversal' of both convictions. Because the government’s misstatement of law during closing argument independently requires us to reverse Williams’s murder conviction, however, we need consider only whether any of these alleged errors separately warrant reversal of his witness-tampering conviction. They do not.
The first evidentiary ruling Williams challenges does not require reversal, because it was not error. The photograph that the district court admitted of Johnson and his wife at an amusement park was relevant as an objective indication of Johnson’s height — an important fact in determining his size relative to Williams’s — and the district court did not abuse its discretion in holding that the photo’s probative value was not substantially outweighed by the risk of prejudice.
Williams correctly argues, however, that testimony of Johnson’s wife that she was pregnant when Johnson died was irrelevant. The district court concluded as much after trial, but denied Williams’s motion for a new trial, because the error was harmless. We agree that the error was harmless as to Williams’s tampering conviction. Our test for harmless error “is clear[:] If (1) the case is not close, (2) the issue not central, or (3) effective steps were taken to mitigate the effects of the error, the error is harmless.” In re Sealed Case, 99 F.3d 1175, 1178 (D.C. Cir. 1996). Although the pregnancy testimony might have enhanced the jury’s sympathy for Johnson as a victim, such sympathy would have had minimal' — if any — influence on the tampering conviction because Johnson was not a victim of that crime. The testimony therefore did not touch upon a “central” issue. Id.
Moreover, the evidence supporting the tampering conviction was not conflicting. Rather, Sims testified, unrebutted, that Williams threatened him. The case was therefore “not close” on this charge. Id. Further, the jury carefully parsed the witness-tampering charges. As to one of the tampering counts, the jury found that Williams threatened Sims but not three other gang members he was charged with threatening at the same time. And the jury acquitted Williams of the other tampering count altogether. Thus, we are confident that the jury was not “swayed by emotional appeals” when it evaluated the tampering charges. United States v. Bass, 535 F.2d 110, 117 (D.C. Cir. 1976).
For the same reasons, the admission of the testimony of gang expert Robert Stasch was at most harmless error with respect to Williams’s tampering conviction. Stasch, a lieutenant in the Chicago Police Department, testified about the background, history, and symbols of the American gang the Gangster Disciples. He also identified some of Williams’s tattoos *19as common among members of the Gangster Disciples. Stasch further explained that the “Brothers of the Struggle,” a name the Ramstein group often called itself, originated as the “prison faction” of the Gangster Disciples and “eventually transferred to the street.” Williams argues that this testimony was irrelevant and unduly prejudicial. But assuming that the admission of this testimony was error, it was harmless; the tampering charge did not present a close question, and the jury carefully assessed the charges, as described above. However, evidence of a defendant’s gang membership is “likely to provoke strong antipathy in a jury,” United States v. Jernigan, 341 F.3d 1273, 1284-85 (11th Cir. 2003), and the harmlessness calculus would look different in a closer case.7
Williams further identifies three instances of alleged prosecutorial misconduct that, in his view, prejudiced his trial. He argues that the government inappropriately asked a defense witness on cross examination whether she had read anything about Johnson’s death in the Stars and Stripes newspaper or seen it featured on the television show Gangland. Even if this questioning was improperly designed to encourage the jury to do outside research, it did not prejudice Williams’s tampering conviction. The question was fleeting, and the district court cured any potential for prejudice by directing the jury to disregard it and reminding the jury that outside research was forbidden.
Williams further contends that the government improperly accused the defense of “blaming the victim” for his death, and that the government inaccurately told the jury that only one person before Johnson had fallen at a jump-in. But these statements had little bearing on the tampering charge, since they focused on the events surrounding Johnson’s death. Moreover, the district court adequately cured the first remark by instructing the government to clarify that it was not implying that the defense believed Johnson was responsible for his own death. And Williams’s counsel highlighted the inaccuracy of the second statement by reading a transcript of the relevant witness testimony to the jury. These alleged instances of misconduct therefore do not warrant reversal of the witness-tampering conviction.
V
We reverse Williams’s murder conviction and remand the case for a new trial. We affirm his witness-tampering conviction.
. Although we reverse Williams's murder conviction on the basis of trial error, we nevertheless choose to address his challenges alleging evidentiary insufficiency. If we conclude that the evidence was insufficient to convict Williams of murder, his retrial would be barred under the Double Jeopardy Clause of the Fifth Amendment. See United States v. Williams, No. 13-3019, 827 F.3d 1134, 1162, 2016 WL 3648552 (D.C. Cir. July 8, 2016) (addressing sufficiency-of-the-evidence arguments after reversing conviction for trial error); Hoffler v. Bezio, 726 F.3d 144, 162 (2d Cir. 2013) (explaining that our sister circuits "are unanimous in concluding that such review is warranted, at a minimum, as a matter of prudent policy”).
. For this reason, this case does not resemble those in which our sister circuits have held that years-old certificates cannot establish that a bank was federally insured at the time of an alleged offense. See, e.g., United States v. Ali, 266 F.3d 1242 (9th Cir. 2001); United States v. Shively, 715 F.2d 260 (7th Cir. 1983); United States v. Platenburg, 657 F.2d 797 (5th Cir. 1981). A bank's federally insured status lapses if premiums are not paid. See Stuart-Caballero, 686 F.2d at 893.
. See, e.g., U.S. Air Force, AFE 36-104, U.S. Forces Civilian Component Determination in the United Kingdom 3-4 (2014) (explaining that "ordinarily resident,” as used in the Status of Forces agreement for the North Atlantic Treaty Organization, "normally involves a number of factors,” and that people who have lived abroad for more than a year "without a US government connection” generally qualify as ordinarily resident in the host nation); U.S. Army, Civilian Human Resources Agency'— Europe Region, Ordinarily Resident, https:// wu. acpol. army .mil/eur/employment/ ordinarily_resident.htm (last visited Aug. 24, 2016) (noting that U.S. citizens may become ordinarily resident in Germany if, among other things, they live there for a year without a connection to the U.S. military).
. Williams also argues that his conviction for witness tampering and the order that he pay restitution must be reversed because the evidence was insufficient to convict him of murder. This argument appears to be grounded in part on the belief that a defendant cannot be convicted of witness tampering unless he actually committed a federal crime — a dubious interpretation of the relevant statute, see 18 U.S.C. § 1512(b), (b)(3) (“Whoever knowingly uses intimidation ... with intent to ... prevent the communication to a law enforcement officer ... of information relating to the commission or possible commission of a Federal offense ... shall be fined under this title or imprisoned[.]” (emphasis added)). At any rate, we need not rule on the propriety of this interpretation because the evidence was sufficient to convict Williams of murder.
. We do not understand Williams to argue before us that the “consent is not a defense” jury instruction, on its own, was a problem. We therefore decline to consider whether that instruction adequately conveyed the relevant law. As we observed above, however, the term “defense” is open to multiple interpretations because of its colloquial use to refer to a defendant’s argument that an element of the crime is missing. See 1 LaFave, supra, § 1.8 n.25.
. To the extent that Williams argues that this error also requires the reversal of his witness-tampering conviction, we disagree. Although Johnson’s behavior was highly relevant in assessing Williams’s state of mind for the purposes of the murder charge, it had little if any bearing on the charge that Williams threatened Sims. The state-of-mind issue was therefore not central to the tampering conviction. Moreover, as we explain below, the witness-tampering. charge did not present a particularly close case. See Gartmon, 146 F.3d at 1026.
. Of course, as we have explained, Williams’s murder charge presented just such a closer case. Because we are already reversing Williams's murder conviction, however, we need not — and therefore do not — -rule on whether Stasch’s testimony was properly admitted to prove the murder charge.