
538 F.3d 547 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Joseph DJOUMESSI, Defendant-Appellant.
No. 07-1740.
United States Court of Appeals, Sixth Circuit.
Argued: July 23, 2008.
Decided and Filed: August 20, 2008.
*548 ARGUED: Bradley R. Hall, Federal Defender Office, Detroit, Michigan, for Appellant. Sarah E. Harrington, United States Department of Justice, Washington, D.C., for Appellee. ON BRIEF: Bradley R. Hall, Andrew N. Wise, Federal Defender Office, Detroit, Michigan, for Appellant. Sarah E. Harrington, Jessica Dunsay Silver, United States Department of Justice, Washington, D.C., for Appellee.
*549 Before: SUTTON and COOK, Circuit Judges; ROSE, District Judge.[*]

OPINION
SUTTON, Circuit Judge.
The federal government successfully prosecuted Joseph Djoumessi for violating one (happily) obscure statute  holding someone in involuntary servitude  and for violating another less obscure statute  harboring an alien for private financial gain. Djoumessi claims that the charges violated his rights under the Double Jeopardy Clause and that the government failed to support the involuntary-servitude conviction (and a related conspiracy conviction) with sufficient evidence. We affirm.

I.
In 1996, Joseph and Evelyn Djoumessi, immigrants from Cameroon living in a Detroit suburb, arranged for then-fourteen-year-old Pridine Fru to immigrate to the United States from Cameroon under a false name and with a fraudulent passport. The idea behind the arrangement was that Fru would perform housekeeping tasks for the Djoumessis and look after their two young children, in exchange for which they would provide for her and send her to school.
The arrangement did not work out that way during the next three years, years that Fru will not soon forget. The Djoumessis required Fru to perform substantially all of their housework and to provide essentially all of the care for their children. She worked every day from 6:00 a.m. to 10:00 p.m. for no compensation other than room and board, and the Djoumessis never sent her to school. Her housing consisted of a dilapidated, dark and sometimes-flooded space in the Djoumessis' basement. The Djoumessis did not allow her to use any of the working showers in the home, reducing her to collecting hot water from the basement sink in a bucket to clean herself. When Fru started her menstrual cycle, Evelyn refused to give her sanitary pads, leaving her to use her clothing instead. The Djoumessis also closely controlled Fru's contact with outsiders, rarely allowing her to leave the property except to take the Djoumessis' children to the bus stop or to other events, and telling her that if she ever contacted the police she would go to jail because she was in the country illegally. When the Djoumessis were not satisfied with Fru's work, they beat her and threatened her. And on top of all of this, Joseph Djoumessi sexually abused Fru on three occasions.
In February 2000, a neighbor contacted the police about Fru's situation, after which the police removed her from the home. Later that year, Michigan charged Joseph Djoumessi with kidnapping, conspiracy to kidnap, first-degree criminal sexual conduct, third-degree criminal sexual conduct and third-degree child abuse. See People v. Djoumessi, No. 238631, 2003 WL 22439688, at * 1 (Mich.Ct.App. Oct.28, 2003). A jury convicted him of third-degree criminal sexual conduct and third-degree child abuse and acquitted him of the other charges. See id. The court sentenced him to 9-15 years for the sexual-conduct conviction and a concurrent 1-year prison term for the child-abuse conviction. See id.
In 2005, a federal grand jury indicted Joseph and Evelyn Djoumessi for holding *550 Fru in involuntary servitude, see 18 U.S.C. § 1584, conspiring to hold Fru in involuntary servitude, see id. §§ 371, 1584, and harboring an alien for private financial gain, see 8 U.S.C. § 1324. After a bench trial, the judge found Joseph guilty on all three counts, sentenced him to 204 months' imprisonment (to run concurrently with his state sentence) and ordered him to pay $100,000 in restitution to Fru. (A jury, who heard the same evidence at the same trial, convicted Evelyn only of conspiracy.)

II.
Joseph Djoumessi challenges his convictions on double-jeopardy grounds and his involuntary-servitude convictions on sufficiency-of-the-evidence grounds.

A.
Noting that a jury acquitted him of similar state-law charges, Djoumessi contends that the Double Jeopardy Clause bars this separate federal prosecution. In making this argument, he correctly acknowledges that state and federal authorities, as independent sovereigns, generally may independently prosecute the same person for similar conduct without offending the double-jeopardy bar. See, e.g., Heath v. Alabama, 474 U.S. 82, 88, 106 S.Ct. 433, 88 L.Ed.2d 387 (1985); United States v. Louisville Edible Oil Prods., Inc., 926 F.2d 584, 587 (6th Cir.1991). But this case is different, he says: The federal prosecution amounted to nothing more than a second state prosecution in disguise, and Bartkus v. Illinois, 359 U.S. 121, 122-24, 79 S.Ct. 676, 3 L.Ed.2d 684 (1959), suggests that a State cannot sidestep the constraints of the Double Jeopardy Clause through a "sham" prosecution by an ostensibly different sovereign.
This argument fails for at least two reasons. To start, the Bartkus sham-prosecution exception is a narrow one and, so far as this circuit is concerned, it is an exception that has yet to affect the outcome of a single case. "Since Bartkus was decided in 1959, this Circuit has never ruled that a prosecution violated double jeopardy protections under [Bartkus'] `sham prosecution' theory." United States v. Clark, 254 Fed.Appx. 528, 533 (6th Cir. Nov.19, 2007). As this track record suggests, there is some room for debate over whether the Bartkus exception is just narrow or whether it is indeed real. See United States v. Angleton, 314 F.3d 767, 773-74 (5th Cir. 2002); United States v. Baptista-Rodriguez, 17 F.3d 1354, 1361 (11th Cir.1994); United States v. Brocksmith, 991 F.2d 1363, 1366 (7th Cir.1993).
Be that as it may, even if we accept the existence of the exception, Djoumessi has not made the startling showing that the Federal Government was "merely a tool" of the State of Michigan in undertaking this prosecution, somehow ceding its sovereign authority to prosecute and acting only because the State told it to do so. Bartkus, 359 U.S. at 123, 79 S.Ct. 676. Djoumessi at most has shown cooperation between the two sovereigns. But that everyday development does not establish that the Federal Government has ceded its prosecutorial discretion and other law-enforcement powers to a State. See id. at 123-24, 79 S.Ct. 676 (explaining that, although the record "establishes ... that federal officials acted in cooperation with state authorities, as is the conventional practice between the two sets of prosecutors throughout the country, ... [i]t does not sustain a conclusion that the state prosecution was a sham and a cover for a federal prosecution"); Louisville Edible, 926 F.2d at 588; Clark, 254 Fed.Appx. at 533; see also, e.g., United States v. Rashed, 234 F.3d 1280, 1284 (D.C.Cir.2000) ("Bartkus acknowledges that extensive law enforcement and prosecutorial cooperation *551 between two sovereigns does not make a trial by either a sham."); United States v. Guzman, 85 F.3d 823, 828 (1st Cir.1996) ("Cooperative law enforcement efforts between independent sovereigns are commendable, and, without more, such efforts will not furnish a legally adequate basis for invoking the Bartkus exception to the dual sovereign rule."). Whether real or not, the sham-prosecution exception was not established here.

B.
Djoumessi's evidentiary challenge to his involuntary-servitude convictions fares no better. In reviewing a sufficiency-of-the-evidence challenge, the issue is not whether we "believe[] that the evidence at the trial established guilt," but instead "whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." Jackson v. Virginia, 443 U.S. 307, 318-19, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979) (internal quotation marks omitted). Djoumessi has not made that showing.
Section 1584 prohibits a person from "knowingly and willfully hold[ing] to involuntary servitude ... any other person for any term." 18 U.S.C. § 1584. As used in this section,
the term "involuntary servitude" necessarily means a condition of servitude in which the victim is forced to work for the defendant by the use or threat of physical restraint or physical injury, or by the use or threat of coercion through law or the legal process. This definition encompasses those cases in which the defendant holds the victim in servitude by placing the victim in fear of such physical restraint or injury or legal coercion.
United States v. Kozminski, 487 U.S. 931, 952, 108 S.Ct. 2751, 101 L.Ed.2d 788 (1988). A § 1584 conviction thus requires proof that the defendant intentionally held the victim in service against her will in one of three ways: (1) by physical restraint or force, (2) by legal coercion or (3) by threats of physical force or legal coercion. See United States v. Alzanki, 54 F.3d 994, 1001 (1st Cir.1995). In assessing whether these things happened, the trier of fact may consider "the vulnerabilities of the victim" as well as "evidence of other means of coercion or of extremely poor working conditions." Kozminski, 487 U.S. at 952, 108 S.Ct. 2751.
In this case, a rational trier of fact could find beyond a reasonable doubt that the government satisfied these requirements. At trial, Fru testified not only about her extremely poor working and living conditions but also about Djoumessi's physical abuse and threats of further abuse. Explaining why she never objected to her assigned tasks, Fru said she had no choice because she was afraid that the Djoumessis would hit her if she did not work. Those fears were not unfounded. Djoumessi once beat her with a belt  severely enough to draw blood  because Fru failed to make him breakfast, change the sheets and turn off the Christmas lights. He beat her again on two separate occasions when she called a family friend without his permission. And he sexually abused Fru three times, two of those times by forcing her to engage in sexual intercourse.
Evelyn did not improve matters, as she, too, regularly abused Fru for failing to meet the Djoumessis' work standards. See United States v. Frost, 914 F.2d 756, 762 (6th Cir.1990) (noting that "each member of a conspiracy becomes responsible for acts in furtherance of the conspiracy committed by his co-conspirators") (internal quotation marks omitted); see also *552 Pinkerton v. United States, 328 U.S. 640, 646-47, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946). On one occasion, Evelyn hit Fru with a spoon because Fru did not prepare a meal properly. On another occasion, she repeatedly struck Fru with a belt, leaving lines on her legs and making it difficult for her to walk, because Evelyn was not satisfied with her work. And in a dispute over an ironing task, Evelyn attempted to strike Fru in the head with the heel of a shoe, cutting and bruising Fru's arm. Evelyn's threats left no doubt that there was more to come, see JA 81 ("[Y]ou haven't seen anything yet."), and she made clear that she and Djoumessi "had [Fru's] life in their hands and they [could] pretty much do whatever they wanted to do with it," JA 128.
Djoumessi also threatened Fru with imprisonment, telling her that she would go to jail if she contacted the police because he would tell the police that she had entered the country illegally. Cf. Alzanki, 54 F.3d at 1004 ("[T]he evidence must establish that the victim reasonably believed she was left with no alternative to continued servitude that was not the equivalent of imprisonment or worse.") (internal quotation marks omitted). In view of her illegal status and in view of Djoumessi's and Evelyn's threats to send her back to Cameroon, Fru also described living and working in fear of deportation. Cf. Kozminski, 487 U.S. at 948, 108 S.Ct. 2751 ("[I]t is possible that threatening ... an immigrant with deportation could constitute the threat of legal coercion that induces involuntary servitude....").
Fru's "special vulnerabilities," id. at 952, 108 S.Ct. 2751, complete this grim picture. Just fourteen years old when the Djoumessis brought her to the United States, she was here illegally, she had no money or other means of support and she had no substantial contact with anyone other than these modern-day Thénardiers. These realities made her more susceptible to the Djoumessis' threats of imprisonment and deportation, even if "such a threat made to an adult citizen of normal intelligence" might be "too implausible to produce involuntary servitude." Id. at 948, 108 S.Ct. 2751.
Djoumessi first resists this conclusion on the ground that Fru voluntarily chose to stay. As Djoumessi reads the record, it shows that Fru did not want to return to Cameroon, see JA 138 ("My [greatest] threat was [that] they had the power to send me home. And everything I have done, and being close to going to school, being close to having a life, was for nothing."), and that she wanted to help her family by coming to this country, see JA 137 ("I wanted to help my family.... So, by me staying there, someday I will go to school and someday I will have a career and someday I will be able to help them. So, putting up with it is not going to kill me."). Voluntariness is of course a defense to this charge, and Djoumessi offers one way to read the record so that it supports this defense. But it is not the only way to read the record, and that makes all the difference. Even if Fru had independent reasons for staying in this country, a rational trier of fact could conclude that it was the Djoumessis' acts of physical abuse and restraint, their threats of more to come and their threats of legal coercion, not Fru's innocent hopes and dreams, that reasonably made her feel compelled to serve.
Even assuming there were moments during Fru's stay when she had an opportunity to escape (without risking imprisonment or worse), moreover, Djoumessi's argument still falls short because a rational trier of fact could conclude that Fru's labor was involuntary for at least some portion of her stay. And that involuntary portion *553 would suffice to sustain the conviction. See 18 U.S.C. § 1584 (requiring the involuntary servitude to be for "any term"); see also United States v. Pipkins, 378 F.3d 1281, 1297 (11th Cir.2004) ("Section 1584 requires that involuntary servitude be for `any term,' which suggests that the temporal duration can be slight."), reinstated by 412 F.3d 1251 (11th Cir.2005).
Djoumessi next points out that Fru's parents placed her in his care under a Cameroonian tradition known as "take my child," by which a poor family entrusts its child to a wealthier one who pledges to care for the child as its own. JA 192-93, 217. Once that tradition is accounted for, Djoumessi argues, it is clear either that Fru became his adopted daughter as a matter of law or that he at a minimum had the consent of Fru's parents, both of which would permit him to require her to perform chores around the house. In one sense, Djoumessi is right. Section 1584 does not restrict parents' (or guardians') rights to require their children (or wards) to help with household chores. See Kozminski, 487 U.S. at 944, 108 S.Ct. 2751 (stating that § 1584 does not interfere with "the right of parents and guardians to the custody of their minor children or wards"). But in at least two material ways, Djoumessi is wrong. The record offers no evidence that Djoumessi was Fru's legal guardian. And even if Djoumessi had the consent of Fru's parents to treat her the way he did (something the record also does not support), that would not do the trick. "When parents explicitly renounce their parental relationship  by selling a child into slavery or abandoning [her] to involuntary servitude  parental consent cannot provide a subsequent defense for the third party." United States v. King, 840 F.2d 1276, 1283 (6th Cir.1988). "[A] parental consent defense is particularly inappropriate on the facts of this case" because Fru's parents "abdicated any semblance of parental supervision and control." Id. at 1282.
Also unavailing is Djoumessi's contention that Fru necessarily remained voluntarily at his home because he never physically restrained her (in the sense of placing a lock on her door) and she never attempted to escape. But opportunities for escape mean nothing if Djoumessi gave her reasons to fear leaving the house  as indeed he did when he told this fourteen-year-old girl that she would either go to jail or be deported because she had entered the country illegally. See Kozminski, 487 U.S. at 948, 952, 108 S.Ct. 2751; see also United States v. Warren, 772 F.2d 827, 834 (11th Cir.1985) ("That the worker had the opportunity to escape is of no moment, if the defendant has placed him in such fear of physical harm that he is afraid to leave.").
Bad as Fru's life in the United States may have been, Djoumessi claims, it was better than what she would have faced had she returned to Cameroon (or stayed there), proving that there was nothing involuntary about her circumstances. Even if we grant the factual premise of Djoumessi's contention (we have no way of knowing), that does not help him: A slave master cannot escape the clutches of § 1584 by contending that he subjected the servant to slightly less wretched conditions than she would have experienced elsewhere. Involuntary servitude is a fixed prohibition, not a relative one. It thus sweeps up all forced labor, even when the victim is freed from the bondages of one bad relationship and placed in another.
A final point deserves mention. "Involuntary servitude" at first blush might seem like strong medicine for what could (charitably) be described as an au pair relationship gone awry. The first answer is that Fru's circumstances bear an unfortunate *554 resemblance to the conditions that victims of the "padrone system" faced, a system outlawed by one of the two predecessors of § 1584. See Kozminski, 487 U.S. at 945-46, 108 S.Ct. 2751 (explaining that the passage of § 1584 resulted from the consolidation "of two earlier statutes: the Slave Trade statute ... and the Padrone statute" and that the histories of those statutes "inform [the] construction of § 1584"). Under the padrone system, children were taken from their families in Italy and brought to the United States to work as street musicians or beggars in large cities. See id. at 947, 108 S.Ct. 2751. Upon their arrival, the children
were literally stranded in large, hostile cities in a foreign country. They were given no education or assistance toward self sufficiency. Without such assistance, without family, and without other sources of support, these children had no actual means of escaping the padrones' service; they had no choice but to work for their masters or risk physical harm. The padrones took advantage of the special vulnerabilities of their victims, placing them in situations they were physically unable to leave.
Id. at 947-48, 108 S.Ct. 2751. It is difficult to see any meaningful difference between the Italian victims of the padrone system and the Cameroonian victim of Joseph Djoumessi.
Another answer is that, even on its own terms, involuntary servitude is not too strong a phrase to describe what Djoumessi and his wife did to this fourteen-year-old girl. "In the jury's view, [the defendant] was part of a conspiracy that substituted for a promised education and compensation a regime of psychological cruelty and physical coercion that took some of the best years of a young girl's life. For that, involuntary servitude is not too strong a term." United States v. Udeozor, 515 F.3d 260, 272 (4th Cir.2008).

III.
For these reasons, we affirm.
NOTES
[*]  The Honorable Thomas M. Rose, United States District Judge for the Southern District of Ohio, sitting by designation.
