SYKES, Circuit Judge.
Kristen Smith took her half-sister’s newborn son from his bassinette in the middle of the night and started out on the long drive from Beloit, Wisconsin, to her home in Colorado. When she reached eastern Iowa, she learned that police in Wisconsin were pursuing leads on the missing infant and wanted to interview her. She spoke by phone with a Beloit police officer who told her to pull over so that local law enforcement could speak with her.
In the pre-dawn hours, Smith pulled off the interstate, wrapped the baby in blankets, placed him in a plastic container, and put the container behind a gas station. There she left the infant to freeze in subzero mid-winter temperatures. She then drove to another gas station, called the Beloit officer back, and was eventually arrested by Iowa police on an unrelated warrant. When the police and FBI agents questioned her, she persistently denied any knowledge of the child’s whereabouts. It was only after the baby was found alive the next day that she admitted taking him. A federal jury convicted her of kidnapping.
Smith raises many issues on appeal. She claims that her statements to law enforcement were the product of coercion. She argues that a subset of her statements— those the district court suppressed based on a
Miranda
violation — were improperly admitted for impeachment purposes. She objects to the government’s inquiry during her cross-examination about the crime for which the arrest warrant was issued. Finally, she asks us to reverse on the ground that no rational jury could conclude that she lacked parental permission to take the child or that she attained a benefit from the kidnapping. We reject these arguments and affirm.
I. Background
A. Kayden’s Disappearance
Brianna Marshall and her boyfriend, Bruce Powell, started trying to conceive a baby in April 2013, and Brianna soon became pregnant. Not long after she announced her pregnancy, Kristen Smith, her estranged half-sister, unexpectedly contacted her via Facebook. Smith lived in Aurora, Colorado; Brianna and Bruce lived in Beloit, Wisconsin. The reunited half-sisters began communicating regularly on Facebook and by text.
A short time later, Smith announced on her Facebook page that she too was pregnant with twins, a boy and a girl. When Smith later learned that Brianna was having a boy, she told her half-sister that she had lost the female twin but was still carrying a healthy male. In August 2013 Smith offered to let Brianna come to Colorado and stay with her and her husband. Brianna declined.
On October 23 Smith posted a sonogram on her Facebook page, claiming it was an image of the child she was carrying. It was not. The original sonogram, dated November 16, 2007, had been downloaded to Smith’s computer, and she had changed the mother’s name to her own.
Between August 2013 and November 2013, Smith’s computer and eBay account were used to search for fake pregnancy bellies and to view websites titled “How to Create a Fake Pregnancy Belly,” “Breastfeeding your Adopted Baby or Baby Born by Surrogate,” and “How to Get a Birth Certificate for a Newborn.” On January 16, 2014, Smith sent her mother-in-law a sonogram image via text. This one, too, was altered.
On February 1, 2014, Brianna gave birth via C-section to a baby boy and named him Kayden. On February 3 Smith emailed her
employer saying she was having labor induced that evening and would not be at work that week. She then left Colorado, alone, and drove to Wisconsin, arriving in Beloit on February 4. She stopped at a Walmart and bought an electric blanket, and then went to the hospital, unannounced, to visit Brianna and Kayden.
Mother and baby were discharged that day; Smith accompanied them, with Bruce, to Brianna’s mother’s house, where they were promptly told they were not welcome. (Brianna’s mother apparently disapproved of her daughter’s relationship with Bruce.) The foursome — Bruce, Brianna, baby Kayden, and Smith — went to stay with Brianna’s grandmother instead. Smith told Brianna’s grandmother that she was pregnant and due in two weeks. That same day Smith emailed her employer announcing that she had given birth to a 6-pound-10-ounce baby boy named “Kaysin.” Brianna’s son Kayden weighed 6 pounds, 10 ounces when he left the hospital.
The next day (February 5) Brianna and Bruce discussed with Smith the possibility of moving to Colorado to live with her in light of the turbulence in their family situation in Wisconsin. Smith told them that she would need to call her husband and clear the idea with him. She did so, and Brianna and Bruce then announced to Brianna’s family that they planned to relocate to Colorado. It didn’t go over well; Brianna’s half-brother Byron was upset by the news and grew increasingly agitated with Bruce during the course of the conversation.
At some point later that day, Smith told the couple that she would get a head start on the move and planned to leave for Colorado late that evening or very early the next morning, taking some of Brianna’s belongings with her. She promised to return immediately with her husband and drive Brianna, Bruce, and Kayden back to Colorado.
Bruce went to bed early that evening because he had a headache. Brianna and her grandmother stayed up until shortly after midnight.
At
about 1:30 a.m. on February 6, while the rest of the household was asleep, Smith quietly lifted Kayden from his bassinette, placed him in the back of her car, and took off for Colorado. Brianna woke up at about 4:30 a.m. to discover her baby missing. She awakened everyone else and frantically searched the house for Kayden, then called Smith in “hysterics,” telling her the baby was gone. Smith, of course, had Kayden with her, but she did not inform her half-sister of that fact.
Brianna immediately called the police to report the kidnapping. She and Bruce initially suspected that Byron had taken the baby. Beloit police officers arrived within minutes. At 4:54 a.m. Smith called back, and Brianna’s grandmother handed the phone to one of the officers, who began questioning Smith about the missing infant. She gave her name as “Kristen Andrews” with a date of birth of July 10, 1985. She denied any knowledge of Kay-den’s whereabouts and blamed his disappearance on Byron. The officer instructed her to pull over as soon as possible to meet with local law enforcement to discuss the matter further. She said she would do so.
Smith did pull off the highway, but not to meet with the police — at least not right away. Instead, she exited 1-80 in West Branch, Iowa, and pulled into a BP gas station. There she wrapped Kayden in blankets (including the electric blanket she purchased in Beloit) and put him in a plastic container. She closed the lid, placed the container on the ground behind the station, and left the baby there. The temperature in West Branch early that morning was -11 degrees Fahrenheit, with a windchill of about -20.
Smith then drove a few hundred yards to a different gas station. At 5:21 a.m. she called the Beloit officer back to report her location. This information was immediately transmitted to local police. While Smith was still on the line with the Beloit officer, a West Branch police squad pulled into the gas station. On the Beloit officer’s instruction, Smith flagged down the local officer and gave him her cell phone so he could speak with the Beloit officer.
The West Branch officer then questioned Smith for a few minutes in the parking lot. She identified herself as Kristen Rose Smith with a date of birth of January 11, 1983. She told him that she first learned about Kayden’s disappearance when Brianna called her at around 4:30 a.m. She permitted the officer to search her car, but of course the baby wasn’t there. The officer asked if she was pregnant; she said, “Yes.” Another West Branch officer arrived to assist, and the dispatcher relayed information about Smith’s criminal history. It turned out she was wanted by Texas on a 2013 warrant for falsifying government documents — specifically, military-deployment orders — to fraudulently break a lease. The officers arrested Smith on the Texas warrant and took her to the Cedar County Jail.
Once in police custody, Smith was
Mir-andized
but not questioned until FBI agents arrived at the jail to take over the investigation. Special Agents James McMillan and Carlton Morgan' arrived at about noon and began a videotaped interrogation.
During the first hour or two of questioning, Agent McMillan asked for consent to search Smith’s car and phone. Smith agreed and signed a consent form, but she repeatedly gave the agents an incorrect access code to unlock her phone. When they confronted her about this evasion, she responded: “[I]f I was being difficulty then why wouldn’t I be like, T don’t want to talk to you; I want an attorney’?” She eventually provided the correct code, and the agents took the phone for forensic examination. At some point Smith also agreed to submit to a polygraph examination.
In the meantime West Branch police did an inventory search of Smith’s car. They recovered clothing, storage containers, a baby car seat, and a prosthetic belly.
Early that evening Agent Riessen of the Iowa State Police arrived at the jail to administer the polygraph. Before beginning, he delivered fresh
Miranda
warnings and read aloud from a polygraph consent form. When Agent Riessen asked Smith to confirm that no one was forcing her to take the polygraph, she replied, “Yes, they are.” Agent Riessen reiterated that no one was forcing her to take the polygraph. Smith then signed the consent form and the examination proceeded.
When the polygraph was finished, Agent Riessen determined that Smith had been deceptive. The FBI agents then resumed the interrogation. At about 1:30 a.m. on February 7, Smith stopped answering questions, so the agents said they would take her to her cell to sleep. Before concluding the interview for the night, Agent McMillan asked her to sign a consent form to access her Yahoo! email account. Smith refused, saying, “I want everything to
go
to an attorney.” When asked to confirm what she meant, Smith said: “Everything else I want an attorney to advise me.” The interrogation immediately ceased and Smith was returned to her cell.
. At around nine o’clock that morning, the agents returned with a new
Miranda
waiver form. Smith read and signed it, but counsel had not yet been provided. The interrogation resumed, but word soon arrived that West Branch police had discoy-
ered Kayden alive and unharmed in the plastic container behind the BP station. When the agents told Smith the baby had been found, she called her husband and told him not to say anything to authorities and to get her out of jail as quickly as possible. She eventually admitted to the FBI agents that she left Wisconsin with Kayden, put him in the plastic container, and placed the container behind the BP station. She even drew a map of the station to show them exactly where she put him.
Agents later searched Smith’s home in Colorado and recovered baby accessories and furniture, infant formula, a hard copy of the altered sonogram she sent to her mother-in-law, and a partially completed birth-certificate application for an infant named “Kaysin Michael Smith.” The application listed Smith and her husband as the parents and their Colorado home as the place where “Kaysin” was born.
A federal grand jury indicted Smith for kidnapping.
See
18 U.S.C. § 1201(a)(1). Because the victim was a minor, she faced a minimum prison sentence of 25 years and a maximum term of life.
Id.
§ 3559(f)(2).
B. The Suppression Hearing
Smith moved to suppress her custodial statements, alleging that the February 6-7 interrogation violated
Miranda
and was coercive. At a hearing before a magistrate judge, Smith took the position that all questioning should have ceased when Agent Riessen asked her if anyone was forcing her to take the polygraph and she answered, “yes, they are,” or at the very latest when she stopped answering questions and asked for an attorney at about 1:30 a.m. on February 7.
The magistrate judge found — and the district court agreed — that Smith unequivocally requested counsel at 1:30 a.m. on February 7. At that point she stopped answering questions, refused to sign a consent form to search her Yahoo! account, and told the agents she wanted “everything to go to an attorney.” The agents immediately halted the interrogation and returned Smith to her cell. But they reini-tiated the interrogation the next morning without counsel present (albeit with new
Miranda
warnings). Because Smith’s request for counsel at 1:30 a.m. was unambiguous, the district judge granted her suppression motion in part, barring the government from using anything she said after 1:30 a.m. in its case-in-chief. But the judge rejected her claim of coercion and found her statements voluntary. That ruling left the door open to using the suppressed statements for impeachment if Smith testified.
See Oregon v. Hass,
420 U.S. 714, 722-24, 95 S.Ct. 1215, 43 L.Ed.2d 570 (1975) (holding that statements obtained in violation of
Miranda,
though excluded from the prosecution’s case-in-chief, may be used to impeach the defendant’s testimony if otherwise voluntary);
Harris v. New York,
401 U.S. 222, 224-25, 91 S.Ct. 643, 28 L.Ed.2d 1 (1971).
C. The Trial
The government’s theory of the case was that Smith faked a pregnancy to coincide with Brianna’s, kidnapped Kayden to pass
him off as her own, and disposed of the infant out of fear that she would be caught. In its case-in-chief, the government introduced evidence establishing the narrative we’ve recounted above.
Smith’s primary defense was that Bruce, the baby’s father, had given her permission to take Kayden to Colorado. She testified in her own defense and told the jury that she woke up at around 1:30 a.m. on February 6 to get an early start on the long drive to Colorado, as she had told Bruce and Brianna she would do. She testified that Bruce was still awake at that hour and specifically instructed her to take Kayden with her. She tried to explain away the government’s evidence of a falsified pregnancy by insisting that she
had
in fact been pregnant with twins but lost the female mid-pregnancy and gave birth to a stillborn boy in January 2014 but hadn’t told anyone about the stillbirth. She said the browsing history on her computer couldn’t be attributed to her because her entire family used the computer. Finally, she admitted leaving Kayden at the BP gas station, but she said she left him
in front of
the station, not behind it, and claimed that she plugged the electric blanket into an outlet to keep him warm. When asked why she concealed his whereabouts for nearly 30 hours, she said she was in a state of “panic” and did not understand why Bruce had not explained to everyone that Kayden was with her.
Three aspects of the government’s cross-examination of Smith are important on appeal. First, to rebut her testimony that she really had been pregnant, the government introduced a statement she made during the 9 a.m. interrogation on February 7 admitting that she had purchased the prosthetic belly and claiming that she did so because she wanted to trick her body into producing breast milk to feed her stepdaughter. Second, to impeach her testimony that she left Kayden in front of the gas station, not behind it, the government introduced the map she drew after the FBI agents told her that Kayden had been found. The map plainly showed that she left the baby
behind
the gas station, where he was indeed found. Third, although the parties had stipulated to the existence of the Texas arrest warrant, the government asked Smith on cross-examination if she had submitted falsified military-deployment orders in May 2013 in an effort to break a Texas lease — the crime for which the warrant was issued. Smith objected, but the judge overruled the objection. Smith then denied the conduct, saying she was in Virginia at her wedding at that time.
The jury returned a verdict of guilty. Smith moved for judgment of acquittal or a new trial. The judge denied the motion and sentenced her to 300 months in prison.
II. Discussion
A. Coercion
On appeal Smith reprises her argument that her interrogation was coercive and therefore not voluntary. Coercive interrogation tactics can include “physical abuse, psychological intimidation, or deceptive interrogation tactics that have overcome the defendant’s free will.”
United States v. Stadfeld,
689 F.3d 705, 709 (7th Cir. 2012) (quotation marks omitted). The inquiry considers the “totality of circumstances.”
United States v. Charles,
476 F.3d 492, 497 (7th Cir. 2007). While the voluntariness of a confession is a question of law that we review de novo,
United States v. Jordan,
223 F.3d 676, 683 (7th Cir. 2000), the district court’s predicate factual findings are reviewed for clear error,
United States v. Walker,
272 F.3d 407, 412 (7th Cir. 2001). “A finding of fact is clearly erroneous when a review of the entire record leaves us with a definite and
firm conviction that a mistake has been made.”
United States v. Dillon,
150 F.3d 754, 757 (7th Cir. 1998).
As we’ve noted, Smith’s interrogation was videotaped. She has not pointed to anything about the conditions or interrogation tactics that was the least bit coercive. There was no physical abuse, psychological abuse, or deception. She has not identified anything about her personal circumstances that made her especially vulnerable. It’s true that the interrogation was lengthy, but she received meals and had regular breaks, so she cannot and does not argue that the conditions of the interrogation were coercive.
Instead, Smith’s argument seems to be that the agents’ repeated requests for consents and waivers — to search her car and phone, to take a polygraph, to search her Yahoo! account, and to resume the interrogation on the morning of February 7— made the interrogation inherently coercive. In support of this theory, Smith cites
United States v. Villegas,
388 F.3d 317 (7th Cir. 2004), but it’s hard to understand why. In that case, DEA agents knocked on the defendant’s door, identified themselves as law enforcement, and politely requested permission to enter his home; no threats were made and no weapons were drawn.
Id.
at 325. The defendant consented to the agents’ entry, and we upheld the district court’s determination that the consent was voluntary.
Id.
at 325-26.
Villegas
plainly does not help Smith’s coercion argument.
Smith places special emphasis on her pre-polygraph colloquy with Agent Ries-sen — specifically, her affirmative response to the agent’s question whether anyone was forcing her to take a polygraph test. (Recall that when she gave this answer, Agent Riessen assured her that she didn’t have to take the polygraph. She then signed the consent form and the examination proceeded.) At the evidentiary hearing on the suppression motion, Smith testified that before the polygraph examination began, Agent McMillan approached her in the hallway and told her that she had to take the polygraph. Agent McMillan denied saying this or anything like it. The magistrate judge credited the agent’s testimony over Smith’s. The district judge accepted this credibility determination, and Smith doesn’t challenge that ruling on appeal. Without more, the pre-polygraph exchange with Agent Riessen is not evidence of coercion.
In the end, Smith hasn’t identified anything in the record to support her claim of coercion. The district court’s voluntariness ruling was sound,
B. Evidentiary Errors
Smith also challenges several aspects of her cross-examination. Evidentia-ry rulings are reviewed for an abuse of discretion; we will reverse “only when no reasonable person could take the view adopted by the trial court.”
United States v. Ozuna,
561 F.3d 728, 738 (7th Cir. 2009) (internal quotation marks omitted).
Smith attacks the government’s use of two statements from the otherwise suppressed interrogation on the morning of February 7. She objects to the government’s introduction of her admission that she purchased a prosthetic belly to trick her body into producing breast milk. She also objects to the admission of her hand-drawn map depicting the location behind the gas station where she left Kayden. These two bits of evidence, she argues, were improper impeachment because they were not in fact inconsistent with her testimony on direct examination.
Rule 613 of the Federal Rules of Evidence permits a cross-examiner to impeach a witness’s testimony with evidence of her prior inconsistent statements. It’s
well-established that “two statements need not be diametrically opposed to be inconsistent.”
United States v. Vasquez,
635 F.3d 889, 898 (7th Cir. 2011) (quoting
United States v. Jones,
808 F.2d 561, 568 (7th Cir. 1986)).
We see nothing improper about the government’s use of Smith’s admission to the FBI agents that she purchased a prosthetic belly. She testified on direct examination that she was pregnant from July 2013 until she delivered a stillborn baby in January 2014. The contemporaneous existence of a real pregnancy necessarily implies a denial that she was faking a pregnancy. The prosecutor asked her whether she had “told the FBI that [she] had been faking a pregnancy' and wearing a fake prosthetic belly so that [she] could convince [her] body to produce breast milk” to feed her stepdaughter. That was directly responsive to, and inconsistent with, Smith’s assertion that she had in fact been pregnant during the relevant time.
By the same token, Smith’s testimony on direct examination that she left Kayden in front of the BP gas station was flatly inconsistent with the map she drew for the agents on the morning of February 7, after the baby was found. Smith doesn’t press very hard on her claim that the two statements were inconsistent. She mainly argues that it didn’t make much difference whether she placed the baby in back of the gas station or in front of it, so the probative value of this evidence was too slight and the court should have disallowed it.
The deficiencies in this argument are so manifold that we’re not sure where to begin. First, Smith did not object to the admission of the map, so the claim is forfeited. Second, the map
directly
contradicted Smith’s assertion on the witness stand that she placed the baby in front of the station, making this evidence highly probative of her credibility as a witness. Third, her prior admission about Kayden’s location was relevant to her state of mind; the degree of concealment was circumstantial evidence of her purpose in abandoning him. Finally, any error in admitting this' evidence was certainly harmless given the abundant evidence of her guilt.
Smith’s final evidentiary challenge is an attack on the government’s inquiry into the conduct underlying the Texas arrest warrant. Before trial Smith had stipulated to the existence of the warrant, and in exchange the government agreed not to introduce the warrant or the specifics of the charge into evidence. On cross-examination, however, the prosecutor asked Smith if she had used falsified military-deployment orders to break a lease in Texas in May 2013 — the specific conduct underlying the warrant. Smith objected, arguing that the stipulation took the entire subject off the table. The judge discussed the matter with the lawyers at sidebar and overruled the objection.
That was not an abuse of discretion. The government’s stipulation did not foreswear the opportunity to cross-examine Smith about the conduct underlying the warrant if she took the stand. That conduct — using falsified military-deployment orders to break a lease — was relevant to her character for untruthfulness under Rule 608(b) of the Federal Rules of Evidence. She denied the conduct anyway, saying she was in Virginia in May 2013. And given the ample evidence of Smith’s guilt, any possible error was harmless.
C. Sufficiency of the Evidence
Smith’s final argument is that the evidence was insufficient to prove that she lacked Bruce’s permission to take Kay-den or that she took the baby for personal benefit. A challenge to the sufficiency of the evidence requires the challenger to shoulder “a heavy, indeed, nearly insurmountable, burden.”
United States v. Warren,
593 F.3d 540, 546 (7th Cir. 2010). We “consider the evidence in the light most favorable to the prosecution,, making all reasonable inferences in its favor, and [must] affirm the conviction so long as any rational trier of fact could have found the defendant to have committed the essential elements of the crime.”
United States v. Paneras,
222 F.3d 406, 410 (7th Cir. 2000) (quotation marks omitted).
Borrowing from the text of the federal kidnapping statute, the jury instructions-to which both parties consented-listed the following four elements of the offense:
1. The defendant knowingly seized, confined, kidnaped, abducted or carried away [Kayden];
2. The defendant held [Kayden] for a reason or purpose that would secure some benefit to herself[;]
3. The defendant willfully transported [Kayden] in interstate commerce from Wisconsin to Iowa; and
4. [Kayden] had not yet attained the age of 18 years.
The third and fourth elements are uncontested; the focus here is on elements 1 and 2. Smith argues that the evidence was insufficient to contradict her testimony that Bruce had instructed her to take his infant son to Colorado. She also argues that the government failed to prove that she took Kayden to secure a personal benefit to herself. Both contentions are belied by the record.
To the first issue, the government’s abundant evidence of Smith’s evasive actions-leaving the baby at the gas station in subzero temperatures and consistently lying to police about her role in his disappearance-convincingly refuted her claim about having Bruce’s permission to take the baby. And if more were needed, the government adduced evidence that Bruce was in extreme distress when he learned his son was missing and overjoyed when the baby was found. Viewed in the light most favorable to the government (or really any light at all), the government’s evidence was easily sufficient-indeed overwhelming-on the first element of the kidnapping charge.
Smith’s challenge to the evidence of a “personal benefit” requires only slightly more analysis. When first enacted, the federal kidnapping statute required that the victim be held “for ransom or reward,” which generally implied “some pecuniary consideration or payment of something of value.”
Gooch v. United States,
297 U.S. 124, 126, 56 S.Ct. 395, 80 L.Ed. 522 (1936). Congress amended the statute to read “for ransom or reward or otherwise.” The Supreme Court has interpreted the amended statute as prohibiting the “transportation in interstate or foreign commerce of persons who were being unlawfully restrained in order that the captor might secure some benefit to himself.”
Id.
at 128, 56 S.Ct. 395.
The government adduced substantial evidence that Smith took Kayden because she wanted a baby. Many courts have held that a personal relationship alone is a “benefit” sufficient to satisfy the broad “or otherwise” language of the kidnapping statute.
See United States v. Montgomery,
635 F.3d 1074, 1086 (8th Cir. 2011) (explaining that the personal-benefit element is satisfied when the perpetrator “held [the infant] for purposes of claiming the infant as her own”);
cf. United States v. Walker,
137 F.3d 1217, 1219 (10th Cir. 1998) (“The facts presented at trial indicate Walker’s
actions were motivated by self-interest, i.e., his interest in convincing [a female friend] to remain in a relationship with him.”). The lengths to which Smith went in concocting and perpetuating the pregnancy myth gave the jury a firm factual foundation to find that Smith kidnapped Kayden for the personal benefit of keeping him and passing him off as her own child.
■ The prosecutor also noted in his closing argument that Smith’s abandonment of Kayden behind the gas station inured to her benefit by increasing her likelihood of escaping criminal liability for the kidnapping. Smith takes issue with this theory of “personal benefit”; she argues that “this act falls outside the statute” because when she left the baby at the gas station, she “relinquished control of the child.” That sounds
almost
like a challenge to the
legal
adequacy of the government’s alternative “personal benefit” theory. If so, the argument is woefully undeveloped and therefore waived.
United States v. Collins,
796 F.3d 829, 886 (7th Cir. 2015) (“[Tjhis [c]ourt has long warned that perfunctory and undeveloped arguments are deemed waived.”) (internal quotation marks omitted).
Regardless, it’s clear enough from the record that the government was
not
offering the jury two different theories of criminal liability, one legally proper and one legally improper. Throughout the trial and in closing argument, the government’s theory of the case was that Smith wanted a baby and kidnapped Kayden to obtain that personal benefit. The prosecutor’s stray observation during closing argument that Smith obtained a (temporary) benefit from concealing the child was brief and inconsequential and is not grounds for reversal.
AFFIRMED.