WILLIAMS, Circuit Judge.

Gerardo Hernandez Lara, a citizen of Mexico, married a U.S. citizen in 1988. Hernandez (the name he uses) gained conditional permanent residency based on that marriage but never completed the process necessary to obtain unconditional permanent residency. When placed in removal proceedings in 2008 — ten years after divorcing his wife — he sought permanent residency through a discretionary waiver available to petitioners who can show that they had entered a failed marriage in good faith. Hernandez testified at the removal hearing that he had entered his marriage in good faith and the government offered no evidence to the contrary. Without making a credibility finding, the immigration judge determined that Hernandez's marriage was not bona fide and ordered him removed. The Board of Immigration Appeals evaluated Hernandez's appeal on the assumption that everything he said about his marriage was credible and yet went on to conclude that he had not met his burden of proving by a preponderance of the evidence that his marriage was bona fide. Given Hernandez's testimony that he had married for love, not immigration benefits — and the government's lack of evidence — the Board's conclusion implies that it demanded from Hernandez more proof than necessary to satisfy a preponderance standard. That reasoning constitutes a legal error warranting remand, and thus we grant Hernandez's petition for review.

I. BACKGROUND

Hernandez did not obtain conditional residency during his marriage because he and his wife, Diana Winger, never showed up for the joint interview that is generally a prerequisite to establishing the bona fides of a marriage and removing the conditions on residency. See 8 U.S.C. § 1186a(c), (d); 8 C.F.R. § 216.4(a). In 1990, Hernandez and Winger filed a joint petition to make Hernandez' residency status permanent, and the required joint interview was scheduled for December 1990. (The joint petition, called a Form I-751, generally must be filed within the 90-day period before the second anniversary of the alien's obtaining conditional permanent residency. 8 U.S.C. § 1186a(d)(2); 8 C.F.R. § 216.4(a)(1).) Winger did not appear for that interview; Hernandez told immigration officials in a sworn statement that Winger had left him a month and a half earlier because she was angry at him for working two jobs and coming home late, and that he had not seen her since. At Hernandez's request the joint interview was rescheduled for November 1992, see 8 C.F.R. § 216.4(b)(3), but this time neither spouse showed. Hernandez mailed a letter explaining that he could not get to the interview because he was in jail (apparently for driving under the influence) but gave no explanation for Winger's absence.

That was how things stood for 16 years until Hernandez stirred the hornet's nest by filing a Form I-751 in 2008 with USCIS requesting a discretionary waiver of the joint-petition requirements (including the joint interview). An alien may obtain this waiver — and with it, unconditional permanent residency — if he can demonstrate that he entered a failed marriage in good faith and that he is not at fault for failing to satisfy the joint-petition requirements. See 8 U.S.C. § 1186a(c)(4)(B); 8 C.F.R. § 216.5(a)(1)(ii). As evidence that his marriage was bona fide, Hernandez submitted joint tax returns for 1988 and 1989, recent accounts from his friends recalling that they had seen the couple together, a "to whom it may concern" letter apparently signed by Winger and dated in 1991 announcing that the couple had "reconciled" their differences and were living together again, a letter dated in 1994 apparently signed by Winger stating that she was jealous because Hernandez was spending too much time with his friends, and his sworn statement from December 1990 explaining that Winger had left him and that he did not know where she was.

In early 2009, after interviewing Hernandez, USCIS denied his request for a waiver on the ground that he had "failed to establish or provide documentation" that his marriage was entered in good faith. The agency relied primarily on Hernandez's "lack of evidence" but also noted that the couple was married in a civil ceremony attended by only one witness, that Hernandez's sworn statement indicated that spending time with his wife was not a priority for him, that he did not know where his wife was when she failed to appear for the 1990 interview, and that the couple had no children. The agency terminated Hernandez's status as a conditional permanent resident, and he was issued a Notice to Appear charging him with removability. See 8 U.S.C. § 1227(a)(1)(D)(i).

Hernandez conceded removability through his attorney at an April 2010 hearing and renewed his request for a discretionary waiver of the joint-petition requirements. In addition to the materials previously supplied to USCIS, he submitted his and Winger's birth certificates; his driver's license; the couple's marriage certificate, divorce decree, and marital settlement agreement; records from the IRS confirming that the couple had filed joint tax returns in 1988 and 1989; records of his criminal history (mostly DUI charges) showing that his last run-in with the law was in 2000; and his tax returns for 1998 to 2011.

At a 2013 hearing before the IJ, Hernandez testified through a translator that he had met Winger in 1986 at a bar in Delavan, Wisconsin, and that, although he spoke little English and she spoke no Spanish, they began dating a week or two later. They continued seeing each other for the next year and a half and eventually moved in together. Hernandez said that Winger had proposed to him and they got married in January 1988, after living together for about two months. When asked why he had married Winger, Hernandez answered that he "loved her a lot." Specifically, he said, he liked "[h]er body," "[h]er face, the way she dressed," and her housekeeping skills. He testified that during the marriage he was working hard to raise money for his parents in Mexico, but he did not immediately tell his mother of the marriage because, he explained, she did not have a telephone.

Hernandez said that his relationship with Winger had been stormy. He acknowledged that his disinterest in learning English had angered Winger and created stress. He and Winger liked going to restaurants and stores together, he said, but he did not have a lot of time for these activities because he was working two jobs. He recounted that, when Winger had disappeared before their first joint interview, he tried finding her by contacting her friends but was unsuccessful because none of them spoke Spanish. After this first falling-out, they had an on-again, off-again relationship, which included their living together for a few months in 1994 or 1995. Although their relationship was contentious, they did not divorce until 1998, Hernandez said, because he "had hopes of ... getting back together with her." When asked whether he had married Winger to get residency, he answered: "No. Never."

When questioned about his drinking and history of DUIs, Hernandez testified that he had stopped drinking in 1999 or 2000 (the last time he was in jail). He quit drinking, he said, because his attending church and being in a relationship with a Mexican woman who had children "change[d] his life."

Hernandez attempted to explain the dearth of documentary evidence related to his marriage. He said he had tried obtaining records showing that he and Winger handled their finances jointly and shared a post office box but that the records were no longer available. And there were no photographs of his wedding, he explained, because they were stolen from his apartment while he was in jail along with the money (five to six hundred dollars) that he kept in a folder with the photos. Hernandez said that he recently had tried finding Winger and even hired a private investigator, but that his efforts were unsuccessful.

A friend of Hernandez's also testified but did not provide much information. He said that he knew about the marriage and had seen the couple in stores around town. He acknowledged that Hernandez had not talked with him about the marriage but said he had been to the couple's home with them and knew they lived together.

The government submitted no evidence. Counsel for Hernandez argued during closing that — unless the IJ found Hernandez not credible — the evidence was sufficient to prove the bona fides of the marriage. Any gaps in Hernandez's evidence, counsel maintained, were attributable to the 25 years that had passed since he and Winger had married. The government countered that Hernandez's request for a waiver should be denied because, the government maintained, there was "little or no evidence" that the marriage was valid.

The IJ denied Hernandez's petition for a waiver and ordered him removed to Mexico. Hernandez had not met his burden to prove by a preponderance that his marriage was bona fide, the IJ reasoned, because his "evidence was not sufficiently detailed and, at times, proved inconsistent" with documents he had submitted. Among the handful of inconsistencies identified by the IJ was Hernandez's testimony "that the marriage broke up because of his refusal to go out partying and drinking with his wife," which the IJ thought was at odds with Winger's assertion in the 1994 letter that she was jealous that Hernandez was spending time with his male friends. The IJ also opined that Hernandez's testimony that he had lost contact with Winger in 1995 and currently could not find her was inconsistent with Winger's appearing in divorce court in 1998. The IJ emphasized throughout her analysis that Hernandez could not meet his burden of proof because, the IJ said, his testimony and other evidence were "vague" and lacking in "detail." The IJ made no express credibility finding, however, except for the determination that Hernandez had "credibly testified that he no longer drinks" and that he had reformed his life.

Hernandez appealed the IJ's decision, arguing (among other things) that the IJ had "failed to apply the appropriate burden of proof" when denying his waiver petition. The Board rejected this argument and the rest of Hernandez's challenges. Recognizing that the IJ had not made an explicit credibility finding, the Board "assume[d] for the purposes of the appeal" that both Hernandez and the friend who testified were credible. But, the Board concluded, "even assuming the credibility of the respondent and his witness," the IJ had correctly determined that Hernandez "did not meet his burden of proving by a preponderance of the evidence that he entered his marriage in good faith." This was so, the Board explained, because Hernandez had "provided little detail" of his relationship with Winger and because there was "a paucity of record evidence supporting the respondent's claim that he entered his marriage in good faith."

II. ANALYSIS

In his petition for review, Hernandez contends that the Board held him to a burden of proof more onerous than the preponderance standard that an alien must satisfy to establish that a failed marriage was bona fide. A denial of a good-faith marriage waiver is a discretionary decision and thus generally unreviewable, see 8 U.S.C. § 1252(a)(2)(B)(ii), Bouras v. Holder, 779 F.3d 665, 670 (7th Cir.2015); Boadi v. Holder, 706 F.3d 854, 857 (7th Cir.2013), but we have jurisdiction under § 1252(a)(2)(D) to consider Hernandez's argument because he claims that the Board applied the wrong legal standard. See Boadi, 706 F.3d at 857; Avila-Ramirez v. Holder, 764 F.3d 717, 722 (7th Cir.2014); Cruz-Moyaho v. Holder, 703 F.3d 991, 997 (7th Cir.2012).

We agree that the Board applied too high a burden of proof and that this error warrants remand. The Board concluded that, even if Hernandez testified truthfully about his marriage, he had not met his burden of proving by a preponderance that the marriage was bona fide because, the Board explained, he "provided little detail of his courtship of his wife or their wedding" and there was "a paucity of record evidence." The Board's analysis misapprehends the preponderance standard. Hernandez testified unequivocally that he did not marry Winger to obtain residency but because he "loved her." If, as the Board assumed, Hernandez testified truthfully, then this testimony alone is enough to prove that his marriage to Winger was more likely than not bona fide. See Lopez-Esparza v. Holder, 770 F.3d 606, 608-09 (7th Cir.2014) (granting petition and remanding on ground that IJ applied incorrect burden of proof and observing that, when preponderance standard governs, "[s]ome evidence would seem to preponderate over no evidence"); Am. Grain Trimmers, Inc. v. Office of Workers' Comp. Programs, 181 F.3d 810, 817-18 (7th Cir.1999) (en banc) (explaining that, under preponderance-of-evidence standard, "[o]ne compelling witness ... can overwhelm ten contrary witnesses or a raft of papers, if the trier of fact chooses to believe the one witness and to disbelieve the ten"); United States v. Cedano-Rojas, 999 F.2d 1175, 1180 (7th Cir.1993) (stating, in context of criminal sentencing, that testimony of arguably biased witness found credible by judge is sufficient to support finding of fact by preponderance); United States ex rel. Wandick v. Chrans, 869 F.2d 1084, 1089 (7th Cir.1989) (observing that "[c]redible testimony of one identification witness is sufficient to support a conviction" under more onerous beyond-a-reasonable-doubt standard); United States v. Noe, 411 F.3d 878, 889 (8th Cir.2005) ("Credible and substantial testimony by an accomplice is sufficient to support a conviction, and can prove firearm possession under the preponderance of the evidence standard." (citations and internal quotation marks omitted)). Because the Board elected to credit all of Hernandez's testimony — including his assurance that love, not residency, motivated him to accept Winger's proposal — the only conclusion it could then logically reach was that Hernandez's marriage was bona fide. The Board's failure to reach that conclusion is a legal error. See Lopez-Esparza, 770 F.3d at 609.

The government suggests that Hernandez never argued that the Board failed to correctly apply the preponderance standard and therefore waived the argument. We disagree with this contention. Hernandez repeats throughout the opening brief that the Board failed to correctly apply the preponderance standard. And again in his reply brief, Hernandez clearly states that "[n]either the Board nor the Immigration Judge made a finding that any of Mr. Hernandez's evidence or testimony was not credible" and contends that in the absence of such a finding, he met his burden of proving the bona fides of his marriage by a preponderance of the evidence. These statements were sufficient to preserve the argument. See United States ex rel. Yannacopoulos v. Gen. Dynamics, 652 F.3d 818, 837 & n. 20 (7th Cir.2011) (noting that while arguments made for first time in reply brief are generally treated as waived, it does not follow that arguments that are better developed in reply brief are waived); accord Hernandez v. Cook Cnty. Sheriff's Office, 634 F.3d 906, 913 & n. 9 (7th Cir.2011).

One could argue, perhaps, that the IJ implicitly found Hernandez not credible and that the Board's opinion should be read together with the IJ's decision to conclude that the proper evidentiary standard was applied when denying Hernandez's waiver application. But the IJ's opinion is opaque with regard to whether the IJ found Hernandez credible. And in any event, because the Board evaluated this appeal on the assumption that Hernandez was credible, our decision cannot rest on the IJ's supposed credibility findings. See Chen v. Holder, 578 F.3d 515, 517 (7th Cir.2009); Zheng v. Gonzales, 409 F.3d 804, 809 (7th Cir.2005); Chen v. Gonzales, 417 F.3d 268, 271 (2d Cir.2005).

The government's lawyer also contended at oral argument that we should deny Hernandez's petition because, the lawyer asserted, the REAL ID Act allows "that the applicant might be credible and still not meet their burden of proof." We assume that the lawyer was referring to the fact that an IJ may demand corroborating evidence even from an alien whose testimony the IJ finds credible. See 8 U.S.C. § 1229a(c)(4)(B); Liu v. Holder, 692 F.3d 848, 853-54 (7th Cir.2012); Abraham v. Holder, 647 F.3d 626, 633 (7th Cir.2011). But this provision of the REAL ID Act is irrelevant here because neither the IJ's nor the Board's ruling rests on a determination that Hernandez had failed to provide available corroborating evidence. See Tandia v. Gonzales, 487 F.3d 1048, 1054-55 (7th Cir.2007). Thus, by invoking the REAL ID Act, the government is once again violating the Chenery doctrine in its defense of a Board ruling, see SEC v. Chenery Corp., 318 U.S. 80, 87, 63 S.Ct. 454, 87 L.Ed. 626 (1943) (agency may not defend administrative decision on new ground not set forth in its original decision), despite our admonishments that flouting the doctrine is obstinate and invites sanctions, see Liu v. Holder, 718 F.3d 706, 709-10 (7th Cir.2013); Chen v. Holder, 715 F.3d 207, 210 (7th Cir.2013).

Hernandez's remaining arguments are frivolous, meriting only brief discussion. He contends that he was prejudiced by the immigration authorities' failure to deny the Form I-751 he filed jointly with Winger because, he says, had the authorities denied that petition, it would have been the immigration authorities' burden under 8 U.S.C. § 1186a(c)(3)(D) to establish that his marriage was not bona fide. But this subsection applies only when an alien's conditional residency is terminated after the alien files the petition and appears for a joint interview. See id. § 1186a(c)(3)(A), (C), (D). Because Hernandez and Winger never appeared for the joint interview, any termination of his status would have been under § 1186a(c)(2), and the burden of proof would have fallen not on the Attorney General but on Hernandez. See id. § 1186a(c)(2)(B).

Hernandez also maintains that, had his conditional residency been terminated earlier, he would have had more evidence of his marriage to Winger. But he points to no statute or regulation that was violated when the immigration authorities declined to terminate his status prior to his petitioning for a waiver of the joint-filing requirements. Nor does he identify any authority for the proposition that an alien can sit on his hands for years before seeking an immigration benefit and then blame the government for his inability to gather evidence because of the passage of time. Hernandez would have borne the same burden of proof under any of the scenarios he identifies, so he had every incentive to gather pertinent evidence when he first filed the joint petition.

Hernandez next contends that the Board ignored "key pieces of evidence," but the only evidence he points to is a letter he wrote in 1995. He asserts that the Board's failure to discuss the letter prejudiced him because, he says, the letter provides the details of his courtship that the Board said were lacking. But the letter is cumulative of — and no more detailed than — his testimony, and thus we do not see how the Board's failure to mention it prejudiced Hernandez. He also asserts that his "case presents a question of law as to what the appropriate interpretation of the phrase `entered into in good faith' entails," but he does not elaborate on what this "question of law" is.

III. CONCLUSION

Accordingly, we GRANT the petition for review and REMAND the case to the Board for further proceedings.