
615 F.3d 391 (2010)
Gene Irving GARLAND, Petitioner-Appellant,
v.
Warden Keith ROY, Respondent-Appellee.
No. 09-40735.
United States Court of Appeals, Fifth Circuit.
August 13, 2010.
*393 Gene Irving Garland, Jr., Texarkana, TX, pro se.
Michael Wayne Lockhart, Asst. U.S. Atty., Beaumont, TX, for Roy.
Before KING, WIENER, and DENNIS, Circuit Judges.
DENNIS, Circuit Judge:
Pro se petitioner Gene Irving Garland appeals the dismissal of his habeas corpus petition brought pursuant to 28 U.S.C. § 2241. In that petition he argues that he is entitled to release in light of United States v. Santos, 553 U.S. 507, 128 S.Ct. 2020, 170 L.Ed.2d 912 (2008), which held that the money-laundering statute's, 18 U.S.C. § 1956(a)(1), term "proceeds" was ambiguous and as a result, in certain circumstances, must be read to mean "profits." Santos clearly applies retroactively to Garland's convictions at issue in this case. United States v. McPhail, 112 F.3d 197, 199 (5th Cir.1997). Garland contends that, under Santos, he was wrongfully convicted of multiple nonexistent money laundering offenses because the indictment and the jury instructions did not require the Government to prove that he used "profits" to pay "returns" to investors in his illegal pyramid scheme. He also argues that his petition satisfies 28 U.S.C. § 2255's "savings clause" and thus can be brought under § 2241. We agree that Garland's petition states a claim falling within § 2255's "savings clause" and thus he may proceed under § 2241. Therefore, we REVERSE the dismissal and REMAND for further proceedings consistent with this opinion.

BACKGROUND
"28 U.S.C. § 2255 . . . is the primary means under which a federal prisoner *394 may collaterally attack the legality of his conviction or sentence." Reyes-Requena v. United States, 243 F.3d 893, 901 (5th Cir.2001). "However, § 2241 may be utilized by a federal prisoner to challenge the legality of his or her conviction or sentence if he or she can satisfy the mandates of the so-called § 2255 `savings clause.'" Id. at 901.
The "savings clause" states:
An application for a writ of habeas corpus in behalf of a prisoner who is authorized to apply for relief by motion pursuant to this section, shall not be entertained if it appears that the applicant has failed to apply for relief, by motion, to the court which sentenced him, or that such court has denied him relief, unless it also appears that the remedy by motion is inadequate or ineffective to test the legality of his detention.
28 U.S.C. § 2255(e).
This court has interpreted § 2255(e) to mean that there are three "factors that must be satisfied for a petitioner to file a § 2241 petition in connection with § 2255's savings clause." Jeffers v. Chandler, 253 F.3d 827, 830 (5th Cir. 2001) (citing Reyes-Requena, 243 F.3d 893). They are: (1) the petition raises a claim "that is based on a retroactively applicable Supreme Court decision"; (2) the claim was previously "foreclosed by circuit law at the time when [it] should have been raised in petitioner's trial, appeal or first § 2255 motion"; and (3) that retroactively applicable decision establishes that "the petitioner may have been convicted of a nonexistent offense." Reyes-Requena, 243 F.3d at 904. See also Christopher v. Miles, 342 F.3d 378, 382 (5th Cir.2003).
The petitioner bears the burden "to demonstrate that the § 2255 remedy is inadequate or ineffective." Christopher, 342 F.3d at 382. He must "com[e] forward with evidence . . . show[ing]" each element of the Reyes-Requena test. Wesson v. U.S. Penitentiary, Beaumont, Tex., 305 F.3d 343, 347 (5th Cir.2002). Therefore, before allowing the petitioner to proceed under § 2241, "[w]e must examine the merits of the petitioner's claim to determine whether" the Reyes-Requena factors are satisfied. Christopher, 342 F.3d at 383. Accordingly, in reviewing the instant dismissal, we need to become familiar with not only the background of Garland's habeas petition, but also the underlying convictions that Garland claims may have been for non-criminal conduct.
The challenged convictions consist in relevant part of 52 counts of money laundering pursuant to 18 U.S.C. § 1956(a)(1)(A)(I). In addition, those money-laundering charges were predicated upon Garland's commission of the unlawful acts described in 62 counts of mail fraud pursuant to 18 U.S.C. § 1341 and one count of securities fraud pursuant to 15 U.S.C. §§ 77q(a) and 77x.
The money-laundering statute under which Garland was convicted established four essential elements of the crime: (1) that he knew "that the property involved in a financial transaction represent[ed] the proceeds of some form of unlawful activity" (emphasis added); (2) that he "conduct[ed] or attempt[ed] to conduct such a financial transaction"; (3) that the financial transaction "in fact involve[d] the proceeds of [the] specified unlawful activity" (emphasis added); and (4) that the transaction was undertaken with "the intent to promote the carrying on of [a] specified unlawful activity." 18 U.S.C. § 1956(a)(1)(A)(I). At the time Garland was convicted, the statute did not define the meaning of the term "proceeds."[1]
*395 The indictment and the jury instructions tracked the language of the money-laundering statute by describing Garland's alleged money laundering as his knowing use of the "proceeds" of his pyramid scheme to pay sums falsely described as earnings to his investor-victims in order to further the operations of his scheme.[2] Thus, neither the indictment nor the jury instructions required the Government to prove that Garland transacted in "profits" of his unlawful activities, rather than "gross receipts," in order to convict him of money laundering. In fact, it appears that the alleged transactions underlying the money-laundering charge could not have involved "profits," as the only allegation was that Garland took "proceeds" from his criminal activities and used it to maintain the criminal enterprise.
As it explains on appeal and is reflected in the indictment, the Government proved that Garland engaged in securities fraud and at least one count of mail fraud by alleging that he conducted a "pyramid scheme" involving the sale of fraudulent securities. In other words, based on the indictment, the Government alleged that using the mails Garland sold fraudulent securities and then used the proceeds from those sales to distribute money to individuals who had previously bought his "securities," under the guise that this was a return on the individuals' initial investments, thereby encouraging their continued investment in his fraud. See 15 U.S.C. § 77q(a) (stating that securities fraud occurs when "any person in the offer of sale or any securities" uses the "mails, directly or indirectly . . . to employ any device, scheme or artifice to defraud; or . . . to obtain money or property by means of any untrue statement of a material fact or . . . to engage in any transaction, practice, or course of business which operates or would operate as a fraud or deceit upon the purchaser");[3] 18 U.S.C. § 1341 (stating that mail fraud occurs when one "places in any post office or authorized depository for mail matter, any matter or thing whatever. . . or knowingly causes to be delivered by mail . . . any such matter or thing" that was part of a "devised or intend[ed] . . . scheme or artifice to defraud or for obtaining money or property by means of false or fraudulent pretenses . . ."). In this manner, it is possible that the same payout of proceeds as "returns" to investors formed the basis of the mail and securities fraud convictions, as well proved the element of the money-laundering charge that *396 Garland transacted in "proceeds" of the underlying unlawful activity.
Following his convictions, Garland filed two unsuccessful habeas petitions. His present petition pursuant to 28 U.S.C. § 2241 argues that the Supreme Court's interpretation of the money-laundering statute in United States v. Santos, 553 U.S. 507, 128 S.Ct. 2020, 170 L.Ed.2d 912 (2008), reveals retroactively that Garland was convicted of nonexistent crimes of using "receipts" rather than "profits" from his pyramid scheme to further the scheme's operations. The combination of the plurality and concurring opinions in Santos holds that in certain circumstances, elaborated on below, "proceeds" must be defined as "profits" instead of "gross receipts." 128 S.Ct. at 2034 n. 7 (Stevens, J., concurring in the judgment).[4]
The district court, which adopted without alteration the recommendations of the magistrate judge, dismissed Garland's petition on two grounds. First, the magistrate judge concluded that Santos's narrow definition of "proceeds" as "profits" is limited to the specific facts of that case, under which the petitioners were convicted of money laundering stemming from the unlawful activity of running an illegal gambling operation. Thus, the magistrate judge reasoned, Santos does not apply to Garland's conviction and therefore he was not convicted of a nonexistent offense in light of that case. Second, the magistrate judge stated that any claim that Garland could have raised in light of Santos was not previously "foreclosed," as this circuit has never specifically held that "proceeds" should be defined as "receipts" rather than "profits." Garland's objections on both points were overruled.

STANDARD OF REVIEW
"This Court reviews de novo a district court's dismissal of a section 2241 petition on the pleadings."[5]Pack v. Yusuff, 218 F.3d 448, 451 (5th Cir.2000).

DISCUSSION
We consider each of the Reyes-Requena factors in turn. We conclude that Garland's petition satisfactorily establishes each factor and therefore his claim may proceed under § 2241.

1. Claim based on a retroactively applicable Supreme Court decision
There can be no question that Garland's petition satisfies the first Reyes-Requena factor, i.e. that his claim is based on a retroactively applicable Supreme Court decision. The Government argues that Santos should not apply retroactively because "the Supreme Court did not make its holding retroactive." Government Br. 15 (emphasis in original). However, as Garland argues, our case law establishes that new decisions interpreting federal statutes that substantively define criminal offenses automatically apply retroactively and Santos is an exemplar of such a decision. See United States v. McPhail, 112 F.3d 197, 199 (5th Cir.1997).
In Davis v. United States, the Supreme Court held that a petitioner could collaterally attack his conviction based on a decision issued "after [the petitioner's] conviction was affirmed" if that decision established that the "conviction and punishment *397 are for an act that the law does not make criminal." 417 U.S. 333, 346, 94 S.Ct. 2298, 41 L.Ed.2d 109 (1974). This court has interpreted Davis to hold that "substantive, non-constitutional decision[s] concerning the reach of a federal statute . . . do[] not implicate the retroactivity analysis set forth in Teague v. Lane, 489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989),[6] [and instead] appl[y] retroactively to cases on collateral review." United States v. McPhail, 112 F.3d at 199 (citing Davis, 417 U.S. at 341-47, 94 S.Ct. 2298; United States v. McKie, 73 F.3d 1149, 1153 (D.C.Cir.1996); United States v. Dashney, 52 F.3d 298, 299 (10th Cir.1995)). McPhail further explained that a decision is "substantive, non-constitutional[,] . . . concerning the reach of a federal statute," if it "articulates the substantive elements that the government must prove to convict a person charged under the statute." Id. By so doing, that decision "explains what conduct is, and has always been, criminalized by the statute" and thus "it applies retroactively to cases on collateral review" without triggering the Teague analysis. Id. Accordingly, the McPhail panel concluded that a petitioner could collaterally attack his conviction for "using" a firearm in furtherance of his crime based on Bailey v. United States, 516 U.S. 137, 147-51, 116 S.Ct. 501, 133 L.Ed.2d 472 (1995), which was handed down subsequent to his conviction becoming final, and which established that the Government must "present evidence sufficient to show active employment of the firearm" in order to sustain such a conviction. McPhail, 112 F.3d at 199.
In light of McPhail, Santos is a prime example of a Supreme Court decision retroactively applicable to cases pending on collateral review. Santos examines the meaning of the word "proceeds" in the money-laundering statute, 18 U.S.C. § 1956. It determines that, in certain circumstances, "proceeds" cannot be understood as "gross receipts," but rather must be defined as "profits." See Santos, 128 S.Ct. at 2034 n. 7 (Stevens, J., concurring in the judgment). Thus, for money laundering falling within the case's holding, Santos "fill[s] gaps in [the] statute" by "defin[ing][a] potentially ambiguous statutory term[]." Id. at 2031. Just as in McPhail, Santos construed the reach of a federal statute more narrowly than its broadest possible meaning, thus requiring the Government to prove additional facts in order to convict Garland of money laundering. Accordingly, Santos applies retroactively. It is not barred from having retroactive effect upon cases on collateral review under the Teague analysis because it is a substantive, non-constitutional decision concerning the reach of a federal statute.

2. Claim was previously foreclosed by circuit law
Likewise, as Garland argues and the Government appears to concede, his present claim was "foreclosed" under our pre-Santos cases. See Government Br. 15. Thus, he satisfies the second Reyes-Requena factor.
Our cases have never explicitly defined the meaning of "foreclosed by circuit law" as used in this Reyes-Requena factor. Nonetheless, we have previously adopted the ordinary meaning of "foreclosed""exclude[d]" by prior controlling case law. 6 *398 Oxford English Dictionary 47 (2d ed.1989). See Garrido-Morato v. Gonzales, 485 F.3d 319, 322 n. 1 (5th Cir.2007); United States v. Cathey, 259 F.3d 365, 368 (5th Cir.2001). We have consistently held that if an argument falls within the scope of, and is excluded by, a prior holding of a controlling case, it is foreclosed by that case. The court need not have specifically considered and rejected the exact claim for it to be foreclosed, as long as the breadth of a prior holding was meant to encompass and preclude the argument.
For instance, in Garrido-Morato we held that circuit case law "foreclosed" the defendant's claim that her conviction "for harboring aliens should not bar her from discretionary relief" from deportation. 485 F.3d at 322 n. 1 (citation and quotation marks omitted). Individuals are barred from such discretionary relief if they have committed an "aggravated felony." See id. A prior case in this circuit had "held that the parenthetical `related to alien smuggling' [in the statute defining aggravated felonies] is descriptive and not limiting." Id. Clearly, harboring aliens, although not part of the process of importing or exporting aliens, could be described as relating to alien smuggling. See Black's Law Dictionary 1516 (9th ed.2009) (defining "smuggling" as "[t]he crime of importing or exporting illegal articles"). Therefore, we concluded that our case law excluded the defendant's narrower interpretation of "aggravated felony" as not including harboring aliens; Garrido-Morato was "foreclosed" from arguing that she was entitled to discretionary relief on the basis that she had not committed an aggravated felony. Id.
Similarly, in Cathey, 259 F.3d at 368, we held that Cathey's argument"that the district court's sentence, based on its finding that [another individual's] death resulted from [Cathey's] distribution of heroin, violated [Cathey's] right to a jury"was "foreclosed" by United States v. Watts, 519 U.S. 148, 117 S.Ct. 633, 136 L.Ed.2d 554 (1997). In Watts, the Supreme Court held "that a jury's verdict of acquittal does not prevent the sentencing court from considering conduct underlying the acquitted charge, so long as that conduct has been proved by a preponderance of the evidence." Cathey, 259 F.3d at 368 (quotation marks omitted) (quoting Watts, 519 U.S. at 157, 117 S.Ct. 633). The Supreme Court had established a general rule that encompassed, rejected and thereby "foreclosed" the defendant's specific argument.
Under this definition, Garland's claim was previously foreclosed by circuit case law. In United States v. Allen, a panel of this court wrote, "[f]raudulent scheme[s] produce[] proceeds, at the latest when the scheme succeeds in disgorging the funds from the victim and placing them into the control of the perpetrators." 76 F.3d 1348, 1361 (5th Cir.1996). The panel then used this definition to conclude that the defendants could be convicted of money laundering because the money "left the control" of the victim and "came into the possession" of the defendants. Id. The court indicated it did not need to determine that the funds were the profits of the unlawful activity; it was sufficient that the Government demonstrated that the defendant had control over the funds. Id. See also United States v. Puig-Infante, 19 F.3d 929, 938 (5th Cir.1994) (stating that "[t]he only permissible inference from the government's proof is that [the defendant] was in possession of the proceeds of unlawful activity," when all the Government had shown was that the defendant had control over money obtained through the sale of illegal drugs). In this manner, this court previously held that the term "proceeds" was defined by whether the defendant had control over the derivatives *399 of an unlawful activity, not the nature of those derivatives, i.e., whether the money or property represented the "gross receipts" or "profits" of the fraud. "We are bound by the decisions of prior panels." United States v. Rose, 587 F.3d 695, 705 (5th Cir.2009). Therefore, as Allen predated Garland's conviction and remained controlling case law until Santos, Garland was previously foreclosed by circuit case law from raising his instant claim.

3. Claim establishes petitioner may have been convicted of a nonexistent offense
Garland argues that he satisfies the third Reyes-Requena factor because the four-Justice plurality opinion in Santos held that "proceeds" must always be defined as "profits." Therefore, because his trial court in its charge to the jury defined "proceeds" as "any property" derived from the specified unlawful activity, he may have been convicted based on a set of facts that did not fall within the statute. He acknowledges that in Santos Justice Stevens wrote a narrower concurrence in the judgment, providing the necessary fifth vote for a majority of the Court. However, Garland argues that we should ignore Justice Stevens' analysis.
While we agree with Garland's ultimate conclusion that he satisfies the final Reyes-Requena element, we cannot agree with his analysis of Santos's holding. "When a fragmented Court decides a case and no single rationale explaining the result enjoys the assent of five Justices, `the holding of the Court may be viewed as that position taken by those Members who concurred in the judgments on the narrowest grounds.'" Marks v. United States, 430 U.S. 188, 193, 97 S.Ct. 990, 51 L.Ed.2d 260 (1977) (quoting Gregg v. Georgia, 428 U.S. 153, 169 n. 15, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976)). As a result and as was conceded by the Santos plurality, Justice Stevens' concurrence controls and therefore determines the scope of the Court's holding. See 128 S.Ct. at 2031 (plurality opinion) ("Since his vote is necessary to our judgment, and since his opinion rests upon the narrower ground, the Court's holding is limited accordingly." (citing Marks, 430 U.S. at 193, 97 S.Ct. 990)).

A.
We begin our analysis of whether Garland's claim is sufficient to establish that he may have been convicted of a nonexistent offense by determining the holding of the Court in light of the splintered Santos decision. Although, as dictated by Marks, our conclusion will ultimately depend on the ways in which Justice Stevens' holding narrowed that of the plurality, we begin by establishing the underlying principles on which he and the four member plurality evidently agreed.
First, as Justice Scalia writing for the plurality explained, at the time the Court rendered its decision, the term "proceeds" in the money-laundering statute was undefined and its meaning ambiguous. "The federal money[-]laundering statute does not define `proceeds.'" Santos, 128 S.Ct. at 2024 (plurality opinion). While, typically, "[w]hen a term is undefined, we give it its ordinary meaning," here "`[p]roceeds' can mean either `receipts' or `profits.'" Id. "Both meanings are accepted, and have long been accepted, in ordinary usage." Id. "`Proceeds,' moreover, has not acquired a common meaning in the provisions of the Federal Criminal Code." Id. "Most leave the term undefined." Id. Therefore, this "ordinary meaning" method of statutory construction was unavailing. "Under either of the word's ordinary definitions, all provisions of the federal money-laundering statute are coherent; no provisions are redundant; and the statute *400 is not rendered utterly absurd." Id. at 2025. Accordingly, "[f]rom the face of the statute, there is no more reason to think that `proceeds' means `receipts' than there is to think that `proceeds' means `profits.'" Id. at 2025. See also id. at 2031 (Stevens J., concurring in the judgment) ("When Congress fails to define potentially ambiguous statutory terms, it effectively delegates to federal judges the task of filling gaps in a statute. Congress has included definitions of the term `proceeds' in some criminal statutes, but it has not done so in 18 U.S.C. § 1956, the money-laundering statute at issue in this case." (citations and footnote omitted)).
Second, if "proceeds" were to be defined as "receipts" rather than "profits," the money-laundering statute would be left open to what a majority of the Court characterized as the "merger problem." Santos, 128 S.Ct. at 2026 (plurality opinion) ("If we accepted the Government's invitation to speculate about congressional purpose, we would also have to confront and explain the strange consequence of the `receipts' interpretation, which respondents have described as a `merger problem.'"); id. at 2033 (Stevens, J., concurring in the judgment) (stating that defining "proceeds" as "receipt" "runs squarely into what can be characterized as the `merger' problem."). The plurality explained the meaning of "merger problem" by relating the phrase to the specific facts of Santos. The "jury found Santos guilty of . . . one count of running an illegal gambling business" and "two counts of money laundering" based upon his "payments to runners, winners and collectors" involved in the gambling business. Id. at 2023 (plurality opinion). See also id. at 2033 (Stevens, J., concurring in the judgment). The plurality concluded that these dual charges resulted in the "merger problem" because:
If "proceeds" meant "receipts," nearly every violation of the illegal-lottery statute would also be a violation of the money-laundering statute, because paying a winning bettor is a transaction involving receipts that the defendant intends to promote the carrying on of the lottery. Since few lotteries, if any, will not pay their winners, the statute criminalizing illegal lotteries would "merge" with the money-laundering statute.
Id. at 2026 (plurality opinion) (citation omitted). Moreover, the plurality continued, "[t]he merger problem is not limited to lottery operators." Id. "For a host of predicate crimes, merger would depend on the manner and timing of payment for the expenses associated with the commission of the crime." Id. "Few crimes are entirely free of cost, and costs are not always paid in advance." Id. "[A]ny wealth-acquiring crime with multiple participants would become money-laundering when the initial recipient of the wealth gives his confederates their shares." Id. at 2026-27. Thereby, corresponding to what may have occurred in Garland's case, the plurality explained that the "merger problem" resulted any time the definition of "proceeds" as "receipts" enabled the money-laundering charge to rely upon the same "transaction" as the "predicate crime." Justice Stevens later adopted this understanding of the merger problem in his concurrence. Id. at 2032-33 (Stevens, J., concurring in the judgment)
As a result of these underlying premises shared by Justice Stevens and the plurality, both agreed that, at least in certain circumstances, "proceeds" must be defined as "profits" rather than "receipts." The plurality would have held that "[b]ecause the `profits' definition of `proceeds' is always more defendant-friendly than the `receipts' definition, the rule of lenity dictates that it should be adopted." Santos, 128 S.Ct. at 2025 (plurality opinion). However, *401 limiting the scope and reasoning of this holding, Justice Stevens' concurrence dictates that the definition of "proceeds" in the money-laundering statute must be determined via a bifurcated analysis. Santos, 128 S.Ct. at 2034 n. 7. (Stevens, J., concurring the judgment). First, a court must determine whether, when "proceeds" are defined as "gross receipts" rather than "profits," the defendant would face the "merger problem." Id. at 2033-34 & n. 7. If so, then, consistent with the plurality's decision, the rule of lenity governs and "proceeds" must be defined as "profits"; and the court need not proceed to the second step of Justice Stevens' analysis. Id. at 2034 n. 7. However, if, instead, there is no "merger problem," Justice Stevens' analysis, unlike the plurality, directs that a court must look to the legislative history of the money-laundering statute to determine how to define "proceeds." Id. A court does so with the default presumption that "proceeds" should be defined as "gross receipts," unless the legislative history affirmatively supports interpreting "proceeds" to mean "profits." Id. at 2031-34.
Our understanding of Justice Stevens' limits on and disagreements with the plurality's rule begins and ends with Justice Stevens' closing footnote, the only place in his short concurrence in which Justice Stevens attempted to lay out an independent holding rather than his partial disagreements with the plurality and the dissent. There, Justice Stevens responded to what the plurality characterized as its effort to determine the "`stare decisis effect'" of the splintered Santos decision. Santos, 128 S.Ct. at 2034 n. 7 (Stevens, J., concurring in the judgment) (quoting id. at 2031 (plurality opinion)). The plurality had argued that, based on Justice Stevens' concurrence, the holding of Santos is that "`proceeds' means `profits' when there is no legislative history to the contrary." Id. at 2031 (plurality opinion). Justice Stevens rejected this interpretation. Id. at 2034 n. 7 (Stevens, J., concurring in the judgment). Instead, he explained that his concurrence in the judgment, "rests on [1] my conviction that Congress could not have intended the perverse result that the dissent's rule [that `proceeds' should always be defined as `receipts'] would produce if its definition of `proceeds' were applied to the operation of an unlicensed gambling business. [2] In other applications of the statute not involving such a perverse result, I would presume that the legislative history summarized by Justice Alito [who dissented arguing that the legislative history of the money-laundering statute demonstrates that `proceeds' should always be defined as `gross receipts'] reflects the intent of the enacting Congress." Id. (citing id. at 2035-36 & n. 1 (Alito, J., dissenting)).
Just above that footnote, Justice Stevens explained what he meant by "the perverse result" by relating that phrase to the facts of Santos. He wrote:
As the plurality notes, there is "no explanation for why Congress would have wanted a transaction that is a normal part of a crime it had duly considered and appropriately punished elsewhere in the Criminal Code [by criminalizing gambling], to radically increase the sentence for that crime [by enabling the same conduct to constitute money laundering]." This conclusion dovetails with what common sense and the rule of lenity would require. Faced with both a lack of legislative history speaking to the definition of "proceeds" when operating a gambling business is the "specified unlawful activity" and my conviction that Congress could not have intended the perverse result that would obtain in this case under Justice Alito's opinion [arguing that "proceeds" always means "receipts," *402 which would have allowed for such dual convictions for the same transaction], the rule of lenity may weigh in the determination. And in that respect the plurality's opinion [defining "proceeds" as "profits"] is surely persuasive.
Id. at 2033-34 (citation omitted) (quoting id. at 2027 (plurality opinion)). Thus, according to Justice Stevens, the "perverse result" is when a defendant could be punished for the same "transaction" under the money-laundering statute as well as under another statute, namely the statute criminalizing the "specified unlawful activity" underlying the money-laundering charge. The "perverse result" and what the plurality and Justice Stevens called the "merger problem" are one and the same. See United States v. Kratt, 579 F.3d 558, 562 (6th Cir.2009) (using "merger problem" and "perverse result" interchangeably); United States v. Bucci, 582 F.3d 108, 124 (1st Cir.2009) (same).
Justice Stevens' concurrence also indicated that he understood Justice Alito to have concluded that the legislative history indicates "proceeds" should always be defined as "gross receipts." Justice Alito's analysis, in the portion of his dissent cited in Justice Stevens' explanatory footnote, argued that the evident congressional intent requires "proceeds" to always be defined as "receipts." Santos, 128 S.Ct. at 2035-36 & n. 1 (Alito, J., dissenting). Specifically, in the cited section, Justice Alito argued that the legislative history of the ratification of the United Nations Convention Against Transnational Organized Crime is "instructive" as to the congressional intent in passing the money-laundering statute and indicates that "proceeds... mean[s] any property derived from or obtained, directly or indirectly, through the commission of an offence." Id. at 2036 (quotation marks omitted) (quoting United Nations Convention Against Transnational Organized Crime, Art. 2(e), Nov. 15, 2000, 2225 U.N.T.S. 209). Further, Justice Stevens stated, "As Justice Alito rightly argues, the legislative history of [18 U.S.C.] § 1956 makes it clear that Congress intended the term `proceeds' to include gross revenues from the sale of contraband and the operation of organized crime syndicates involving such sales." Id. at 2032 (Stevens, J., concurring in the judgment).
In sum, Justice Stevensthrough his footnote explicating his conclusion and the remainder of his opinion clarifying the meaning of that footnoteturned the plurality's rule, that "proceeds" must always be defined as "profits," into a two-part holding. See Santos, 128 S.Ct. at 2034 n. 7 (Stevens, J., concurring the judgment). First, he stated that he was joining the plurality's rule, that the rule of lenity dictates that "proceeds" must be defined as "profits" in cases where defining "proceeds" as "gross receipts" would result in the "perverse result" of the "merger problem." Id. In other circumstances, however, he could not agree with the plurality that "proceeds" must have one uniform meaning, "profits." Instead, second, he stated that "in other applications of the statute not involving such a perverse result," he would start from the presumption that "proceeds" should be defined as "gross receipts," but he would look to the legislative history of the money-laundering statute, 18 U.S.C. § 1956, to challenge this presumption. Santos, 128 S.Ct. at 2034 n. 7 (Stevens, J., concurring the judgment). Only if he could locate adequate legislative history to rebut this presumption, indicating that "proceeds" should be defined as "profits," would he conclude that Congress meant for the narrower definition to apply. Id.
The other circuits that have analyzed Santos and Justice Stevens' concurring opinion, have adopted four different views *403 of Santos's holding. Reluctantly, we refrain from joining any of these camps but must follow our own reading of Santos. We do not reach this outcome lightly, but we believe that each of their interpretations violates the rule of Marks: that when the Supreme Court issues a splintered decision, we are bound by the entire "position taken by those Members who concurred in the judgment on the narrowest grounds." Marks, 430 U.S. at 193, 97 S.Ct. 990. Each of the existing interpretations of Santos's holding either interprets Justice Stevens as too narrowly limiting the decision of the plurality or fails to give full effect to the concurrence's meaning. Nonetheless, we note that our rule is largely consistent with, although distinguishable from, the holdings of the Sixth and Ninth Circuits and, likely, the First Circuit.
The Fourth, Eighth and Eleventh Circuits have held that in light of Justice Stevens' concurrence, Santos defines "proceeds" as "profits" only when courts are presented with the particular facts of Santos, where the petitioners were convicted of laundering money from the "unlawful activity" of running an illegal gambling operation. United States v. Spencer, 592 F.3d 866, 879-80 & n. 4 (8th Cir.2010); United States v. Demarest, 570 F.3d 1232, 1242 (11th Cir.2009); see also United States v. Howard, 309 Fed.Appx. 760, 771 (4th Cir.2009) (unpublished). The Third and Seventh Circuits have concluded that Justice Stevens' concurrence indicates "proceeds" must be defined as "profits" any time the legislative history of the money-laundering statute does not affirmatively indicate otherwise. United States v. Lee, 558 F.3d 638, 643 (7th Cir.2009); United States v. Yusuf, 536 F.3d 178, 186 n. 12 (3d Cir.2008). Analogous to the first step of Justice Stevens' bifurcated rule, the Ninth Circuit and, likely, the First Circuit have held that "proceeds" must be defined as "profits" any time the "merger problem" articulated in Santos would result if "proceeds" is defined as "gross receipts." United States v. Van Alstyne, 584 F.3d 803, 814 (9th Cir.2009); United States v. Bucci, 582 F.3d 108, 123-24 (1st Cir. 2009) (suggesting this interpretation in dicta). Finally, similar to both steps in Justice Stevens' rule, the Sixth Circuit has held, "`proceeds' does not always mean profits, as Justice Scalia concluded; it means profits only when the § 1956 predicate offense creates a merger problem that leads to a radical increase in the statutory maximum sentence and only when nothing in the legislative history suggests that Congress intended such an increase." United States v. Kratt, 579 F.3d 558, 562 (6th Cir.2009) (emphasis added).
However, as demonstrated by the analysis above, we believe that each of these interpretations of Santos is mistaken. Undermining the Fourth, Eighth and Eleventh Circuits conclusion that Santos's holding is limited to the facts of that case, Justice Stevens' concurrence stated that his opinion sought to address the facts of Santos and "other applications of the [money-laundering] statute." Santos, 128 S.Ct. at 2034 n. 7 (Stevens, J., concurring in the judgment). Contradicting the Third, Seventh, Ninth and, likely, the First Circuits' holding that Santos's rule was driven entirely by either the merger problem or the money-laundering statute's legislative history, Justice Stevens stated that the holding of his concurrence took account of both considerations, although to different extents. In tension with the Sixth Circuit's holdingthat "proceeds" should be defined as "profits" only when the "merger problem" would occur, it would result in a substantial increase in the defendant's sentence, and the legislative history does not indicate otherwise Justice Stevens stated that his desire to *404 avoid the "merger problem" and to defer to congressional intent motivated different facets of his holding. The "merger problem" does not need to coexist with legislative history indicating that "proceeds" should be defined as "profits" for that definition to apply. Furthermore, Justice Stevens did not state that the defendant needed to suffer a harsh increase in his sentence in order for "proceeds" to be defined as "profits." He wrote that the fifteen-year increase in the Santos's sentences made the merger in Santos "particularly unfair," but the particular sentence was just a symptom of the unfairness of the merger that his opinion was crafted to avoid. Id. at 2033-34. Therefore, we conclude that a more nuanced, bifurcated analysis is required to fully apply Justice Stevens' concurrence.

B.
Applying our view of the holding of Santos to the instant case, we do not reach the second step of the inquiryin which we would examine the money-laundering statute's legislative history. As laid out in the background section, we conclude that in light of the statute, indictment, and jury instructions of this case, it appears that (1) the Government did not prove or attempt to show that Garland engaged in money laundering with "proceeds," narrowly defined as "profits" rather than as "gross receipts"; (2) the same "transaction" may have been used to prove both the underlying unlawful activity and the money-laundering charges; and therefore (3) Garland's convictions for mail and securities fraud potentially "merged," as defined by Justice Stevens and the plurality, with his money-laundering conviction. Accordingly, Garland was potentially convicted of a nonexistent offense, satisfying the third Reyes-Requena factor.

CONCLUSION
Because we find that in light of Santos Garland has brought a claim that satisfies each of the Reyes-Requena factors, his petition falls within § 2255's "savings clause," allowing him to bring a habeas petition under § 2241. Therefore, we REVERSE the district court's dismissal and REMAND this case to the district court for further proceedings consistent with this opinion.
NOTES
[1]  In May 2009, subsequent to Garland's conviction, appeals and prior petitions and the Santos decision, Congress amended the money-laundering statute to provide a definition of "proceeds." Fraud Enforcement and Regulatory Act of 2009, Pub.L. No. 111-21, § 2(f)(1), 123 Stat. 1617, 1618 (2009). Specifically, it provided a broader definition of "proceeds" than the interpretation of the term offered in Santos, that proceeds "means any property derived from or obtained or retained, directly or indirectly, through some form of unlawful activity, including the gross receipts of such activity." 18 U.S.C. § 1956(c)(9).
[2]  Specifically the indictment alleged that the "financial transaction" involving "proceeds," in which Garland engaged, was that Garland used money taken in by the securities and/or mail frauds and "caused checks to be issued. . . which were made payable to" a defrauded individual and "which payment purposed to be legitimate . . . return," thereby seeking to maintain the fraud. The jury instructions stated that in order to conclude Garland transacted in "proceeds" the jury only needed to find that Garland attempted or engaged in a transaction that involved "any property, or interest in property . . . acquire[d] or retain[ed] as a result of the commission of the underlying specified unlawful activity."
[3]  15 U.S.C. § 77x, under which Garland was also convicted, specifies the punishment for committing securities fraud under "any of the provisions of this subchapter." It does not represent a separate offense.
[4]  As will be discussed at more length below, Justice Stevens' opinion is controlling.
[5]  Because Garland seeks to proceed "under § 2241, he was not required to obtain a certificate of appealability to proceed on appeal." Padilla v. United States, 416 F.3d 424, 425 (5th Cir.2005).
[6]  In Teague, the Supreme Court "adopt[ed] Justice Harlan's view of retroactivity for cases on collateral review. Unless they fall within an exception to the general rule, new constitutional rules of criminal procedure will not be applicable to those cases which have become final before the new rules are announced." 489 U.S. at 310, 109 S.Ct. 1060.
