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HULL, Circuit Judge: Petitioner Dudley Bryant appeals the district court’s dismissal of his 28 U.S.C. § 2241 habeas petition, brought pursuant to the “savings clause” in 28 U.S.C. § 2255(e). Bryant’s appeal presents the issue to which this Court alluded in Wofford v. Scott, 177 F.3d 1236 (11th Cir.1999), and subsequently left undecided in Gilbert v. United States (Gilbert II), 640 F.3d 1293 (11th Cir.2011) (en banc), cert. denied, — U.S. -, 132 S.Ct. 1001, 181 L.Ed.2d 743 (2012), and Williams v. Warden, 713 F.3d 1332 (11th Cir.2013). The issue is whether the savings clause in § 2255(e) permits a federal prisoner to bring a § 2241 petition when he has established that his current 235-month sentence for an 18 U.S.C. § 922(g) conviction exceeds the 10-year statutory maximum penalty authorized by Congress under 18 U.S.C. § 924(a). When a conviction has become final, a federal prisoner usually may challenge the legality of his detention only through a § 2255 motion. However, the savings clause in § 2255(e) permits the prisoner to file a § 2241 habeas petition when a § 2255 motion was “inadequate or ineffective to test the legality of his detention.” 28 U.S.C. § 2255(e). After review of the record, the briefs of the parties and the amicus, and having the benefit of oral argument, we conclude Bryant has satisfied the savings clause’s requirements in § 2255(e). Bryant has proven that his prior § 2255 motion was “inadequate or ineffective to test the legality of his detention” and that his § 2241 petition can now proceed under § 2255(e) because: (1) from the time of his initial sentencing in 2002 throughout his first § 2255 proceeding in 2005, our Circuit’s binding precedent in United States v. Hall, 77 F.3d 398, 401-02 (11th Cir.1996), held that a concealed-firearm offense under Fla. Stat. § 790.01 was a “violent felony” under § 924(e) and squarely foreclosed Bryant’s claim that he was erroneously sentenced above the 10-year statutory maximum penalty in § 924(a); (2) subsequent to Bryant’s first § 2255 proceeding, the Supreme-Court’s decision in Begay v. United States, 553 U.S. 137, 128 S.Ct. 1581, 170 L.Ed.2d 490 (2008), set forth a new standard to evaluate which crimes constitute violent felonies under § '924(e), and Begay, as interpreted by United States v. Archer, 531 F.3d 1347, 1352 (11th Cir.2008), and United States v. Canty, 570 F.3d 1251, 1255 (11th Cir.2009), overturned our Circuit precedent in Hall; (3) Begay’s new rule is substantive and applies retroactively to Bryant’s § 924(e) claim on collateral review; (4) as a result of pure § 92A(e)-Begay ■ error and retroactive application of Begay, Bryant’s 235-month sentence exceeds the 10-year statutory maximum authorized by- Congress in § 924(a); and (5) the savings clause in § 2255(e) reaches his claim of illegal detention above the statutory maximum penalty. Accordingly, we vacate the district court’s dismissal of Bryant’s § 2241 petition and remand with instructions set forth herein. We first review the procedural history of Bryant’s case, the savings clause in § 2255(e), and our Circuit’s prior rulings about § 2255(e). We then summarize the five specific requirements a § 2241 petitioner must satisfy to proceed under § 2255(e) and explain why Bryant has satisfied them. I. PROCEDURAL HISTORY A. Indictment in 2000 In December 2000, a federal grand jury indicted Bryant on one count of knowingly possessing firearms and ammunition while being a convicted felon, “[i]n violation of [18 U.S.C. §§] 922(g)(1) and 924(e).” While § 922(g)(1) prohibits the possession of any firearm or ammunition by a convicted felon, § 922 contains no penalty provision. See 18 U.S.C. § 922(g). The penalties for § 922(g) offensés are laid out in various provisions of § 924. As to Bryant’s § 922(g)(1) crime, § 924(a)(2) provides that a person who is convicted óf knowingly violating § 922(g)(1) shall be “imprisoned not more than 10 years.” 18 U.S.C. § 924(a)(2). The statutory maximum penalty for a § 922(g)(1) crime is 10 years’ imprisonment under § 924(a)(2). Section 924(e), known as the Armed Career Criminal Act (“ACCA”), prescribes different and higher statutory penalties for the § 922(g)(1) felon-in-possession offense.' Section 924(e)(1) provides that, “[i]n the case of a person who violates section 922(g)” and “has three previous convictions by any court ... for a violent felony or a serious drug offense, or both,” that person “shall be ... imprisoned not less than fifteen years.” 18 U.S.C. § 924(e)(1). The statutory maximum under § 924(e)(1) is life in prison. United States v. Brame, 997 F.2d 1426, 1428 (11th Cir.1993). The increased statutory penalties in .§ 924(e) are often referred to as the “ACCA enhancement.” Bryant’s indictment gave him notice that the government intended to seek the increased statutory penalties in § 924(e) based on his prior concealed-firearm conviction and two drug convictions. Bryant’s indictment charged that he had these felony convictions: (1) a 1988 Florida conviction for delivery and possession of cocaine; (2) 1989 Florida convictions for carrying a concealed firearm and being a felon in possession of a firearm; and (3) 1991 Florida convictions for delivery and possession of cocaine and for obstructing or opposing an officer without violence. B. Guilty Plea in 2001 In July 2001, Bryant pled guilty to his one-count indictment. During the plea hearing, the district court informed Bryant that, because he had “3 qualifying felony convictions,” he was facing a mandatory minimum sentence of 15 years and maximum sentence of life imprisonment, pursuant to § 924(e). Bryant acknowledged his understanding of these penalties. C. Presentence Investigation Report Bryant’s Presentence Investigation Report (“PSI”) indicated that, because Bryant had 3 prior felony convictions for a “violent felony” or a “serious drug offense,” he was subject to a mandatory minimum penalty of 15 years’ imprisonment and a statutory maximum penalty of life, pursuant to § 924(e). In Paragraph 12 of the “Offense Conduct” section, the PSI referenced the same prior felony convictions as the indictment. Bryant’s base offense level was 24, pursuant to U.S.S.G. § 2K2.1, for his § 922(g)(1) felon-in-possession offense. Bryant received a 4-level increase under § 2K2. 1(b)(5) for possessing firearms in connection with another felony offense, and a 1-level increase under § 2K2. 1(b)(1)(A) for possessing three or more firearms, which resulted in an initial adjusted offense level of 29. In the criminal history section, the PSI listed not only Bryant’s three convictions shown in the indictment, but also his other convictions. Among them was a 1988 felony conviction for “Burglary of a Structure.” Given all of his prior convictions, the PSI assigned Bryant 18 criminal history points and placed him into criminal history category VI. Bryant’s offense level of 29 and criminal history category of VI yielded a guidelines range of 151 to 188 months’ imprisonment. See U.S.S.G. ch. 5, pt. A, Sentencing Table (2000). The PSI also raised Bryant’s offense level from 29 to 33 under U.S.S.G. § 4B1.4(b)(3)(B), the armed-career-criminal guideline. This armed-career-criminal classification did not change Bryant’s criminal history category of VI, which was already the highest available. The offense level of 33, combined with a criminal history category of VI, resulted in a guidelines range of 235 to 293 months in prison. D.Objections to the PSI and Sentencing Hearing in 2002 Bryant raised several objections to the PSI, including an objection to his classification as an - armed career criminal. Bryant reiterated this objection at the sentencing hearing, arguing that his prior concealed-firearm conviction, which was referenced in the indictment, did not qualify as a “violent felony” under § 924(e)(2)(B) and, therefore, he should not be subject to the increased statutory maximum penalty of life in § 924(e)(1). The government countered that Bryant had “5 or 6 felony convictions which also could have been used” for § 924(e) purposes. In response to the government’s claim that Bryant had several other qualifying felony convictions, the district court stated: “I’m going through all of [Bryant’s prior convictions], because there’s a reference to 4 or 5 other felonies that could have been used from the government, and I’m going to find out if that’s accurate.” The district court then conducted a thorough examination of the felony offenses listed in paragraphs 33 through 49 of the criminal history section of Bryant’s PSI to determine which offenses could support an increased statutory maximum penalty under § 924(e). The district court’s review was so thorough that the court specifically addressed all of Bryant’s prior convictions, including his misdemeanor convictions, other than Bryant’s obviously non-qualifying misdemeanor convictions for public drinking and attempting to cash stolen checks. During the district court’s review, the government and Bryant were afforded multiple opportunities to respond directly to the qualifying nature of the convictions. The parties agreed that Bryant’s two prior convictions for delivery of cocaine were qualifying offenses pursuant to § 924(e). These were the two drug convictions listed in Bryant’s indictment. The parties disagreed as to the qualifying nature of Bryant’s prior concealed-firearm conviction, which was the third qualifying conviction listed in his indictment. After its exhaustive review, the district court found that, “[a]t most we’ve got three” qualifying predicate convictions. The district court then asked the government, “What are the four or five that you were talking about?” In response, the government conceded, “Maybe they were non qualifying....” The government then suggested that it had mistakenly counted non-qualifying drug offenses. The government did not object to the district court’s finding that there were “[a]t most ... three” qualifying predicate convictions, which were the two qualifying drug convictions and the single concealed-firearm conviction. The government never directed the district court to Bryant’s prior burglary conviction. In fact, the government failed to suggest at any point during the district court’s thorough review of Bryant’s prior convictions that his prior burglary conviction was a § 924(e)-qualifying offense. Ultimately, the district court overruled Bryant’s objection to his concealed-firearm conviction based on this Court’s decision in Hall, 77 F.3d at 401-02 (expressly holding that a conviction for carrying a concealed firearm under Florida law is a “violent felony” under § 924(e)(2)(B) because that offense posed a “serious potential risk of physical injury”). Consequently, after its thorough review of all of Bryant’s criminal history, the district court found only three § 924(e)-qualifying convictions: two cocaine-delivery convictions and one concealed-firearm conviction. This finding changed Bryant’s statutory maximum penalty from 10 years to life in prison. The district court sentenced Bryant to 235 months in prison, the low end of the guidelines range, to be followed by 3 years of supervised release. E. Direct Appeal in 2002 Bryant filed a direct appeal, raising only a suppression issue that he had preserved when he pled guilty. In October 2002, this Court summarily affirmed. See United States v. Bryant, 52 F. App’x 487 (11th Cir.2002). F. First § 2255 Motion in 2005 In October 2005, Bryant filed his first § 2255 motion to vacate his sentence. Bryant argued that he was “actually innocent” of the increased statutory penalties in § 924(e) because the government, failed to prove, using Shepard “-approved documents, that his two Florida drug convictions qualified as “serious drug offense[s]” under § 924(e)(2)(A). Bryant also argued generally that the government failed to prove, using Shepard-approved documents, that he had a conviction for a violent felony under § 924(e)(2)(B). But, he did not specifically reference his concealed-firearm conviction in his first § 2255 motion. The district court denied Bryant’s first § 2255 motion as time-barred. Both the district court and this Court denied a Certificate of Appealability (“COA”). G. Second § 2255 Motion in 2008 In September 2008, Bryant attempted to file a second § 2255 motion in the district court, arguing that, under the Supreme Court’s decision in Begay, he did not qualify for the life statutory maximum penalty in § 924(e). The district court dismissed Bryant’s second § 2255 motion because he failed to obtain the requisite authorization from this Court required by 28 U.S.C. §§ 2244(b)(3)(A), 2255(h). H. Request for Leave to File Successive § 2255 Motion In November 2008, Bryant sought authorization from this Court to file a second or successive § 2255 motion, relying on Begay as a “new rale” of law for purposes of § 2255(h). In 1996, Congress substantially restricted second or successive collateral attacks by enacting the Anti-Terrorism and Effective Death Penalty Act of 1996 (“AED-PA”). Under § 2255(h), AEDPA bars the filing of a second or successive § 2255 motion unless this Court certifies that the proposed § 2255 motion is based on (1) “newly discovered evidence that, if proven and viewed in light of the evidence as a whole, would be sufficient to establish by clear and convincing evidence that no reasonable factfinder would have found the movant guilty of the offense”; or (2) “a new rule of constitutional law, made retroactive to cases on collateral review by the Supreme Court, that was previously unavailable.” 28 U.S.C. § 2255(h) (emphasis added); In re Dean, 341 F.3d 1247, 1248 (11th Cir.2003). In November 2008, this Court denied Bryant’s application for leave to file a second or successive § 2255 motion, reasoning that Begay was not a “new rale of constitutional law” under § 2255(h) because it merely interpreted a substantive criminal statute, i.e., § 924(e). (Emphasis added). I. Present § 2241 Petition In December 2008, in the district court, Bryant filed a pro se habeas corpus petition, pursuant to 28 U.S.C. § 2241, and a memorandum of law in support. In his § 2241 petition, Bryant asserted that § 2255 had been “inadequate or ineffective” to challenge the legality of his 235-month sentence because our Circuit’s precedent in Hall had foreclosed his § 924(e) claim during his first § 2255 motion in 2005. Bryant contended that, under Begay and Archer, this Court’s precedent in Hall was effectively abrogated; therefore, his concealed-firearm conviction did not qualify as a “violent felony” under § 924(e)(2)(B), and he did not have the three predicate convictions necessary to increase his sentence under § 924(e). Bryant essentially argued his 235-month sentence exceeded his statutory maximum penalty of 10 years for his § 922(g) crime. Bryant further argued the savings clause in § 2255(e) permitted him to bring his § 2241 petition challenging his illegal sentence. The district court dismissed Bryant’s § 2241 petition. Bryant timely appealed in 2012. II. PROCEDURAL DEFAULT At the outset, one wonders why procedural default or waiver by Bryant does not resolve his case. Bryant did not raise on direct appeal (or even in his first § 2255 motion) a claim that his concealed-firearm conviction was not a “violent felony” and that he was illegally sentenced above the 10-year statutory maximum in § 924(a) for that reason. In § 2255 and § 2241 cases, this would result in a procedural default, unless Bryant can establish “cause and prejudice for his failure to assert his claims on direct appeal.” McCoy v. United States, 266 F.3d 1245, 1258-59 (11th Cir.2001) (applying the procedural-default rule to a § 2255(a) motion to vacate); Sawyer v. Holder, 326 F.3d 1363, 1366 (11th Cir.2003) (applying the procedural-default rule to a § 2241 habeas petition). This Court has made clear that futility of a claim due. to adverse Circuit precedent at the time of direct appeal does not constitute cause to excuse a procedural default in a first § 2255 motion. McCoy, 266 F.3d at 1258-59 (applying the procedural default rule in a first § 2255 motion because petitioner did not raise his Appren-di claim on direct appeal, even though the claim was rejected by. “every circuit which had addressed the issue” at the time). A ruling based on procedural default would obviate the need for us to address the difficult issue here about the savings clause in § 2255(e). We cannot take that easy way out because the procedural-default rule is not jurisdictional, but is an affirmative defense that is subject to waiver by the government. Howard v. United States, 374 F.3d 1068, 1073 (11th Cir.2004); Shukwit v. United States, 973 F.2d 903, 904 (11th Cir.1992); United States v. Jordan, 915 F.2d 622, 629 (11th Cir.1990). In the district court and how on appeal, the government has' not asserted any procedural default as a defense to Bryant’s § 2241 petition or his attempt to proceed under the § 2255(e) savings clause. By every reasoned measure, the government intentionally has waived any procedural default defense. See Shukwit, 973 F.2d at 904; Jordan, 915 F.2d at 629. Nothing herein should be read as indicating that Bryant has shown cause and prejudice. Before leaving procedural default, there is one more reason why Bryant’s failure to raise this particular § 924(e)-violent felony claim in his first -§ 2255 motion does not matter here. As discussed below, the language of § 2255(e) states that the savings clause applies regardless of whether a federal prisoner “has failed to apply” for § 2255 relief or whether the sentencing court “has denied him” § 2255 relief. See 28 U.S.C: § 2255(e). Therefore, Bryant’s failure to raise this particular § 924(e) claim in his first § 2255 motion does not preclude him from at least attempting to proceed under the savings clause in § 2255(e). In addition, this Court recently held that whether the savings clause in § 2255(e) may open the portal to a § 2241 petition is a “threshold” jurisdictional issue that must be decided before delving into the merits of the petitioner’s claim and the applicable defenses. See Williams, 713 F.3d at 1337-40 (concluding the savings clause is jurisdictional and, thus, limits- the district court’s subject-matter jurisdiction to entertain a § 2241 petition even when the government wishes to concede that the savings clause allows the § 2241 petitioner’s claim); see also Sawyer, 326 F.3d at 1366-67 (concluding the savings clause in § 2255(e) did not apply to § 2241 petitioner’s claim, but alternatively assuming that the petitioner had made the necessary showing to invoke the savings clause, and only then deciding the petitioner’s claim was procedurally defaulted). For these reasons, we must decide the jurisdictional question of whether the savings clause in § 2255(e) permits Bryant to bring a § 2241 petition claiming that his sentence is above the authorized statutory maximum penalty. III. STANDARD OF REVIEW “Whether a prisoner may bring a 28 U.S.C. § 2241 petition under the savings clause of § 2255(e) is a question of law we review de novo.” Williams, 713 F.3d at 1337. The petitioner bears the burden of demonstrating that the § 2255 remedy was “inadequate or ineffective to test the legality of his detention” for purposes of § 2255(e). Turner v. Warden, 709 F.3d 1328, 1333 (11th Cir.), cert. denied, — U.S. -, 133 S.Ct. 2873, 186 L.Ed.2d 923 (2013). - IV. THE SAVINGS CLAUSE Section 2255(e) states in full: 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). Section 2255(e)’s language — “An application for a writ of habe-as corpus” — includes a petition filed under 28 U.S.C. § 2241, which Bryant filed here. Section 2255(e) thus provides that a § 2241 petition “shall not be entertained” if a federal prisoner has failed to apply for relief by a § 2255 motion, or has already been denied such 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) (emphasis added). This quoted exception to § 2255(e)’s bar on a § 2241 petition is commonly referred to as the “savings clause.” Section 2255(e)’s language — “shall not be entertained” — speaks “in imperative terms regarding a district court’s power to entertain a [§ 2241] claim,” and “in enacting § 2255(e), Congress clearly restricted the subject-matter jurisdiction of the federal courts” over § 2241 petitions. Williams, 713 F.3d at 1340. And, as noted earlier, § 2255(e) by its own terms applies regardless of whether a federal prisoner “has failed to apply” for § 2255 relief or whether the sentencing court “has denied him” § - 2255 relief. Rather, the touchstone of the savings clause is whether a § 2255 motion would have been “inadequate or ineffective to test the legality of [the prisoner’s] detention.” 28 U.S.C. § 2255(e). In prior cases, we found nothing in the legislative history explaining what this language in the savings clause means. See Wofford, 177 F.3d at 1239-41; see also Gilbert II, 640 F.3d at 1307 (“The history behind the savings clause does not provide much help with its meaning.”). However, our decisions in Wofford, Gilbert II, and Williams do discuss what the terms “inadequate or ineffective” and/or “detention” mean and what type of claim might open the savings clause portal to § 2241 jurisdiction. See Wofford, 177 F.3d 1236; Gilbert II, 640 F.3d 1293; Williams, 713 F.3d 1332. We review these decisions, which guide our analysis. V. WOFFORD v. SCOTT (1999) In our first case addressing the savings clause, we framed the issue before this Court as a broad one, asking “what circumstances other than those involving practical difficulties are covered by the savings clause[?]” Wofford, 177 F.3d at 1242. In light of § 2255’s legislative history and other circuits’ decisions, we identified only one situation, conviction of a nonexistent offense, when the savings clause applies, and only speculated as to the possible existence of another in the sentencing context. See id. at 1244-45. In Wofford, the petitioner, Charlie Wof-ford, pled guilty in federal court to a drug conspiracy and being a felon in possession of a firearm. Wofford, 177 F.3d at 1237. He was sentenced to 300 months for the drug conspiracy and 60 months, concurrently, for the felon-in-possession offense. Wofford’s first § 2255 motion was denied. Id. This Court denied Wofford’s application to file a second § 2255 motion because he failed to meet § 2255(h)’s exceptions to AEDPA’s bar on second or successive § 2255 motions. . Id. at 1238. Wofford then filed a § 2241 habeas petition, raising, inter alia, a claim that his classification as a career offender under the guidelines “was improperly predicated upon the [district] court’s belief that it could not examine the underlying offenses in making that determination.” See id. Wofford did not claim, however, that his 300-month sentence exceeded the statutory maximum penalty. See id. The district court dismissed the § 2241 petition, and Wofford appealed. Id. A. Meaning of the Savings Clause On appeal, this Court described the savings clause’s legislative history, which, as mentioned above, yielded no concrete answers. See id. at 1239-42. After canvassing other circuits’ decisions, we determined that the best approach was the Seventh Circuit’s decision in In re Davenport, 147 F.3d 605 (7th Cir.1998). See Wofford, 177 F.3d at 1242-44. The Seventh Circuit’s Davenport decision rejected the argument that the § 2255(e) savings clause allows a § 2241 habeas petition whenever AEDPA bars a second or successive § 2255 motion. See Wofford, 177 F.3d at 1244. The essence of habeas relief, and all that the Constitution requires, is to allow a prisoner “ ‘a reasonable opportunity to obtain a reliable judicial determination of the fundamental legality of his conviction and sentence,’ ” either on direct appeal, in a first § 2255 motion, or in a successive § 2255 motion authorized by AEDPA. Id. (quoting Davenport, 147 F.3d at 609). Citing Davenport, this Court in Wofford described, in dicta, two circumstances under which the savings clause may allow a federal prisoner to proceed under § 2241. First, the Wofford panel opined, in dicta, that the savings clause “applies to a claim” when (1) a petitioner’s claim “is based upon a retroactively applicable Supreme Court decision”; (2) “the holding of that Supreme Court decision establishes the petitioner was convicted for a nonexistent offense”; and (3) “circuit law squarely foreclosed such a claim at the time it otherwise should have been raised in the petitioner’s trial, appeal, or first § 2255 motion.” Id. at 1244. This analysis in Wofford covers actual innocence challenges akin to the post-Bailey' § 2241 petitions, such as when a Supreme Court decision subsequent to conviction means that a petitioner’s offense conduct is no longer criminal. See Williams, 713 F.3d at 1343 (discussing Wofford). Second, Wofford observed, in dicta again, that the savings clause “might apply to some claims involving a ‘fundamental defect’ in sentencing where the petitioner had not had an opportunity to obtain judicial correction of that defect earlier.” Wofford, 177 F.3d at 1244 (quoting Davenport, 147 F.3d at 611). We declined to decide, however, “whether the savings clause extends to [such] sentencing claims ... or what a ‘fundamental defect’ in a sentence might be.” Id. at 1244-45. “It is enough .to hold, as we do, that the only sentencing claims that may conceivably be covered by the savings clause are those based upon a retroactively applicable Su-prente Court decision overturning circuit precedent.” Id. at 1245. B. Application to Wofford’s Claims Applying these principles, we concluded that the savings clause did not cover Wof-ford’s claims because (1) he “was not convicted of any crime which a retroactively applicable Supreme Court decision overturning prior circuit precedent has made clear is nonexistent”; (2) none of his sentencing claims rested upon a “circuit law-busting, retroactively applicable Supreme Court decision”; and (3) he had a “procedural opportunity to raise each of his claims and have it decided either at trial or on appeal.” Id. at 1245. We concluded that Wofford was “attempting to use § 2241 simply to escape the restrictions on second or successive § 2255 motions.” Id. VI. GILBERT v. UNITED STATES (2011) In our next savings clause decision, Gilbert II, we held definitively that the savings clause does not reach a guidelines-error sentencing claim when the prisoner’s sentence does not exceed the statutory maximum. Gilbert II, 640 F.3d at 1295. A. Procedural History in Gilbert’s Case In 1997, petitioner Ezell Gilbert pled guilty to two drug crimes, including possession of crack cocaine with intent to distribute. Id. at 1298. His offense involved 50 grams or more of crack cocaine and carried a maximum penalty of life imprisonment under • 21 U.S.C. § 841(b)(1)(A) (1996). Id. At Gilbert’s sentencing in 1997, the district court classified him as a career-offender under § 4B1.1 of the guidelines (which were mandatory at the time), in part due to his prior Florida § 790.01 concealed-firearm conviction. Id. at 1298-99. This career-offender status increased Gilbert’s offense level and criminal history category, yielding a guidelines range of 292 to 365 months’ imprisonment. Id. at 1299-1300. The district court sentenced Gilbert to 292 months in prison. Id. at 1300. Importantly, this sentence was less than Gilbert’s statutory maximum sentence of life imprisonment for his drug offense. Id. at 1298-1300. On direct appeal, Gilbert challenged his career-offender status, arguing that a concealed-firearm offense did not qualify as a “crime of violence” under § 4B1.2 of the guidelines. Id. at 1300. In 1998, in United States v. Gilbert (Gilbert I), 138 F.3d 1371, 1372 (11th Cir.1998), this Court rejected Gilbert’s argument, based on our 1996 Hall decision, and held that a concealed-firearm offense under Fla. Stat. § 790.01 “ ‘presents a serious potential risk of physical injury’ ” within the meaning of § 4B1.2(a)(2)’s definition of “crime of violence.” Gilbert I, 138 F.3d at 1372. In 1999, Gilbert filed his first § 2255 motion but did not challenge his career-offender status under § 4B1.1 of the guidelines. Gilbert II, 640 F.3d at 1301. The district court denied the motion, and this Court denied a COA. Id. Ten years later in 2009, Gilbert filed a motion to reopen or amend his first § 2255 motion. Gilbert wanted to challenge his § 4B1.1 career-offender status due to the intervening decisions from the Supreme Court in Begay and our Circuit in Archer. We review Begay and Archer to place our subsequent en banc decision in Gilbert II in context. B. Intervening Decisions in Begay and Archer In 2008, the Supreme Court, in Begay, addressed § 924(e)(2)(B)(ii), which defines “violent felony” as a crime that “is burglary, arson, or extortion, involves use of explosives, or otherwise involves conduct that presents a serious potential risk of physical injury to another.” 18 U.S.C. § 924(e)(2)(B)(ii). The question before the Supreme Court was whether a New Mexi-co conviction for driving under the influence (“DUI”) qualified as a “violent felony” under the last clause in § 924(e)(2)(B)(ii). Begay, 553 U.S. at 139-48, 128 S.Ct. at 1584-88. The Supreme Court determined in Be-gay that the term “violent felony” (1) does not apply to “every crime that presents a serious potential risk of physical injury to another,” but (2) refers only to crimes that are “roughly similar, in kind as well as in degree of risk posed,” to the offenses enumerated in § 924(e)(2)(B)(ii), namely, “burglary, arson, extortion, or crimes involving the use of explosives.” Id. at 142-43, 128 S.Ct. at 1584-85 (internal quotation marks omitted). These enumerated crimes “all typically involve purposeful, violent, and aggressive conduct.” Id. at 144-45, 128 S.Ct. at 1586 (internal quotation marks omitted). The Supreme Court concluded that (1) strict liability crimes such as DUI generally do not involve purposeful, violent, and aggressive conduct and can be committed without “any criminal intent at all,” and (2) thus, New Mexico’s DUI offense did not qualify as a “violent felony” under the last clause in § 924(e)(2)(B)(ii). Id. at 145, 148, 128 S.Ct. at 1586-88. Several months after Begay, this Court decided United States v. Archer, concluding that Begay “clearly set forth a new standard to evaluate which crimes constitute ‘violent felonies’ and ‘crimes of violence.’” Archer, 531 F.3d at 1352. Although Begay was a “violent felony” case under the § 924(e) statute, we applied Be-gay to the “crime of violence” designation in the guidelines because the definitions of those terms are virtually identical. Id. In Archer, we held that Begay undermined Gilbert I to the point of abrogation, and that “the crime of carrying a concealed firearm may no longer be considered a crime of violence under the Sentencing Guidelines.” Id. C.Gilbert II En Banc Based on these intervening decisions in Begay and Archer, Gilbert’s motion asked the district court either to reopen his first § 2255 proceeding or to construe his motion as a § 2241 petition and allow it to proceed under the savings clause in § 2255(e). Id. at 1301-02. After the district court denied relief, Gilbert appealed. Id. at 1302. On rehearing en banc in Gilbert II, this Court framed the issue presented as follows: “Does the savings clause of § 2255(e) apply to claims that the sentencing guidelines were misapplied in the pre-Booker mandatory guidelines era in a way that resulted in a substantially longer sentence that does not exceed the statutory maximum?” Id. at 1306 (emphasis added). We included the statutory-maximum qualification “to make it clear we are not deciding that issue, and we do not imply any view about how that issue should be decided when and if it is presented in some other case.” Id. D. Two Assumptions in Gilbert II Before delving into its discussion, the en banc Court in Gilbert II made two assumptions. Id. at 1302-05. First, we assumed that, if Begay and Archer had been decided at the time of Gilbert’s sentencing, his guidelines range would have been lower, and he would have received a lesser sentence than his current 292 months. Id. at 1305. Second, we assumed that, were we to rule in Gilbert’s favor, he would receive a lesser sentence on remand, given his lowered guidelines range. Id. We stressed, however, that these were only assumptions and that we were “not so sure of either proposition.” Id. at 1302-05. E. Gilbert’s Sentence Did Not Exceed the Statutory Maximum Even assuming Gilbert’s guidelines range and sentence would have been lower, we rejected Gilbert’s argument that, because he was sentenced in the pre-J3oo/c er, mandatory-guidelines era, his statutory maximum sentence was the high end of his guidelines range, not the maximum penalty prescribed by statute. Id. at 1306-07. We indicated that a critical difference existed between pre-Booker mandatory guidelines and statutory maximum penalties. Id. We explained that a “statutory maximum sentence” is a “punishment ceiling beyond which no defendant convicted for committing that particular crime may be sentenced regardless of the circumstances of the crime, regardless of the defendant’s history, and regardless of the sentencing guidelines.” Id: at 1306. “To the extent of any inconsistency [between the guideline range and the statute], the guidelines would have to bend to statutorily prescribed limits, not the other way around.” Id. at 1307. We reiterated that Gilbert’s statutory maximum penalty was life imprisonment for his crack cocaine offense under 21 U.S.C. . § 841(b)(1)(A) (1996), without regard to his criminal history. See id. at 1306. Gilbert’s statutory maximum penalty was not the top end of the correctly calculated guidelines range. Id. at 1306-07. F. Savings Clause Does Not Trump § 2255(h) In addressing the meaning of the savings clause in § 2255(e), we also concluded in Gilbert II that the AEDPA restrictions in § 2255(h) on successive motions do not render a § 2255 remedy “ ‘inadequate or ineffective’ ” for purposes of the savings clause in § 2255(e). Id. at 1308. Otherwise, we explained, “the savings clause would eviscerate [AEDPA’s] second or successive motions bar [in § 2255(h)], and prisoners could file an endless stream of § 2255 motions, none of which could be dismissed without a determination of the merits of the claims they raise.” Id. We observed that other circuits addressing the relationship between § 2255(e) and (h) also refused to interpret the savings clause in § 2255(e) “in a way that would drop the § 2255(h) bar on second and successive motions, defeat its purpose, and render it pointless.” Id. Moreover, according to fundamental canons of statutory construction, the “generally worded and ambiguous savings clause” in • § 2255(e) could not override AEDPA’s “specifically worded and clear statutory bar on second or successive motions” in § 2255(h). Id. G. Finality Interests The en banc Gilbert II Court then heavily emphasized the importance of finality interests in criminal convictions and balanced those finality interests against challenges to guidelines-based errors. We reasoned: “The critically important nature of the finality interests safeguarded by § 2255(h) ... weighs heavily against an interpretation of the savings clause [in §_ 2255(e)] that would lower the second or successive motions bar and permit guidelines-based attacks years after the denial of an initial § 2255 motion.” Id. at 1309. We explained that the “[sentencing guidelines provisions are many and complex, the English language and those who use it are imperfect, and the case law about what various and sundry guidelines mean and whether they apply in different factual situations is in a constant state of flux.” Id. Gilbert sought to create a rule that “would apply to every type and kind of enhancement, of which there are scores in the sentencing guidelines.” Id. at 1309-10. We stated, however, that allowing a guidelines-misapplication claim to proceed under the savings clause and avoid the AEDPA bar in §. 2255(h) “would wreak havoc on the finality interests that Congress worked so hard to protect with the AEDPA provisions.” Id. at 1310. The en banc Gilbert II Court stressed that finality of judgments was one of the central principles behind AEDPA’s restrictions on second or successive § 2255 motions. Id. After all, if second or successive § 2255 motions were not “greatly restricted,” there would be “no end to collateral attacks on convictions and sentences.” Id. at 1311 (internal quotation marks omitted and alteration adopted). We cited several Supreme Court cases explaining the importance of finality, such as McCleskey v. Zant, 499 U.S. 467, 111 S.Ct. 1454, 113 L.Ed.2d 517 (1991), which stated that a “ ‘procedural system which permits an endless repetition of inquiry into facts and law in a vain search for ultimate certitude implies a lack of confidence about the possibilities of justice that cannot but war with the effectiveness of underlying substantive commands.’ ” Gilbert II, 640 F.3d at 1311 (quoting McCleskey, 499 U.S. at 492, 111 S.Ct. at 1469). We concluded that, “for claims of sentence error, at least where the statutory maximum was not exceeded, the point where finality holds its own against error correction is reached not later than the end of the first round of collateral review.” Id. at 1312 (emphasis added). H. Savings Clause May Permit Actual-Innocence Claims In Gilbert II, the en banc Court acknowledged that other circuits permit federal prisoners to use the savings clause to bring “actual innocence” claims in § 2241 petitions, such as claims originating under Bailey. Id. at 1318-19. We explained that the Wofford panel had Bailey-type, actual-innocence-of-the-crime claims in mind when it stated that the savings clause would permit a prisoner to bring a § 2241 petition based on a “retroactively applicable, circuit law-busting” Supreme Court decision establishing that he was “convicted of a nonexistent crime.” Id. at 1319. We cautioned, however, that this statement in Wofford was dicta because (1) all of Wofford’s claims “were sentencing claims, ‘none of which rested upon a circuit law-busting, retroactively applicable Supreme Court decision’ and “[a]ll of them could have been presented at trial or on appeal.” Id. (quoting Wofford, 177 F.3d at 1245) (alteration omitted). We stated: “The actual holding of the Wofford decision, which is undoubtedly correct, is simply that the savings clause does not cover sentence claims that could have been raised in earlier proceedings.” Id. (citing Wofford, 177 F.3d at 1244-45). I. Savings Clause May Permit Pure § 92i(e)-Begay Error Claims In Gilbert II, the en banc Court also appended a footnote explaining what the Wofford Court may have meant when it suggested that “the savings clause ‘may conceivably’ apply to some sentencing claims in some circumstances where there was a fundamental defect in sentencing that the prisoner had no opportunity to have corrected before the end of his § 2255 proceeding.” Id. at 1319 n.20 (citing Wofford, 177 F.3d at 1244-45). We explained in dicta that “the Wofford panel may have had in mind ... pure Begay errors, by which we mean errors in the application of the ‘violent felony’ enhancement, as defined in 18 U.S.C. § 924(e)(2)(B), resulting in a higher statutory minimum and maximum sentence under § 924,(e).” Id. (emphasis added). We noted that a “Begay .error in the classification of a prior conviction that was used to impose an enhanced sentence under § 924(e)'would necessarily have resulted in the defendant being sentenced to a term of imprisonment that exceeded • what would have been the statutory maximum without the error.” Id. Thus, a pure Begay error “would fit within the government’s concession that the savings clause applies to errors that resulted in a sentence beyond the statutory maximum that would have applied but for the error.” Id. (emphasis added). We reiterated that pure Begay error was not Gilbert’s claimed error. Id. Gilbert’s claimed error was “that his sentence calculation involved an Archer error in the application of § 4B1.1 of the guidelines, and that error did not result in a sentence beyond the statutory maximum.” , Id. What the en banc Court decided in Gilbert II was that “the savings clause does not apply to sentencing errors that do not push the term of imprisonment beyond the statutory maximum.” Id. J. Gilbert Was Not Actually Innocent of Being a Career Offender We also rejected Gilbert’s argument that he was actually innocent of being a career offender under § 4B1.1 of the guidelines, explaining that Gilbert “was not charged with, nor was he convicted of, being a career offender.” Id. at 1320. “If guidelines enhancements were crimes, they would have to be charged in the indictment and proven to the jury beyond a reasonable doubt.” Id. And, the actual-innocence exception articulated in Sawyer v. Whitley, 505 U.S. 333, 112 S.Ct. 2514, 120 L.Ed.2d 269 (1992), did not apply to Gilbert because (1) his case was not a death penalty case; (2) his claim was not a constitutional claim; (3) he would fail to meet the requirement that, but for the error, he would have been statutorily ineligible for the sentence he received; and (4) the narrow pre-AEDPA actual-innocence-of-sentence exception did not- survive after AED-PA was enacted. Id. at 1320-22. We pointed out in Gilbert II that, because of “the drug crimes for which he was convicted, Gilbert was statutorily eligible for a sentence of between 10 years and life.” Id. at 1322 (emphasis added). And “[e]ven if the error in application of the § 4B1.1 career offender enhancement were undone, Gilbert" would still be statutorily eligible for a sentence of 10 years to life.” Id. (emphasis added). In Gilbert II, because Gilbert’s sentence did not exceed his statutory maximum penalty of life imprisonment, we emphasized we were not deciding whether the savings clause would permit a prisoner to bring a § 2241 petition claiming his sentence exceeds the statutory maximum penalty: We do not decide whether a claim that the sentencing guidelines were misapplied may be brought in a first time § 2255 motion. Nor do we decide if the savings clause in § 2255(e) would permit a prisoner to bring a § 22J/.1 petition claiming that he was sentenced to a term of imprisonment exceeding the statutory maximum. What we do decide is that the savings clause does not authorize a federal prisoner to bring in a § 2241 petition a claim, which would otherwise be barred by § 2255(h), that the sentencing guidelines were misapplied in a way that resulted in a longer sentence not exceeding the statutory maximum. Id. at 1323 (emphasis added). VII. WILLIAMS v. WARDEN (2013) Our third savings clause decision, Williams, did involve a prisoner’s claim that his sentence exceeded the authorized statutory maximum penalty. Williams, 713 F.3d at 1334. In Williams, we faced the issue left open in Wofford and Gilbert II — whether the savings clause reaches claims that a sentence exceeds the statutory maximum. See id. In 1998, the petitioner, Albert Williams, was tried and convicted on one count of being a felon in possession of a firearm, in violation of § 922(g). See id. at 1335. Williams was subject to the increased statutory penalty of life in prison under § 924(e) due to his three prior Florida convictions: two for burglary of a dwelling and one for robbery. Id. Williams was sentenced to 293 months’ imprisonment. Id. At trial and on direct appeal, Williams did not object to the application of increased statutory penalties under § 924(e)(1) based on the theory that his prior convictions did not qualify as “violent felonies” under § 924(e)(2)(B). Id. In 1999, this Court affirmed Williams’s conviction and sentence. United States v. Williams, 182 F.3d 936 (11th Cir.1999) (unpublished table op.). In his first § 2255 motion, Williams argued that his counsel rendered ineffective assistance by failing to object to the use of his burglary convictions as predicate offenses to support his increased statutory penalties under § 924(e). Williams, 713 F.3d at 1335. He also argued that the Florida crime of burglary of a dwelling was not a “violent felony” under § 924(e)(2)(B). Id. The district court denied Williams’s § 2255 motion and his request for a COA. Id. In 2004, this Court denied a COA and his motion for reconsideration, noting that, even if Williams’s burglary conviction did not qualify as a violent felony, his other prior convictions supported the increased statutory penalties under § 924(e). Id. After several other unsuccessful collateral attacks, and after Begay was decided, Williams filed another § 2255 motion. Id. at 1336. In that motion, Williams argued that, under Begay, his burglary offenses did not qualify as violent felonies for § 924(e) purposes and, therefore, his 293-month sentence exceeded the 10-year statutory maximum for his § 922(g)(1) felon-in-possession conviction. Id. Denying relief, the district court concluded that it lacked jurisdiction over Williams’s successive § 2255 motion because he had not moved this Court for authorization to file a successive § 2255 motion. Id. Williams did not appeal. Id. In 2010, Williams filed a § 2241 habeas petition, arguing that the savings clause in § 2255(e) allowed the district court to hear his § 2241 petition and rule upon the Be-gay claim he raised in his previous § 2255 motion, i.e., that his prior burglary convictions did not qualify as predicate felonies under § 924(e) and that, as a result, his sentence was above the statutory maximum applicable to his § 922(g)(1) offense. Id. The district court dismissed Williams’s § 2241 petition. Id. The government conceded in the district court and on appeal that the savings clause applied to the type of sentencing claim Williams sought to bring in his § 2241 petition — a claim of pur e-Begay error in a § 924(e) sentence that exceeds the statutory maximum penalty for a § 922(g) crime. Id. A. Savings Clause is Jurisdictional On appeal, this Court in Williams first addressed the question of whether we could accept the government’s concession that the savings clause applied to Williams’s claim. Id. at 1337-38. After a thorough discussion, we concluded that “in enacting § 2255(e), Congress clearly restricted the subject-matter jurisdiction of the federal courts” over § 2241 petitions. Id. at 1340. Because the savings clause in § 2255(e) was jurisdictional, the government could not waive the issue of its applicability. See id. at 1337-40. ■ B. The Williams Court Explained Why Gilbert II Did Not Apply In determining whether the savings clause applied to Williams’s § 924(e) claim, we first noted that Gilbert II “addressed— and explicitly limited its holding to — circumstances where a federal prisoner sought to attack a potential misapplication of the Sentencing Guidelines that resulted in a higher sentence, but one that remained within the statutory maximum.” Id. at 1341. Gilbert II “expressly reserved the issue of whether the savings clause applied to [Williams’s] species of claim,” that is, claims that an erroneous application of § 924(e) increased a sentence above the statutory maximum penalty. Id. We then concluded that Wofford, not Gilbert II, was “fatal to Williams’s attempt to pass through the savings clause.” Id. C. Wofford and the Tension Between § 2255(e) and § 2255(h) In Williams, this Court stated that the Wofford Court approved of the Seventh Circuit’s Davenport because that approach “addressed and harmonized two serious concerns that are in some tension with one another.” Id. On the one hand, “the essential function of habeas corpus is to give a prisoner a reasonable opportunity to obtain a reliable judicial determination of the fundamental legality of his conviction and sentence, and it may be necessary to apply the savings clause to some claims inadequately addressed in a first § 2255 motion in order to satisfy the Constitution’s Suspension Clause.” Id. (internal quotation marks and alteration omitted). On the other hand, “letting the savings clause apply too broadly would eviscerate [AED-PA’s] bar on second or successive motions, which was intended to limit most prisoners to one clean shot at postconviction relief.” Id. - . We' reasoned in Williams that “the savings clause cannot simply mean that every § 2255 motion that appears to have been incorrectly decided based on subsequent Supreme Court precedent may be revisited through a § 2241 habeas petition; if it did, then the bar on second or successive motions would effectively be written out of the statute.... ” Id. “Yet by the same token, the circumstances delineated in [AEDPA’s] § 2255(h)(1) and (2) cannot be the only instances 'in which the § 2255 remedy is inadequate; if that were true, then it would be the savings clause that was rendered meaningless.” Id. at 1342-43 (emphasis added). We stated that a statute should not be interpreted “in such a way that anj part of it becomes mere surpltisage.” Id. at 1343. The Williams Court observed that Wof-ford, in dicta, described two different kinds of challenges to which the savings clause may conceivably apply that are not covered by § 2255(h) in AEDPA. Id. As discussed above, these two circumstances are: (1) when a retroactively-applicable Supreme Court’s decision establishes that the petitioner was convicted of a “nonexistent offense,” and circuit law squarely foreclosed the petitioner from raising that claim at “trial, [direct] appeal, or first § 2255 motion”; and (2) when a “fundamental defect in sentencing” occurred, and, again, the petitioner had no “opportunity to obtain judicial correction of that defect earlier.” Id. (emphasis added) (quoting Wofford, 177 F.3d at 1244) (internal quotation marks omitted). Referring to these two circumstances, the Williams Court stated: “This interpretation of the savings clause harmonizes [the savings clause] with the bar on second or successive motions [in AEDPA] while also avoiding constitutional questions under the Suspension Clause.” Id. This Court in Williams concluded that the Wofford decision “establishes two necessary conditions — although it does not go so far as holding them to be sufficient — for a sentencing claim to pass muster under the savings clause.” Id. “First, the claim must be based upon a retroactively applicable Supreme Court decision.” Id. Second, “the Supreme Court decision must have overturned a circuit precedent that squarely resolved the claim so that the petitioner had no genuine opportunity to raise it at trial, on appeal, or in his first § 2255 motion.” Id. (emphasis added). This Court in Williams explained why, under the second condition, the savings clause requires a prisoner’s § 2241 claim to have been squarely foreclosed by prior Circuit precedent at the time of his trial, direct appeal, and first § 2255 motion. Id. at 1347. We stated that, if an issue had not been decided against a prisoner’s position by prior precedent, then his first § 2255 motion “would have been an adequate procedure for testing his claim.” Id. “The courts would have heard the claim and decided its merits, unlike in the case where adverse precedent already existed and thus stare decisis would make us unwilling to listen to him.” Id. (internal quotation marks and ellipses omitted). In Williams, we cautioned, however, that an incorrect decision :ón a non-foreclosed claim does not render a proceeding inadequate or ineffective. Id. at 1348. We explained that, “simply because a procedurally adequate test may get the answer wrong ... cannot mean that a petitioner is entitled to utilize the savings clause to have his claim reevaluated still again in light of novel Supreme Court precedent.” Id. We reiterated that what makes the § 2255 proceeding inadequate is when “erroneous circuit precedent foreclosed [the petitioner’s] argument” at trial, direct appeal, or in his first § 2255 proceeding. Id. Similar to the Williams analysis, we observe that simply because a defendant faces a procedural bar in his first § 2255 motion — such as a limitations period or procedural default — this also does not render the first § 2255 motion inadequate or ineffective. Otherwise, a defendant could sit on his § 924(e) claim at trial and direct appeal, have it procedurally barred in a first § 2255 motion, but much later raise it in a § 2241 petition through the § 2255(e) portal. What makes the § 2255 proceeding “inadequate or ineffective” for petitioner Bryant is that he had no “genuine opportunity” to bring his § 924(e) claim because Circuit precedent squarely foreclosed that claim throughout his trial, direct appeal, and first § 2255 motion. See Williams, 713 F.3d at 1343, 1348. D. Circuit Precedent Did Not Foreclose Williams’s Burglary Claim In Williams, we concluded that Williams could not “show that this Circuit’s law foreclosed him from raising an objection to the treatment of his two Florida burglary convictions [under Fla. Stat. 810.02] as violent felonies under the ACCA.” Id. at 1343^44. During Williams’s “direct and collateral attacks” from 1998 to 2004, no Eleventh Circuit precedent “squarely held that burglary of a dwelling, as defined in Fla. Stat. § 810.02, was a violent felony for ACCA purposes.” Id. at 1344. “[I]t was an open question in this Circuit whether § 810.02 might categorically constitute a violent felony ... under the so-called residual clause ... [in] § 924(e)(2)(B)(ii).” Id. at 1345. “Only after both Williams’s direct appeal and his collateral attack did this Court decide” that burglary of a dwelling under Florida law qualified as a violent felony under the last clause in § 924(e)(2)(B)(ii). Id. The Williams Court concluded that “no Circuit precedent on the books during Williams’s collateral attack foreclosed his argument and rendered his § 2255 motion an ineffective test of his clainis.” Id. (emphasis added). Stated differently, “there was no adverse precedent at the time of Williams’s § '2255 motion that would have made us unwilling to listen to his claim.” Id. at 1347. Even if Williams’s initial § 2255 proceeding had resulted in the wrong answer, this was “not dispositive of the question of whether Williams now may pursue relief through the savings clause.” Id. at 1348. “[W]hat is dispositive is that his claim was not foreclosed at the time by binding Eleventh Circuit precedent that Begay overruled or abrogated.” Id. In Williams, we rejected the petitioner’s attempt to use Begay as the “ ‘circuit law-busting, retroactively applicable Supreme Court decision’ ” demanded by Wofford. Id. at 1346. We explained that, for Begay to be “circuit-law busting” in the savings clause context, “we must find that Begay overturned circuit precedent, specifically addressing the claim Williams now asserts [in his § 2241 petition] — namely, that Fla. Stat. § 810.02 [the burglary statute] is not a violent felony for ACCA purposes.” Id. at 1347 (emphasis added) (internal quotation marks omitted). Begay was not “circuit law-busting” in Williams’s case because (1) Begay “changed the analytical framework for determining whether a given state offense is a violent felony at a high level of abstraction” and “did not abrogate all of this Court’s pre-Begay violent-felony jurisprudence,” (2) Begay would not have necessarily abrogated any Circuit precedent holding that Florida’s burglary ■ statute was a violent felony; and, (3) in any event, “there was no circuit precedent for Begay to bust” at the time Williams’s first § 2255 proceeding ended in 2004. Id. at 1345, 1347 (emphasis added). For all of these reasons, we determined that ‘Williams’s first § 2255 motion was not ‘inadequate or ineffective to test the legality’ ” of his increased statutory penalties under § 924(e). Id. at 1348 (quoting § 2255(e)). E. Williams Did Not Show Miscarriage of Justice We also rejected Williams’s argument that he could open the savings clause portal using an alternative, miscarriage-of-justice standard set forth in Davis v. United States, 417 U.S. 333, 346-47, 94 S.Ct. 2298, 2305, 41 L.Ed.2d 109 (1974) (holding that, where a precedent later establishes that the prisoner was convicted and punished “for an act that the law does not make criminal,” he may seek collateral relief in his first § 2255 motion despite losing the issue on direct appeal). Williams, 713 F.3d at 1345. First, we reasoned that Williams was not convicted of a “nonexistent offense,” in Wofford’s sense of the term, because he was “not asserting that he is ‘actually innocent’ of either his possession of a.firearm offense or his underlying burglary offenses, nor could he.” Id. at 1345-46. “[H]e is asserting only legal innocence: that his burglary convictions should not have been considered violent felonies under the ACCA.” Id. at 1346. Second, in Williams we said that Davis involved “a different issue: whether a claim ‘unsuccessfully litigated on direct review could be ‘asserted on collateral attack.’ ” Id. (quoting Davis, 417 U.S. at 342, 94 S.Ct. at 2303 (ellipses omitted and alteration adopted)). In Davis, the Supreme Court held that, “where a precedent later establishes that the prisoner was convicted and punished ‘for an act that the law does not make criminal,’ he may seek collateral relief in his first § 2255 motion despite losing the issue on direct appeal.” Id. (quoting Davis, 417 U.S. at 346-47, 94 S.Ct. at 2305). But, “Davis did not address whether the savings clause permits what is effectively a second or successive motion under the miscarriage of justice standard.” Id. The Williams Court concluded that the miscarriage-of-justice standard in Davis was inapplicable to Williams’s sentencing claim concerning the savings clause. Id. VIII. SYNTHESIS OF WOFFORD, GILBERT II, & WILLIAMS Wofford, Gilbert II, and Williams guide us on what the statutory terms in § 2255(e)’s savings clause mean and how to read § 2255(e) in a way that does not eviscerate or undermine § 2255(h)’s restrictions on second or successive § 2255 motions but also affords some meaning to the savings clause. To show his prior § 2255 motion was “inadequate or ineffective to test the legality of his detention,” Bryant must establish that (1) throughout his sentencing, direct appeal, and first § 2255 proceeding, our Circuit’s binding precedent had specifically addressed Bryant’s distinct prior state conviction that triggered § 924(e) and had squarely foreclosed Bryant’s § 924(e) claim that he was erroneously sentenced above the 10-year statutory maximum penalty in § 924(a); (2) subsequent to his first § 2255 proceeding, the Supreme Court’s decision in Begay, as extended by this Court to Bryant’s distinct prior conviction, overturned our Circuit precedent that had squarely foreclosed Bryant’s § 924(e) claim; (3) the new rule announced in Be-gay applies retroactively on collateral review; (4) as a result of Begay’s new rule being retroactive, Bryant’s current sentence exceeds the 10-year statutory maximum authorized by Congress in § 924(a); and (5) the savings clause in § 2255(e) reaches his pure § 924(e)-Begay error claim of illegal detention above the statutory maximum penalty in § 924(a). We now explain why Bryant has satisfied each of these requirements. IX. BRYANT’S § 924(e) CLAIM A. Foreclosure by Circuit Precedent As to the first requirement, Bryant has carried his