MEMORANDUM OPINION AND ORDER
Elaine E. Bucklo, United States District JudgeCarl Stevenson (“Stevenson”) has filed a pro se motion to vacate, correct, or set aside his sentence pursuant to 28 U.S.C. § 2255(f)(4). Because Stevenson has previously filed a § 2255 motion seeking to challenge his sentence, and because he has not obtained authorization from the Seventh Circuit to file a second or successive motion, I dismiss the instant motion for lack of jurisdiction.
Background
On May 11, 1998, a jury found Stevenson guilty of conspiracy to possess cocaine base with intent to distribute in violation of 21 U.S.C. § 846; use of persons under age 18 in drug operations in violation of § 861(a)(2); and distribution of a controlled substance in violation of § 841(a)(1). Based on the Sentencing Guidelines in effect at that time and the amount of crack cocaine for which he was accountable, Stevenson’s base offense level was 32. See U.S.S.G. § 2Dl.l(c)(4). That offense level was subject to a two-level increase due to his possession of a dangerous weapon during commission of the offense, see U.S.S.G. § 2Dl.l(b)(l), and an additional one-level increase due to his use of minors in committing the offense, see U.S.S.G. § 2D1.2(3). This resulted in an offense level of 35, which corresponded to a guideline range of 292-365 months’ imprisonment. On March 16, 2001, I sentenced Stevenson to 292 months’ imprisonment.
During his sentencing, however, I also found that Stevenson was a career offender under U.S.S.G. § 4B1.2.1 The offense *955level for career offenders is 84, but it applies only where it is greater than the offense level otherwise applicable. See U.S.S.G. § 4Bl.l(b). Since the level for Stevenson’s offense of conviction (plus the enhancements) was the higher of the two, I did not rely on the career offender level in sentencing him. In short, while I found that Stevenson was a career offender, I did not sentence him based on that finding.
On March 11, 2006, after Stevenson and several of his codefendants unsuccessfully challenged their convictions on direct appeal, see United States v. Hernandez, et al., 330 F.3d 964, 991 (7th Cir. 2003), he filed his initial § 2255 motion, see United States of America v. Stevenson, No. 05-cv-01448(N.D. Ill. filed Mar. 11, 2006).2 I denied the motion, see Stevenson v. United States, No. 05 C 1448, 2006 WL 3524001, at *1 (N.D. Ill. Dec. 5, 2006), order vacated (June 29, 2007); Stevenson v. United States, No. 05 C 1448, 2007 WL 1888810 (N.D. Ill. June 29, 2007). Stevenson appealed, but the Seventh Circuit dismissed the appeal as untimely. See United States of America v. Stevenson, No. 08-2569 (7th Cir. Sept. 30, 2008).
On June 9, 2010, Stevenson filed a motion pursuant to 18 U.S.C. § 3582 to reduce his sentence based on Amendment 706 to U.S.S.G. § 2D1.1. Enacted in order to reduce disparities in sentencing between crack cocaine and powder cocaine offenses, the Amendment modified the Drug Quantity Table downward two levels for most offenses involving crack cocaine. See U.S.S.G. Supp. to Fed.Appx. C, Amend. 706 (Nov. 1, 2009).3 1 granted Stevenson’s motion. United States v. Stevenson, 97 CR 510 (N.D. Ill. Mar. 29, 2011). Based on Amendment 706, his new offense level became 30; and after applying the enhancements imposed during his initial sentencing (i.e., for his possession of a dangerous weapon and use of minors in commission of the offense), Stevenson’s total offense level became 33. In light of the reduction, however, the career offender level (34) was now greater than the level for his offense of conviction. Noting that Stevenson was a career offender, I therefore concluded that the appropriate offense level was 34. Id. Using the latter offense level resulted in a reduction of the applicable guideline range from 292-365 months to 262-327 months. I reduced Stevenson’s sentence to 262 months. Id.
On June 27, 2012, Stevenson filed a second § 3582 motion seeking further reduction of-his sentence. The second motion was based on Amendment 750 to the Sentencing Guidelines, which, like Amendment 706, lowered the offense lével for certain crack-cocaine offenses. I denied the motion because a sentence reduction is permitted under § 3582(c)(2) only where an amendment to the guidelines lowers the, defendant’s guidelines range. See, e.g., United States v. Broadwater, 471 Fed.Appx. 534, 535 (7th Cir. 2012). In this case, the Amendment did not reduce Stevenson’s sentencing guidelines range. See United States v. Stevenson, 97 CR 510 (N.D. Ill. Sept. 4, 2012) (Doc. # 1148). Stevenson appealed the decision and the Seventh Circuit affirmed. See United States v. Stevenson, 749 F.3d 667, 670 (7th Cir. 2014). On January 12, 2015, the Supreme Court denied Stevenson’s petition for certiorari. See Stevenson v. United States, — U.S. —, *956135 S.Ct. 1011, 190 L.Ed.2d 882 (2015). The instant § 2255 motion followed.
Discussion
“Section 2255 gives a federal prisoner one opportunity to challenge a conviction and sentence following a direct appeal.” Suggs v. United States, 705 F.3d 279, 281-82 (7th Cir. 2013) (citing 28 U.S.C. § 2255(a), (h)). Thus, “[i]f a prisoner seeks to challenge his conviction or sentence a second time, he must persuade a court of appeals to certify the motion and authorize the district court to hear it.” Suggs, 705 F.3d at 282 (citing 28 U.S.C. §§ 2244(a)-(b), 2255(h)). “Without authorization from the court of appeals, the district court has no jurisdiction to hear the petition.” Id. Nevertheless, “[n]ot all literally subsequent motions ... are ’second or successive’ within the meaning of the statutes.”Id. Rather, the phrase “second or successive” is a “term of art in the technical world of habeas procedure.” Id.
As recounted above, Stevenson previously filed a § 2255 motion in 2005. Thus, if the current motion counts as “second or successive” in the relevant sense, I am without jurisdiction to entertain it. Stevenson advances a number of arguments attempting to show that his present motion is not “second or successive.” Stevenson first argues that I violated Dillon v. United States, 560 U.S. 817, 130 S.Ct. 2683, 177 L.Ed.2d 271 (2010) during his first § 3582 sentence-reduction hearing on March 29, 2011. He asserts that because of this error, he is entitled under the Supreme Court’s decision in Johnson v. United States, 544 U.S. 295, 125 S.Ct. 1571, 161 L.Ed.2d 542 (2005), to bring the present motion. See Pet’r’s Reply Br. at 5 (“When the District Court violated Dillon v. United States, 130 S.Ct. 2683, 2691 (2010), the violation resulted in [a] new fact that was not available during the original 28 U.S.C. § 2255 motion. Therefore], this motion is not second or successive. This Honorable Court has jurisdiction pursuant to 28 U.S.C. § 2255(f)(4).”) (citing Johnson v. United States, 544 U.S. 295, 125 S.Ct. 1571, 161 L.Ed.2d 542 (2005)).
In order to understand this argument, it is necessary to examine the Dillon and Johnson decisions. The defendant in Dillon was convicted and sentenced for drug offenses prior to the Supreme Court’s decision in U.S. v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). See Dillon, 560 U.S. at 822, 130 S.Ct. 2683. After the Booker decision and Amendment 706 to the Sentencing Guidelines, Dillon moved for a reduction of his sentence under § 3582. Id. at 823, 130 S.Ct. 2683. The district court granted the motion and reduced his sentence. Id. However, in addition to the reduction based on Amendment 706, Dillon sought an additional reduction based on his post-sentencing conduct (his educational pursuits, volunteering activities, etc.). Id. The district court declined to further reduce the sentence, citing U.S.S.G. § 1B1.10, which directs courts in proceedings under § 3582(c)(2) to substitute the amended guideline range and to “leave all other guideline application decisions unaffected.” U.S.S.G. § lB1.10(b)(l). Dillon argued that in light of Booker, U.S.S.G. § lB1.10(b) was advisory and did not apply to § 3582(c)(2) proceedings. Dillon, 560 U.S. at 823, 130 S.Ct. 2683. The Supreme Court rejected Dillon’s contention, holding that “Congress intended to authorize only a limited adjustment to an otherwise final sentence and not a plenary resentencing proceeding.” Id. at 826, 130 S.Ct. 2683.
In Johnson, the defendant pleaded guilty to a federal drug charge in 1994 and for purposes of his sentencing was deemed a career offender based on his prior conviction for state-law offenses. Johnson, 544 U.S. at 298, 125 S.Ct. 1571. Johnson later filed a habeas petition under state law and *957succeeded in having one of his convictions vacated. Id. at 298-99, 125 S.Ct. 1571. He then filed a motion under § 2255 arguing that his federal sentence should be vacated because it was based in part on the finding that he was a career offender, which in turn had been based on his now-vacated state-law conviction. Id. at 301, 125 S.Ct. 1571. The lower courts had concluded that the petition was barred by § 2255⅛ one-year statute of limitations. Id. The Supreme Court disagreed, holding that the limitations period began to run when Johnson received notice of the order vacating his prior conviction.4 Id. at 302, 125 S.Ct. 1571. In other words, as the Seventh Circuit has put it, Johnson held that vacatur of an underlying conviction is a new ’fact’ that opens a one-year window to seek collateral relief.' Unthank v. Jett, 549 F.3d 534, 535 (7th Cir. 2008).
Stevenson’s argument, as I understand it, is that I ran afoul of Dillon by finding him to be a career offender for purposes of his first § 3582 motion. This is because under U.S.S.G. § 1B1.10,1 am required in proceedings under § 3582(c)(2) to substitute the amended guideline range and to “leave all other guideline application decisions unaffected.” U.S.S.G. § lB1.10(b)(l). I further understand him to be arguing that this purported error represents a previously undiscoverable fact that, like the vacatur of Johnson’s state-law conviction, opens up a one-year window within which he may file a new § 2255 motion.
This argument is problematic in several respects, but its central difficulty is that it is premised on the claim that the career-offender determination was made not in the course of his initial sentencing proceedings, but when I decided his first § 3582 motion. As previously noted, I did find that Stevenson was a career offender for purposes of his initial sentencing. The fact that I did not sentence Stevenson based on that finding does not alter the fact that the finding was made. Indeed, the Seventh Circuit previously addressed and rejected this very argument when Stevenson asserted it during his appeal from my ruling denying his second § 3582 motion. The court explained:
At Stevenson’s original sentencing, the district court sentenced him using the crack cocaine offense guideline, which produced a higher offense level than the applicable career offender guideline. But that decision did not erase the court’s determination that Stevenson was a career offender, as the ruling on Stevenson’s first § 3582(c) motion demonstrates.
United States v. Stevenson, 749 F.3d 667, 670 (7th Cir. 2014). Thus, Stevenson’s argument based on Dillon and Johnson fails.
Stevenson asserts a second argument, this time based on the Supreme Court’s decision in Magwood v. Patterson, 561 U.S. 320, 130 S.Ct. 2788, 177 L.Ed.2d 592 (2010). However, this argument, too, is based on the same mistaken premise. The petitioner in Magwood was sentenced to death for murdering a sheriff and, after unsuccessfully seeking state post-conviction relief, filed a federal habeas petition pursuant to 28 U.S.C. § 2254. Id. at 323, *958130 S.Ct. 2788. The district co.urt found that the state court had failed to address certain mitigating circumstances at Mag-wood’s sentencing, and held that Magwood must either be resentenced or released. Id. In 1986, the state court held further sentencing proceedings and again sentenced Magwood to death. Magwood then filed a habeas petition to challenge the new death sentence on the ground that he did not have fair warning at the time of his offense that his conduct could have resulted in the imposition of the death penalty. Id. at 328, 130 S.Ct. 2788. The Eleventh Circuit held that Magwood’s petition was barred as “second or successive” because he could have raised the same challenges in his original habeas petition. Id. The Supreme Court reversed, holding that Magwood’s habeas application challenged a new judgment for the first time, and hence was not “second or successive” within the 'meaning of § 2244(b). Id.
Stevenson appears to argue that, by finding that he was a career offender for purposes of his first § 3582 motion, I effectively imposed a new sentence upon him. He thus appears to claim that, like Magwood, he is challenging a new judgment for the first time, and that his current motion is therefore not second or successive. Again, this argument is based on the misapprehension that I made the career-offender determination for the first time in ruling on his first § 3582 motion.
However, Stevenson argues that I could not have made the career-offender determination during his initial sentencing, because if I had done so, I would have had no authority to grant his first § 3582 motion on the basis of Amendment 706. See Reply Br. at 5. This is because, he claims, Amendment 706 is inapplicable to career offenders.
Stevenson is once again mistaken, though the error is perhaps an understandable one. Language in some Seventh Circuit cases might indeed appear to support the categorical proposition that Amendment 706 does not apply to career offenders. Stevenson cites United States v. Forman, 553 F.3d 585 (7th Cir. 2009), in which the court stated that “Amendment 706 provides no benefit to career offenders,” id. at 589, and United States v. Taylor, 627 F.3d 674 (7th Cir. 2010), in which the court stated that “as a general rule ... Amendments 706 and 713 did not affect offenders who were sentenced as career offenders under U.S.S.G. § 4B1.1,” id. at 676.
However, the Seventh Circuit has acknowledged the potential for confusion based on language of this sort, and the court has taken pains to clarify the matter. As Judge Posner explained in United States v. Williams, 694 F.3d 917 (7th Cir. 2012):
We write ... to refine the statement in our opinion in United States v. Forman, that “Amendment 706 provides no benefit to career offenders.” Passages in other cases state correctly that Amendment 706 does not affect a sentence calculated under the career-offender guideline, but could be misunderstood to agree with the statement in Forman that a career offender cannot benefit from the amendment. That statement is imprecise ... because not all (though certainly most) career offenders are sentenced on the basis of the offense levels in the career-offender guideline, and the defendant in this case was one who was not. But he was a career offender, and this shows that the dictum in Forman (and other cases) that “Amendment 706 provides no benefit to career offenders,” while generally correct, is not invariably so.
Id. at 918-19 (citations omitted).
In the usual case, where a defendant is sentenced under the career-offender guideline, a reduction in the offense level *959for his underlying conviction will not affect his guideline range. This is because the career offender level is, ex hypothesi, greater than the level for the underlying offense. Since a change in the offense level will therefore result in no change to the guideline range, and since § 3582 permits a sentence reduction only where there is such a change, see, e.g., Broadwater, 471 Fed.Appx. at 535, Amendment 706 will not benefit a defendant sentenced under the career-offender guideline. However, the Amendment might reduce the guideline range of a career offender in cases where the defendant, though found to be a career offender, is not sentenced on the basis of the career-offender guideline. That is precisely what happened in Stevenson’s case. Amendment 706 was “applicable” under these circumstances because a reduction in his offense level resulted in a reduction of his guideline range.
All of this is just to say that my reduction of Stevenson’s sentence in response to his first § 3582 motion lends no support to his contention that the career-offender determination was not made during his initial sentencing proceedings. Since all of Stevenson’s attempts to circumvent the prohibition on second or successive § 2255 motions are premised on the mistaken notion that I made the career-offender determination in the context of his first § 3582 motion, it follows that he was required to obtain authorization from the Seventh Circuit before filing the present motion. Because Stevenson failed to take this step, I have no jurisdiction to consider his motion.
Transfer/Dismissal of Stevenson’s Petition
In its response brief, the government states that Stevenson’s motion “should be dismissed for lack of jurisdiction and then transferred to the Seventh Circuit for consideration of whether it will authorize the motion as a successive collateral attack.” Gov’t Resp. Br. at 14.5 Typically, where a court lacks jurisdiction to entertain a § 2255 motion, dismissal is the appropriate procedure. It is true that in many circuits, district courts may transfer an improperly-filed second or successive § 2255 motion to the court of appeals. See Brian R. Means, Federal Habeas Manual § 11:81 (2015) (citing cases). In this Circuit, however, it is not clear that such a procedure has been approved. See, e.g., U.S. ex rel. Rickard v. Roth, 108 F.Supp.2d 1017, 1022 (N.D. Ill. 2000) (“[T]he Seventh Circuit’s directive is clear; because § 2243(b)(3)(A) vests subject matter jurisdiction in the court of appeals, the district court must dismiss any second or successive petition.”). In any event, I have been unable to find any cases in this Circuit authorizing a procedure whereby a court may both dismiss a § 2255 motion and subsequently transfer it to the court of appeals. Under these circumstances, I shall therefore dismiss Stevenson’s motion without transferring it. If Stevenson wishes to seek authorization from the Seventh Circuit to file a second or successive § 2255 motion, he is free to do so.
Certificate of Appealability
Lastly, Rule 11 of the Rules Governing § 2255 Proceedings states that a “district court must issue or deny a certificate of appealability when it enters a final order adverse to the applicant.” See Rules Governing Section 2255 Proceedings for the United States District Courts, Rule 11(a). A “district court’s dismissal of a motion on the ground that it is an unauthorized successive collateral attack constitutes a final *960order -within the scope of 28 U.S.C. § 2253(c).” Sveum v. Smith, 403 F.3d 447, 448 (7th Cir. 2005). When the district court denies a § 2255 motion on procedural grounds without reaching the prisoner’s underlying constitutional claim, “a COA should issue when the prisoner shows, at least, that jurists of reason would find it debatable whether the petition states a valid claim of the denial of a constitutional right and that jurists of reason would find it debatable whether the district court was correct in its procedural ruling.” Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000). In light of the analysis above, I conclude that these criteria are not met here. I therefore decline to issue a COA.
Conclusion
For the reasons discussed above, Stevenson’s motion to vacate, correct, or set aside his sentence is dismissed, and I decline to issue a certificate of appealability.
. As the Seventh Circuit noted, I made the career-offender determination by formally adopting the presentence report in Stevenson's case. See United States v. Stevenson, 749 F.3d 667, 670 & n.2 (7th Cir. 2014). Stevenson himself acknowledges that he was found *955to qualify as a career offender in the presen-tence report. See Reply Br. at 2 ("Stevenson is aware that he was label [sic] as a career offender in the presentencing report[.]”).
. Stevenson’s initial § 2255 motion asserted claims for ineffective assistance of counsel.
. Amendment 706 was made retroactive by Amendment 713 to the Guidelines. See U.S.S.G. § 2D1.1(c); U.S.S.G. Supp. App. C, Amdts. 706 and 713 (2008); see also United States v. Guyton, 636 F.3d 316, 318 (7th Cir. 2011).
. Despite this holding, the Court ultimately found that Johnson’s petition was untimely due to his failure to act diligently. Specifically, the Court held that although Johnson knew that he was subject to the career-offender enhancement based on his prior conviction, he did not attack the conviction until three years after entry of judgment in his federal case. Johnson, 544 U.S. at 311, 125 S.Ct. 1571. Thus, putting aside other problems with Stevenson's reliance on Johnson, there is a separate question as to whether he acted with reasonable diligence. Stevenson contends that he has acted diligently by means of his § 3582 motions and appeals. Since I conclude that Stevenson’s argument fails on other grounds, I do not address the question of his diligence here.
. Elsewhere in its brief, the government asks that the matter be transferred without making any mention of dismissal. See Gov’t's Resp. Br. at 1 ("Therefore, the district court lacks jurisdiction to consider Stevenson’s motion, and it should be transferred to the Seventh Circuit so that it may consider authorization of the motion.”).