Thomas Spellissy was convicted of conspiring to defraud the United States, in violation of 18 U.S.C. § 371, by a jury in the District Court for the Middle District of Florida. He then filed multiple post-trial motions, including the one that is the subject of the present appeal. The district court dismissed that motion in part as an improper successive challenge to the legality of his conviction under 28 U.S.C. § 2255 and denied it in part as an unpersuasive motion for a new trial under Fed. R.Crim.P. 33. Spellissy appeals both the dismissal and denial, arguing that his motion was not a successive habeas petition and that he did present newly discovered evidence that would lead to a different outcome in his trial. In addition, he requests that, if remanded, the case be reassigned to a new trial judge.
We remand this case to the district court because it has yet to rule on whether to grant Spellissy a Certificate of Appealability (“COA”) to challenge the partial dismissal of his motion on the ground that it was a successive § 2255 petition. In addition, we deny Spellissys request for a new judge and affirm the denial of his Rule 33 motion.
I.
Spellissy, a colonel in the United States Army, worked for the United States Special Operations Command (“USSOCOM”) and, within the year prior to his retirement from the Army, had pending under his official responsibility matters involving a 70mm warhead designed by the Nordic Ammunition Company (“NAMMO”). On July 30, 2004, Spellissy gave up his procurement authority and he went on regular leave from the United States Army until October 21, 2004. Between October 21, 2004 and December 31, 2004, Spellissy was on transitional leave. During his periods of leave and transitional leave, Spellissy worked for his own company, Strategic Defense International (“SDI”), which provided consulting services both to companies that wished to do business with United States agencies and to USSOCOM on several of its ammunition programs. He retired from active duty in the Army on December 31, 2004.
After he retired from the Army, it is alleged that Spellissy, through SDI, began working for NAMMO and, less than two years after his retirement, traveled to Norway to represent NAMMO during a meeting where he discussed the 70mm warhead with the United States. If true, his presence at the meeting in Norway would be in violation of 18 U.S.C. § 207(a)(2), which prohibits for two years a former employee of the executive branch from participating in a matter he reasonably would have known was pending under his official responsibility within a year of his retirement. Spellissy’s presence at that Norway meeting formed the basis of an affidavit for a search warrant for his *448house, and the subsequent search found evidence which led to his conviction.
In November 2005, a grand jury indicted Spellissy and SDI for: (1) conspiracy to defraud the United States, in violation of 18 U.S.C. § 371; (2) two counts of bribery of a public official in December 2004 and January 2005, in violation of 18 U.S.C. § 201; and (3) two counts of wire fraud in December 2004 and January 2005; in violation of 18 U.S.C. §§ 2, 1343, and 1346. The indictment alleged that various companies employed Spellissy as a consultant to transact business with USSOCOM, and that Spellissy conspired with William E. Burke, a private contractor working for USSOCOM, to provide preferential treatment to the specific companies he represented in exchange for payment.
In March 2006, Spellissy filed a motion to suppress, in particular to suppress a series of emails sent between Spellissy and Burke, found during the search of Spellissy’s house, alleging that the search warrant was based on an affidavit containing false statements. Specifically, Spellissy argued that he had given up his military procurement authority in July 2004 and retired from the Army in August 2004, contrary to claims in the affidavit that he had retired in December 2004; therefore, he claimed that he had retired before associating with a foreign military contractor and could not have violated the law.
The search warrant affidavit was executed by Department of Defense Special Agent Robert Calvert, who was investigating Spellissy for possible violations of 18 U.S.C. §§ 207(a)-(b) and 208(a), and alleged that Spellissy previously worked for USSOCOM and retired in December 2004. It further stated that Calvert had received information, prior to Spellissy’s retirement, that he was involved with a foreign interest to influence the awarding of future government contracts. Particularly, the affidavit claimed that Spellissy was instrumental in having USSOCOM submit a request to purchase a 70mm warhead from NAMMO, and that, in December 2004, Spellissy traveled to Norway and Sweden on behalf of USSOCOM to attend meetings concerning the 70mm warhead and other programs. The affidavit also alleged that Spellissy made this trip as a contractual employee and billed USSOCOM for the work performed, but did not bill USSOCOM for three days of the trip. It said “[according to Major Shannon Jackson, Special Projects, U.S. Army Picatinny Arsenal, and a co-attendee of the meetings, Spellissy attended the meetings in Sweden as the USSOCOM representative, but in Norway he represented NAMMO.” Finally, the affidavit alleged that Calvert learned from Don Jones, a program manager with USSOCOM, that Spellissy had told him prior to the trip to Norway that he was going as a representative of NAM-MO, not as a USSOCOM consultant.
After a hearing, the district court denied Spellissy’s motion to suppress, finding that, while the search warrant did contain false statements and material omissions, it still provided probable cause that Spellissy had violated the two-year prohibition on participating in a matter that he reasonably knew was also pending under his official responsibility. Specifically, the district court held that there was probable cause that (1) after his retirement, Spellissy began working for NAMMO and had represented NAMMO during a meeting in Norway where he discussed the 70mm warhead with the United States government, and (2) Spellissy had reason to know the warhead was a matter under his previous official responsibility within the last two years as prohibited by 18 U.S.C. § 207(a)(2).
In May 2006, Spellissy was convicted by a jury of all five counts in the indictment. *449However, the district court partially granted Spellissy’s motion of acquittal; the only count left standing was a conviction for conspiracy to defraud the United States in violation of 18 U.S.C. § 871.
We affirmed that conviction on appeal, agreeing with the district court’s conclusion that the search warrant affidavit supported a finding of probable cause and that sufficient evidence supported the conspiracy conviction. United States v. Spellissy, 243 Fed.Appx. 550 (11th Cir.2007).
Since we affirmed that conviction, Spellissy has filed seven motions with the district court seeking to overturn his conviction. In September and October 2007, he filed five motions asking that the district court (1) vacate his conviction pursuant to Rule 33 because of constitutional violations and his discovery of new evidence that undercut his conviction and sentence, and (2) stay the execution of his sentence pursuant to § 2255. The district court denied all of these motions, and Spellissy did not appeal.
In December 2007, Spellissy filed a motion for a new trial pursuant to Fed. R.Crim.P. 33 and § 2255, asserting violations of his constitutional rights, as well as alleging new evidence that he claimed undercut the validity of the search warrant and asking the district court to vacate his conviction or grant him a new trial. The district court denied this motion for lack of subject matter jurisdiction, finding it was a successive § 2255 motion. Spellissy did not appeal that ruling either.
In July 2008, Spellissy filed a motion with the district court entitled an “alternative authority motion for new trial pursuant to Fed.R.Crim.P. 33(a) and/or 60(b)(6).” In that motion, he asked the court to vacate his conviction or grant him a new trial based on newly discovered evidence. First, Spellissy argued that the district court should not automatically construe his claim under Fed.R.Civ.P. 60(b) as a successive habeas claim because he was merely asserting that the district court’s prior denial of § 2255 relief on a procedural basis was in error. Second, he claimed that his conviction violated the Fourth and Sixth Amendments, because the government failed to present key witness testimony at his suppression hearing and the prosecutor and Calvert, the agent who provided the affidavit underlying the search warrant, made false and misleading statements. Third, Spellissy said that he possessed new evidence revealing that the affidavit for the search warrant contained fraudulent statements, and the district court improperly denied his motion to suppress. Further, he claimed that the prosecutorial misconduct in this case — the government’s knowing use of perjured testimony in the affidavit — violated his constitutional rights. Spellissy also asserted in his motion for a new trial that he wanted to testify at the suppression hearing and at trial as well, but his counsel prevented him from doing so, and that the government’s failure to call other persons who attended the meeting in Norway to testify at the suppression hearing violated his Confrontation Clause rights.
The district court dismissed part of Spellissy’s motion as a successive § 2255 motion, and denied the remaining part of his motion for a new trial based on newly discovered evidence under Rule 33. First, it found that the motion was a successive § 2255 motion, because it attacked the legality of Spellissy’s conviction despite its designation as a Fed.R.Civ.P. 60(b) motion.
Second, the district court found that the Rule 33 portion of Spellissy’s motion was without merit, because Spellissy knew the identities of his “new” sources of information — Donald Jones, a former Program Manager for Ammunition at USSOCOM, and James Rooney, a former president of *450NAMMO, both of whom were present at the 70mm warhead meeting in Norway— and that both of those sources would testify that Spellissy was not in attendance at the 70mm warhead meeting in Norway before the suppression hearing. Thus, Jones’s deposition and Rooney’s affidavit were not new evidence. The district court then determined that Spellissy did not exhibit due diligence, because he did not attempt to secure the testimony of Jones or Rooney for the suppression hearing as he did with his other witnesses. Finally, it concluded that, even if this evidence was actually new, it would do nothing more than contradict the statement from Jackson that Spellissy was present at the 70mm warhead meeting upon which Calvert relied in his affidavit. The “new” evidence would not have shown that the affidavit was definitively false, or that Calvert recklessly relied on that information in drafting the affidavit. The district court concluded that, while Spellissy’s presence at the NAMMO meetings in Norway was material, his presence at any particular meeting was not determinative, and it found that Spellissy did not show that the alleged new evidence would produce a different result as it did not negate probable cause for the search warrant.
II.
Because we are obliged to review our subject matter jurisdiction sua sponte, we must decide as a threshold issue whether a COA must issue before we can entertain the portion of Spellissy’s appeal regarding the denial of his motion as a successive § 2255 petition. See Boone v. Sec’y of Dep’t of Corr., 377 F.3d 1315, 1316 (11th Cir.2004).
Unless a habeas petitioner, such as Spellissy, obtains a COA, he may not appeal “the final order in a proceeding under section 2255.” 28 U.S.C. § 2253(c)(1)(B). A petitioner’s application for a COA must first be considered by a district court before this Court can consider the issue. Fed. R.App. P. 22(b)(1); Edwards v. United States, 114 F.3d 1083, 1084 (11th Cir.1997). Even if the petitioner does not expressly request a COA from the district court, the district court still must treat a notice of appeal filed by a movant, following the denial of a § 2255 motion, as an application for a COA and make a determination on that motion. Fed. R.App. P. 22(b)(1). Because we cannot review a motion for a COA unless and until the district court has ruled on the propriety of issuing the COA, we must remand any appeal of an order denying a § 2255 motion as successive if that appeal is filed before the district court has ruled on the COA. Edwards, 114 F.3d at 1084-85.
Put simply, there is no indication whatsoever in the record that Spellissy requested a COA to appeal the issues raised in what the district court construed to be his § 2255 motion, nor is there any indication that the district court construed his notice of appeal as requesting a COA. Thus, because the district court has not yet granted (or denied) a COA in this case, we must remand it to the district court for that determination.
Spellissy does raise arguments pertaining to the invalidity of his conviction other than that the district court erred in dismissing his motion in part as a successive § 2255 motion. However, we decline to address those challenges unless and until Spellissy is granted a COA. See id. at 1084-85. A petitioner making a collateral challenge to his conviction on any ground other than newly discovered evidence demonstrating actual innocence may do so only through a § 2255 motion. See United States v. Jordan, 915 F.2d 622, 629 (11th Cir.1990) (explaining that collateral challenges to the legality of a conviction must *451be brought under 28 U.S.C. § 2255). Thus, because this is an appeal of Spellissy’s seventh post-sentencing motion1 and we have already affirmed his conviction on direct appeal, any argument challenging that conviction — including his arguments dealing with prosecutorial misconduct, ineffective assistance of counsel, sufficiency of the evidence, and his right to confrontation — can be raised only in the context of a proper § 2255 motion. And we can only hear an appeal of the issues that can be raised in a § 2255 motion if a COA has been granted.
Accordingly, the case is remanded to the district court for a ruling on whether a COA will issue as to the dismissal of Spellissy’s motion as an improperly filed successive § 2255 motion.
III.
Spellissy also has requested that a new district judge be assigned to his case if it is remanded on the ground that the trial judge presiding over his case sua sponte addressed its jurisdiction to hear his claims. This request is without merit.
We have “the authority to order reassignment of a criminal ease to another district judge as part of our supervisory authority over the district courts in this Circuit.” United States v. Torkington, 874 F.2d 1441, 1446 (11th Cir.1989). Such reassignment is a “severe remedy.” United States v. Remillong, 55 F.3d 572, 577 (11th Cir.1995). In deciding whether it is necessary to reassign the case to another judge on remand, we consider “(1) whether the original judge would have difficulty putting his previous views and findings aside; (2) whether reassignment is appropriate to preserve the appearance of justice; (3) whether reassignment would entail waste and duplication out of proportion to gains realized from reassignment.” Torkington, 874 F.2d at 1447 (citation omitted).
In this case, the district court acted squarely within its powers in addressing the jurisdictional issues. Indeed, the district court is required to consider its jurisdiction to rule on Spellissy’s motion for a new trial sua sponte. Williams v. Chatman, 510 F.3d 1290, 1293 (11th Cir.2007) (“Federal courts are obligated to inquire into subject-matter jurisdiction sua sponte whenever it may be lacking.”) (quotation marks omitted). Accordingly, this case will not be reassigned.
IV.
Finally, the district court did not abuse its discretion in denying Spellissy’s request for a new trial under Rule 33. See United States v. Campa, 459 F.3d 1121, 1151 (11th Cir.2006) (a denial of a motion for a new trial is reviewed for an abuse of discretion).
Spellissy faces a high burden in demonstrating that a new trial is warranted. As we explained in Campa, “[mjotions for a new trial based on newly discovered evidence are highly disfavored in the Eleventh Circuit and should be granted only with great caution. Indeed, the defendant bears the burden of justifying a new trial.” Id. at 1151 (quotation marks omitted). To receive a new trial based on newly discovered evidence under Fed.R.Crim.P. 33, Spellissy must demonstrate that: (1) he discovered the evidence after trial; (2) his failure to discover the evidence was not due to a lack of due diligence; (3) the *452evidence is not merely cumulative or impeaching; (4) the evidence is material; and (5) the evidence is of such character that a new trial would probably produce a different result. United States v. Schlei, 122 F.3d 944, 991 (11th Cir.1997); Bentley v. United States, 701 F.2d 897, 898 (11th Cir.1983). “The failure to satisfy any one of these elements is fatal to a motion for a new trial.” Schlei, 122 F.3d at 991 (quotation marks omitted). Further, “facts concerning an alibi are peculiarly within the knowledge of a defendant himself,” thus it is difficult for a defendant to show that alibi evidence was available but unobtainable with due diligence before the time of the trial. United States v. Williams, 816 F.2d 1527, 1530 (11th Cir.1987) (quotation marks omitted). Spellissy cannot surpass this high hurdle.
The new evidence Spellissy proffers is found in the testimony of two witnesses who said that Spellissy did not attend the 70mm warhead meeting in Norway, as had been alleged in the affidavit underlying his search warrant. In particular, Spellissy offers the December 21, 2007 deposition testimony of Jones and the November 29, 2007 affidavit executed by Rooney. However, Spellissy knew that Jones and Rooney were at the meetings in Norway and knew of their likely testimony at the very time of the meeting, let alone at the time of his suppression hearing months later. Indeed, during an interview with the government on April 13, 2005, Spellissy stated that he was present in Norway in November 2004, explained that he was working with Rooney’s group as a consultant, and said that he went with Jones to NAMMO to discuss the 70mm warhead. Spellissy also referred to Rooney’s group in his pleadings filed early in the litigation of this case and, in a pleading filed before the suppression hearing, Spellissy expressly named Jones as an individual with whom Calvert must have spoken in drafting the affidavit underlying the search warrant. Moreover, Spellissy listed Jones as a USSOCOM witness he wanted to interview during pretrial proceedings. Accordingly, he cannot meet the first prong of our test for a new trial as outlined in Schlei because there can be no question that this was not evidence discovered after his trial had concluded.
Nor has Spellissy explained how, with due diligence, he was unable to obtain the testimony of Jones or Rooney before the suppression hearing. Although it is true that Jones was in Iraq from March to August 2006, Spellissy was aware of Jones’s attendance at the 70mm warhead meeting, and that he was being indicted for his attendance at that meeting long before Jones left for Iraq in March 2006. Indeed, the search warrant in this case was issued in April 2004, and Spellissy filed his first motion to suppress evidence based on challenges to the search warrant affidavit in February 2006. There is no evidence in the record that Spellissy took any substantial steps to secure Jones and Rooney as witnesses in support of his defense. He did not issue subpoenas or seek alternative means to obtain their testimony. After being informed by Jones that Spellissy needed to request permission to interview him from the United States due to his status as an active duty member of the military, Spellissy did not make an official request seeking such approval. This omission is particularly striking because Spellissy did serve subpoenas on five other active duty military officers and the district court agreed to allow Spellissy to depose one of those officers to preserve his testimony.
Nor can Spellissy meet the third prong of the Schlei test. Jones’s and Rooney’s testimony would have done nothing more than contradict the testimony of Jackson and an e-mail provided by NAMMO’s Di*453rector of Business Operations Jerry Kaffka that Spellissy did attend the 70mm warhead meeting, which formed the basis of Calvert’s affidavit. But, Jones’s and Rooney’s statements would not have conclusively demonstrated that the information Calvert relied on was false, nor that he was reckless in relying upon it. All that Spellissy has demonstrated is that two individuals had a different recollection of the pertinent events than two other people.
Finally, there is no indication that the testimony of Jones or Rooney would have produced a different result in this case. Their testimony would not have negated the probable cause determination underlying the search warrant, based on Jackson’s statement and Kaffka’s email, that Spellissy was in Norway less than two years after his termination from the military as a consultant for NAMMO, and that Spellissy had reason to know that NAMMO’s 70mm warhead had been a matter under his official responsibility within one year of his termination from service as prohibited by § 207(a)(2). The most this “new” evidence could have done is raise a doubt as to whether Jackson and Kaffka were correct, and such doubts are permissible under the probable cause standard. Moreover, Spellissy has not detailed what evidence should have been suppressed, how that evidence was used at trial, or how the exclusion of that evidence would have affected the outcome of the trial.
Accordingly, we remand the portion of Spellissy’s appeal challenging the partial denial of his motion as an improperly filed successive § 2255 petition for a determination as to whether a COA should issue; we deny Spellissy’s request for a new judge on remand; and we affirm the district court’s denial of the portion of Spellissy’s motion that was properly plead as a Rule 33 motion.
AFFIRMED IN PART, DENIED IN PART, REMANDED IN PART.