
515 F.3d 722 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Reginald D. CHAVERS, Defendant-Appellant.
No. 06-4303.
United States Court of Appeals, Seventh Circuit.
Argued October 3, 2007.
Decided January 25, 2008.
*723 Carol L. Kraft (argued), Penelope L. Coblentz, Office of the United States Attorney, Milwaukee, WI, for Plaintiff-Appellee.
Lewis A. Wasserman (argued), Kies & Wasserman, Milwaukee, WI, for Defendant-Appellant.
Before COFFEY, RIPPLE, and KANNE, Circuit Judges.
COFFEY, Circuit Judge.
Reginald Chavers pleaded guilty to knowingly attempting to bring a loaded semiautomatic pistol on an airplane. Two months later, he moved to withdraw his plea, claiming he did not know the gun was loaded when he gave it to airport officials. The district court disagreed and denied the motion. We affirm.

I. Background
In May 2004 Chavers was arrested at Milwaukee County's General Billy Mitchell International Airport, where he was checking in for a flight to Atlanta. He told airline staff that he needed to declare a weapon without any ammunition. The airline's customer-service representative, Carrie Jackson, asked Chavers to sign an Unloaded Firearm Declaration. Chavers complied and placed the signed declaration inside his gun case. Jackson asked Chavers again whether he had any ammunition, and Chavers responded "no." Jackson next told Chavers that he needed to buy a lock for his gun case before he could check the case. Chavers complained that the Transportation Security Administration (TSA) screeners were always breaking the locks on his gun case, but he purchased a lock from the airport concessionaire nonetheless. Chavers then gave his gun case to the TSA screeners, who after examining the case discovered that the gun was loaded with 10 rounds of ammunition and that the case also contained an extra magazine with another 10 rounds. When confronted with this information, Chavers claimed falselythat he was a law enforcement officer and was entitled to carry the loaded weapon on board.
Thereafter, Chavers was charged in a two-count indictment with knowingly attempting to place a loaded firearm in checked luggage. 49 U.S.C. § 46505(b)(2). He was also charged with knowingly and willfully making a false representation to airport personnel regarding the firearm. 18 U.S.C. § 1001. He agreed, to plead guilty to the firearm charge in exchange *724 for the government's promise to dismiss the false representation charge.
During the plea colloquy, Chavers testified that he wanted to plead guilty because he was, in fact, guilty as charged. He also testified that he agreed with the factual basis for his plea as described in the plea agreement. Furthermore, Chavers testified that he had an adequate opportunity to discuss the charges and any defenses he might have with his appointed counsel, that counsel had accommodated all of his requests, and that he was fully satisfied with counsel's representation. After informing Chavers that his criminal conviction would affect his civil rights, including his ability to own a gun and his ability to obtain a license for certain kinds of employment, the trial judge accepted the guilty plea. The district court did not explicitly ask Chavers if he knew the gun was loaded when he gave it to the TSA screeners.
Almost two months later, Chavers wrote a letter to the court asking to withdraw his guilty plea and have new counsel appointed. In his letter, he asserted that he was innocent and blamed his decision to plead guilty on his attorney, who he now claimed was ineffective. He maintained that his lawyer failed to locate a crucial witness, neglected to postpone the trial date in consideration of Chavers's health problems, and told Chavers that he was not prepared to try the case.
In response to Chavers's letter, the district court appointed new counsel. Chavers's new counsel filed a formal motion to withdraw the guilty plea, arguing that Chavers did not know the gun was loaded when he gave it to the TSA officials and that no one told Chavers his felony conviction would bar him from gun ownership or operating a security business. The district denied Chavers's motion to withdraw the guilty plea and sentenced Chavers to 5 years' probation. Chavers appeals, challenging only the district court's, denial of his motion to withdraw his plea.

II. Discussion
Chavers makes two arguments in support of his contention that the district court erred in denying his motion to withdraw his guilty plea. Initially, he claims that he did not know the gun was loaded when he gave it to airport personnel, thus undermining the factual basis of his guilty plea. Second, he argues that the district court applied the wrong legal standard in evaluating his motion to withdraw.
We have frequently observed that "[a] defendant does not have an absolute right to withdraw a plea before sentencing, although the court may allow him to do so if he has a `fair and just reason' for doing so." United States v. Carroll, 412 F.3d 787, 792 (7th Cir.2005) (quoting Fed.R.Crim.P. 11(d)(2)(B)). Because the defendant's statements at the plea colloquy are presumed to be true, the defendant bears a heavy burden of persuasion in showing that such a fair and just reason exists. United States v. Logan, 244 F.3d 553, 558 (7th Cir.2001). A defendant faces an uphill battle in seeking to withdraw a guilty plea after a thorough plea colloquy. United States v. Bennett, 332 F.3d 1094, 1099 (7th Cir.2003). We will uphold a district court's factual findings about the existence of a fair or just reason to withdraw the plea unless they are clearly erroneous, and we review the district court's ruling on the motion to withdraw for abuse of discretion. Carroll 412 F.3d at 792.
Chavers argues that he did not know the gun was loaded when he handed it to airport personnel and that the district court consequently erred in finding a sufficient factual basis for his plea. In essence, Chavers claims that because knowing the *725 gun was loaded is a necessary element of the crime to which he pleaded guilty, and because he did not in fact possess the requisite knowledge, he is actually innocent of the crime. We have frequently. held that actual innocence is a valid ground for withdrawing a guilty plea. See, e.g., Carroll, 412 F.3d at 792. But "bare protestations of innocence" are insufficient to withdraw a guilty plea, particularly after a knowing and voluntary plea made in a thorough Rule 11 colloquy. Id. Rather, the defendant must produce some credible evidence of his innocence. Id.
The record shows that Chavers testified that he was in fact guilty, that he had discussed the plea agreement with his attorney, and that the facts contained in the plea agreement were correct and a sufficient factual basis for his guilty plea. Chavers has provided no additional evidence beyond his own assertions of innocence, which contradict his sworn testimony at the plea colloquy. See Carroll, 412 F.3d at 792 (holding that defendant's denials of guilt, which contradicted his testimony during the plea colloquy, were insufficient evidence of actual innocence). While the district court could have expressly asked Chavers whether he knew the weapon was loaded at the plea colloquy, its failure to do so is harmless, since the government's evidence together with his concessions at the plea colloquy are sufficient to support a finding that Chavers possessed the necessary knowledge. See, e.g., United States v. Schier, 438 F.3d 1104, 1111-12 (11th Cir.2006) (rejecting defendant's argument that trial evidence was insufficient where court could infer knowledge from the record); see also United States v. Moore, 586 F.2d 1029, 1032 (4th Cir.1978) (interpreting a prior, materially unchanged version of § 46505(b)(2) and holding that the "knowing" element of offense required only that the defendant knew the gun was in his briefcase, not that he intended to use it for an illegal purpose); United States v. Lee, 539 F.2d 606, 608 (6th Cir.1976) (also interpreting a prior version of statute and observing that the "knowing" element required only that the defendant knew of the presence of a concealed weapon, not that the defendant knew possessing the weapon was illegal). Moreover, Chavers had the burden of showing he did not know the weapon was loaded, and he provided the district court with no alternative explanation of the facts that might support his claim of ignorance. On this record, the district court did not abuse its discretion in concluding that Chavers failed to proffer enough evidence to show a fair and just reason why he should be permitted to withdraw his guilty plea.
Chavers next argues that the district court, in deciding whether to grant his motion to withdraw the guilty plea, applied an amorphous "interest of justice" standard rather than the appropriate "fair and just reason" standard. Chavers rests this argument on the final sentence in the order denying his motion, in which the district court observes that "the interest of justice" would not be served by allowing Chavers to withdraw his plea. Chavers also notes that the phrase "fair and just reason" does not appear in the district court's decision. He concludes that the district court reviewed his motion under an impermissibly stringent "interest of justice" standard, and contends that if the court had applied the "fair and just reason" standard, it would have been compelled to grant his motion.
We have frequently held in the sentencing context that a district court need not recite "magic words" to assure a reviewing court that it applied the appropriate legal standard. See, e.g., United States v. Tyra, 454 F.3d 686, 687 (7th Cir.2006) (holding *726 that a district court need not recite magic words at sentencing to ensure that the correct standard is being used but must only sufficiently articulate reasons for its decision consistent with correct standard). The same is true here: so long as the district court substantively complied with the requirements for evaluating a motion to withdraw a guilty plea, the court need not recite formulaic language. The district court's choice of language does not resolve the question whether it was correct to deny Chavers's motion. Rather, we must look at the specific reasons Chavers advanced in support of his motion to withdraw and whether the district court erroneously concluded that he had failed to meet his burden.
Although Chavers characterizes the "interest of justice" language as requiring a greater showing than the "fair and just reason" standard, he points to no substantive way in which the court's decision was in fact stricter. He concedes as much when he admits that, had the district court used both the "interest of justice" language and the "fair and just reason" standard, he would not have quibbled with the court's choice of words. The record demonstrates that the trial judge properly considered whether Chavers's asserted reason to withdraw was fair and just, and concluded it was not. The court observed that Chavers was competent at the time of his plea, was ably represented by counsel, understood the charge against him and that he knowingly waived his rights in pleading guilty, and did not object to the factual basis for his plea at the Rule 11 colloquy although he was given the opportunity to do so. These are the precise factors that a court applying the "fair and just reason" standard would articulate. See, e.g., Bennett, 332 F.3d at 1099-1100; United States v. Underwood, 174 F.3d 850, 854 (7th Cir. 1999).
Finally, the government responds to a claim of ineffective assistance of counsel, but although Chavers raised that issue in his letter to the district court, he has not raised or developed the issue before this court. See Fed. R.App. P. 28(a)(9). Should Chavers wish to pursue his contention that his counsel was ineffective, he would be better served by bringing that claim through a collateral proceeding under 28 U.S.C. § 2255. See, e.g., Massaro v. United States, 538 U.S. 500, 504-05, 123 S.Ct. 1690, 155 L.Ed.2d 714 (2003); United States v. Turcotte, 405 F.3d 515, 537 (7th Cir.2005).

III. Conclusion
Because Chavers has not supplied a fair and just reason for withdrawing his guilty plea, the district court did not err in denying his motion. Accordingly, we affirm.
