CUDAHY, Circuit Judge.

John Thomas Martin pleaded guilty to bombing a private dwelling, 18 U.S.C. § 844(i), and obstruction of justice. 26 U.S.C. § 5841. Martin appeals his conviction and sentence, arguing that (1) the impact of the bombing on interstate commerce was too slight to satisfy the interstate commerce requirement of § 844(i); and (2) the court wrongly calculated his base offense level under the Sentencing Guidelines, because he "merely" tried to damage, rather than destroy, the dwelling, and did not knowingly create a risk of death or serious bodily harm to the occupant of the house he bombed. We affirm.

I.

John Thomas Martin was divorced from his wife, Lynn Webster, and not happy about it. Before they separated, Martin told Webster that if she ever saw another man, he would kill the other man. Martin told his friends that he followed Webster around to see if she was seeing anyone. On September 14, 1995, Webster obtained a restraining order against Martin. Martin, however, continued to be obsessed with his ex-wife. He learned that Webster had been seen talking to a man who drove a black car. Thereupon, Martin tracked down the man's identity, and learned that he and Webster worked together. The man in question was James Bowyer. Though Martin denies doing so, his co-workers later told investigators that because he believed (falsely, as it turned out) that Bowyer was dating Webster, Martin offered to pay them to beat up Bowyer, talked of blowing Bowyer up and also talked about setting off a bomb at Bowyer's house. In fact, Martin did more than talk: he brought a pipe bomb to work, and boasted that Webster was going to pay for cheating on him. The pipe bomb was just over five inches long and one-and-a-half inches in diameter.

On the night of October 5, 1995, Martin ran into his friend Martin Campton and informed Campton that he was going to bomb either Webster's or Bowyer's house. Martin and Campton went to Bowyer's house about 10:30 p.m. The house was dark, but Bowyer's car was in the driveway. According to Campton, Martin planted the pipe bomb at the back door of the house, and lit the fuse. Martin maintained that he set the bomb ten feet from the back door, after which Campton detonated it. Bowyer was not injured in the ensuing explosion, but the bomb caused $4,000 in damage to the back door, the porch and a refrigerator on the porch, and another $3,500 in damage to a building behind Bowyer's house. Needless to say, it also roused Bowyer and his neighbors.

After fleeing the scene of the explosion, Martin called a friend from work, William Rabe, whom he met to work out an alibi. Martin gave Rabe the materials left over from constructing the pipe bomb, which Rabe subsequently destroyed. Martin also destroyed the shoes he had worn during the bombing and asked several other co-workers to lie about the incident to investigators.

The attempts to thwart the investigation were in vain. Campton cooperated with the government, which, with Campton's consent, recorded a conversation between Martin and Campton about the bombing. In that conversation, Martin indicated that he made and detonated the bomb and believed he could face attempted murder charges as a result. Martin was arrested and indicted. He eventually pleaded guilty to one count of destruction of property by explosive, 18 U.S.C. § 844(i), and one count of obstruction of justice. 26 U.S.C. § 5841. Martin stipulated that the bomb was set off to frighten Bowyer. The plea agreement also stipulated that the utilities connected to Bowyer's residence "affected commerce or moved in interstate commerce." Martin disputed several of the factual findings in the Presentence Investigation Report, including the Probation Office's recommendation that his base offense level be calculated at 24, for knowingly attempting to harm Bowyer and destroy his house. The district court concluded that Martin planted the bomb himself, knowingly created a substantial risk of death or serious bodily injury to Bowyer when he did so and intended to destroy the dwelling. For those reasons, the court determined that Martin's base offense level was 24, U.S.S.G. § 2K1.4(a)(1), and sentenced him to 108 months in prison, $7,396.50 in restitution and a term of supervised release. Martin appeals.

II.

The federal bombing statute requires that the damaged property be used in or affect interstate commerce. 18 U.S.C. § 844(i). Martin's principal contention is that the residence which he bombed had too small an impact on interstate commerce to satisfy that requirement. Martin argues that under the Supreme Court's decision in United States v. Lopez, 514 U.S. 549 (1995), Congress may only regulate activities which have a substantial effect on interstate commerce. Id. at 559. Martin argues that the only proven nexus of Bowyer's residence with interstate commerce is non-business, private telephone service, provided by a company with corporate offices in Florida. This telephone service was not interrupted by the bombing, and, Martin notes, the record is devoid of evidence that Bowyer even used his phone. Therefore, Martin concludes, the bombing had no substantial effect on interstate commerce. Because the requisite nexus with interstate commerce was lacking, according to Martin, the district court lacked jurisdiction over his crime.

Martin's argument rests on the concept that a guilty plea does not waive jurisdictional defenses to the crime at issue. United States v. Nash, 29 F.3d 1195, 1201 (7th Cir. 1994). But the nexus with interstate commerce, which courts frequently call the "jurisdictional element," is simply one of the essential elements of § 844(i). Although courts frequently call it the "jurisdictional element" of the statute, it is "jurisdictional" only in the shorthand sense that without that nexus, there can be no federal crime under the bombing statute. Kanar v. United States, 118 F.3d 527, 530 (7th Cir. 1997). It is not jurisdictional in the sense that it affects a court's subject matter jurisdiction, i.e., a court's constitutional or statutory power to adjudicate a case, here authorized by 18 U.S.C. § 3231. See Steel Co. v. Citizens for a Better Env't, 118 S. Ct. 1003, 1110 (1998). This court has recognized for decades that, despite defendants' tendency to "confuse facts essential to be alleged as elements of the crime with jurisdictional requirements arising as a matter of law," once a defendant pleads guilty in "[a] court which has jurisdiction of the subject matter and of the defendant, as did the court in the instant case," the court's judgment cannot be assailed on grounds that the government has not met its burden of proving "so-called jurisdictional facts." United States v. Hoyland, 264 F.2d 346, 352-53 (7th Cir. 1959); La Fever v. United States, 279 F.2d 833, 834 (7th Cir. 1960). Even if the government fails to establish the connection to interstate commerce, the district court is not deprived of jurisdiction to hear the case. See generally Steel Co., 118 S. Ct. at 1110-13.

Relying on certain language in this court's opinion in United States v. Stillwell, 900 F.2d 1104, 1110 n. 2 (7th Cir. 1990), Martin argues that the adequacy of the interstate commerce element is jurisdictional and may be raised for the first time on appeal despite his guilty plea. In Stillwell, the defendants were charged with arson under § 844(i). At trial, the parties stipulated that the only nexus between the house that was burned and interstate commerce was that it received gas from the Northern Illinois Gas Company, which was supplied from sources outside of Illinois. Id. at 1106. On appeal, the defendants asserted that it was beyond Congress' power to outlaw arson of a private residence where the only connection with interstate commerce was the supply of interstate natural gas. This court rejected the government's position that the defendants had waived this argument on appeal because they had not raised it before the district court stating:

While we agree that defendants did not raise this issue at the district court level, defendants may raise this issue on appeal because it is jurisdictional. If the application of § 844(i) to defendants exceeds Congress' power under the commerce clause, the district court could not exercise jurisdiction over the subject-matter contained in Count One (the arson conspiracy charge) and Count Two (the substantive arson charge). Lack of subject-matter jurisdiction, whether through statutory interpretation or constitutional prescription, is never waived.

Id. at 1110 n. 2 (citations omitted); see also United States v. Prevatte, 16 F.3d 767, 771 n. 3 (7th Cir. 1994) (in a § 844(i) case, citing Stillwell and addressing adequacy of the interstate commerce nexus sua sponte on appeal because it was "jurisdictional"). Martin relies on this language in support of his assertion that the required nexus to interstate commerce is jurisdictional, and thus, he cannot have waived the argument by pleading guilty.

We acknowledge that the language in footnote 2 of Stillwell is mistaken and imprecisely states the basis on which this court permitted the defendants in that case to raise their argument for the first time on appeal. Accordingly, we take this opportunity to correct our explanation for allowing the defendants in Stillwell to challenge the interstate commerce element on appeal. We explain why Stillwell does not support a similar ground for appeal in the instant case. In Stillwell, the defendants had stipulated to certain facts regarding the house's connections to interstate commerce, but argued on appeal that the connections to which they had stipulated did not satisfy the interstate commerce element of the statute. The defendants in Stillwell, then, essentially argued that the indictment failed to state an offense. This argument was not presented to the district court but the defendants claimed that it might be raised for the first time on appeal. Today we explain by way of clarification that review by this court for plain error was appropriate in that case despite the defendants' failure to raise the argument on appeal. See Fed.R.Crim.P. 52(b); see also United States v. Quintanilla, 2 F.3d 1469, 1476-77 (7th Cir. 1993). A challenge to the indictment based on the adequacy of the interstate commerce stipulation had no relation to subject matter jurisdiction — the power to adjudicate — but instead went only to an alleged failure of proof. See Bell v. Hood, 327 U.S. 678, 680 (1946); see also Turner/Ozanne v. Hyman/Power, 111 F.3d 1312, 1316-17 (7th Cir. 1997) ("Jurisdiction under the federal question statute is not defeated by the possibility that the averments, upon close examination, might be determined not to state a cause of action.").

Unlike in Stillwell, Martin has admitted every element of the offense by pleading guilty. See United States v. Broce, 488 U.S. 563 (1989). Martin's plea agreement stipulated that several utilities connected to the house were utilities "which affected commerce or moved in interstate commerce." The stipulation is to facts that are colorably probative and they may not be challenged on appeal. Had Martin sought to go to trial, the government would have had the burden to prove the interstate commerce element of the offense. However, by pleading guilty, Martin relieved the government of this burden. Martin cannot now argue for the first time on appeal that the interstate commerce element has not been established. Stillwell may be readily distinguished since it is a forfeiture case and there may be review for plain error under Rule 52(b). However, the case before us involves waiver by guilty plea as to which no such review is available. See Olano v. United States, 507 U.S. 725, 732-34 (1993). It is elementary that "a guilty plea is an admission of all the elements of a formal criminal charge[.]" McCarthy v. United States, 394 U.S. 459, 466 (1969). Consequently, Martin's guilty plea admitted the facts necessary to establish the commerce element of a violation of the federal bombing statute. Hoyland, 264 F.2d at 352. By accepting the plea agreement, Martin waived any challenge to these facts and his reliance on Stillwell is misplaced.

A defendant does not, according to recent Circuit precedent, "waive the right to contest whether [the] facts [which he admitted] are sufficient to constitute a crime," when a change in the law changes the nature of the conduct deemed to be criminal. Stanback v. United States, 113 F.3d 651, 654 (7th Cir. 1997) (Bailey challenge); but cf. Broce, 488 U.S. at 570-72. Martin argues that under the rationale of Stanback, the guilty plea does not preclude him from arguing that the nexus with interstate commerce was not sufficient, under Lopez, to implicate the Commerce Clause. But the Supreme Court decided Bailey after Stanback pleaded guilty to "using or carrying a firearm." Lopez, on the other hand, was decided more than a year before Martin pleaded guilty. Thus, the law was established at the time Martin, who was represented by counsel, entered the guilty plea. It should have been apparent that the stipulated facts were intended to establish the commerce element of § 844(i). By not reserving his right to challenge whether, under Lopez, his conduct was sufficient to meet the commerce element of § 844(i), Martin has waived the right to raise a Lopez challenge on appeal.

III.

Martin also contends that the court should have calculated his base offense level at 20, not 24. The Sentencing Guidelines establish a base offense level of 20 if a bombing created a substantial risk of death or serious bodily injury to someone other than the bomber, or endangered a dwelling. U.S.S.G. § 2K1.4(a)(2)(A), (C). If the bomber knowingly created a substantial risk of death or serious bodily injury, or if the bombing involved the destruction or attempted destruction of a dwelling, the base offense level is 24. U.S.S.G. § 2K1.4(a)(1)(A)-(B). The sentencing court's findings of fact are reviewed for clear error. United States v. Hickok, 77 F.3d 992, 1007 (7th Cir.), cert. denied, 116 S. Ct. 1701 (1996).

Martin notes that the bombing damaged only the back door of the residence, part of the eaves and a refrigerator on the back porch. Consequently, he maintains, he merely endangered the dwelling. Martin stipulated in the plea agreement that he set off the bomb in order to scare Bowyer. Because Martin wanted only to frighten Bowyer rather than hurt him; because the bomb was small, untested and placed at a back door rather than by a bedroom or living room; and because the government failed to prove that Martin knew Bowyer was in the house (which was completely dark at the time he set off the bomb); Martin reasons that there was insufficient evidence to establish that he either knowingly created a substantial risk of serious bodily harm to Bowyer, or was trying to destroy rather than simply to damage the house. As a result, he concludes that he is entitled to a base offense level of 20 under § 2K1.4(a)(2).

Unfortunately for Martin, the government provided a different version of events, and the sentencing court believed the government. The sentencing court's credibility determinations are entitled to special deference. United States v. Pippen, 115 F.3d 422, 425 (7th Cir. 1997). In the conversation with Campton which the government recorded, Martin indicated that he set off the bomb. And, while Martin stipulated that he only intended to scare Bowyer, the government presented evidence that Martin had solicited people to beat Bowyer up, talked at work about blowing Bowyer up and told his wife before they separated that if she ever saw another man, he would kill the man. In particular, an ATF agent testified that Martin admitted to his supervisor at work that he knew Bowyer was at home when he detonated the bomb. Martin denied saying any such thing and complains that the government failed to prove that he made the statement because it never called the supervisor to testify.

But sentencing depends on proof by a preponderance of the evidence, not proof beyond a reasonable doubt. United States v. Adams, 125 F.3d 586, 592 (7th Cir. 1997). Moreover, the rules of evidence do not apply at sentencing hearings and "a sentencing judge is free to consider a wide variety of information that would be inadmissible at trial, including hearsay." United States v. Barnes, 117 F.3d 328, 337 (7th Cir. 1997) (internal citations and quotation marks omitted). The sentencing court believed that the ATF agent's hearsay evidence was reliable, credited her version of events, and disbelieved Martin. The district court's choice among the competing credibilities of the various witnesses cannot be clearly erroneous if both sides present permissible views of the evidence. United States v. Green, 114 F.3d 613, 619 (7th Cir. 1997); see also Anderson v. City of Bessemer City, 470 U.S. 564, 574 (1985).

Under the language of § 2K1.4(a)(1), the inquiry is not whether Martin intended to harm his victim: it is whether Martin knew that his actions created a risk of harm. United States v. Altier, 91 F.3d 953, 956 (7th Cir. 1996) ("knowingly" is not the same as "purposefully"). If Martin intentionally detonated a pipe bomb at the back door of the house, knowing that Bowyer was asleep inside, that is enough for the court to conclude that he knowingly created a substantial risk of harming the victim. In the case at bar, the evidence as a whole does not show that the court clearly made a mistake in concluding that Martin knew the bomb might seriously harm Bowyer. See United States v. Gabel, 85 F.3d 1217, 1221 (7th Cir. 1996). The court correctly assessed Martin's base offense level at 24, under U.S.S.G. § 2K1.4(a)(1).

By pleading guilty, Martin admitted every element of the offense, including the effect on interstate commerce. Broce, 488 U.S. at 569 ("A plea of guilty and the ensuing conviction comprehend all of the factual and legal elements necessary to sustain a binding, final judgment of guilt"). Moreover, the evidence supports the district court's finding that Martin knew the occupant of the dwelling was at home when he planted the bomb, and therefore knowingly created a risk of death or serious bodily injury. Therefore, the court correctly calculated Martin's base offense level under U.S.S.G. § 2K1.4(a)(1). AFFIRMED.