By a superceding indictment, a federal grand jury charged Delon J. Adams with three crimes: one count charged that as a felon he had unlawfully possessed a firearm on March 18, 2002, in violation of 18 U.S.C. § 922(g)(1) (2000) (count I); the other two counts charged him with using and carrying a firearm in relation to drug trafficking crimes committed on two different dates, February 6 and 12, 2002, in violation of 18 U.S.C. § 924(c)(l)(A)(ii) (2000) (counts II and III). Several motions to suppress evidence were denied and a jury trial began on December 4, 2002.
The parties stipulated to Adams’ prior felony conviction. At trial, the government presented evidence that Adams had moved to Maine and in June 2001 married a woman named Laurie; and that in June 2001 she had purchased a handgun (a Sturm Ruger pistol) and in October 2001 another (a Kel Tec). Her attempted purchase of a third gun, two days after the second, alerted the police who stopped Adams driving away with Laurie and who, under his seat, found both previously purchased guns.
After this incident, Adams and Laurie separated and in February 2002 Adams began to stay at least intermittently with a woman named Amanda Whitmore and her boyfriend Christopher Wright at their apartment in Biddeford, Maine. Two witnesses testified that Adams, 33 years old, sometimes slept in the bed of Amanda’s 15-year-old sister, Chrissy, and that sometimes Adams and Chrissy shared a bed. Chrissy testified that Adams had slept in the same bed with her and, over a defense objection, that he had a sexual relationship with her.
In February 2002, Adams began a set of robberies with Wright, aimed at relieving drug dealers of cash or drugs. The first robbery, of Jaime Morales, took place on February 6, 2002. Wright testified that Adams had taken a gun into Morales’ motel room, returned with marijuana and cash, and to Wright admitted hitting Morales with a pistol. Morales (and his girlfriend who was present) confirmed this story, adding that the pistol had a laser sight (the Sturm Ruger had such a sight).
There was also testimony from several witnesses including Wright that on February 12, 2002, Adams, armed with a gun, had robbed money and drugs from James Frazier. Wright and still other witnesses testified to a third, similar robbery in February 2002 in which Adams took money but not drugs; this third incident was not charged in the indictment, presumably because there were no drugs and therefore nothing in which to ground a federal charge.
On March 8, 2002, Wright was arrested for an unrelated offense and offered up Adams. Based on Wright’s disclosures and other evidence, the police secured a warrant for the apartment where Adams had been staying from time to time with Wright, Amanda and Chrissy; In the living room the police found a Kel Tec pistol in a box, along with a plastic bag containing ammunition. In Chrissy’s bedroom, they found a gun magazine on a television top and, under Chrissy’s bed, a lockbox containing both ammunition and a Sturm Ruger with a laser sight.
At trial, Adams himself admitted to the robberies including the theft of drugs from Morales but denied that he had at any time possessed the handgun. His story, *111partly corroborated by testimony from Adams’ girlfriend Sarah Blake, was that Laurie had given the two guns to Sarah rather than Adams, and that he had told her where to take them. By this tactic, Adams’ asserted aim, naive if true, was to avoid possessing or appearing to possess a weapon.1
The jury convicted Adams of having had the Sturm Ruger in his possession on March 18, 2002, when the police found it in the apartment. He was also convicted of using a firearm during and in relation to the Morales robbery on February 6, 2002. On the third count, relating to the Frazier robbery on February 12, 2002, the jury acquitted Adams. Adams was thereafter sentenced to 120 months for firearms possession and 84 months (to be served consecutively) for using the gun during the Morales drug robbery. Adams now appeals.
Adams’ first argument on appeal is that the district court committed error by allowing Chrissy to testify that she and Adams had a sexual relationship. He points out that he, a 33-year-old African-American male, was said to have an interracial relationship with a girl who was 15 at the time, and that a jury might also have conceived that he was guilty of statutory rape. The potential for prejudice, he says, substantially outweighed whatever slight relevance the sexual relationship testimony might have had.
Evidence must be excluded where its relevance is “substantially outweighed” by its prejudicial effect, that is, by its tendency to encourage the jury to decide the case on improper grounds. See Fed.R.Evid. 403 and advisory committee note; Old Chief v. United States, 519 U.S. 172, 180, 117 S.Ct. 644, 136 L.Ed.2d 574 (1997). Probative value and prejudicial effect are both matters of degree, United States v. Li, 206 F.3d 78, 84 (1st Cir.2000), and whether the government has alternative means of effectively proving the same thing without the prejudicial evidence is also pertinent. See Old Chief, 519 U.S. at 184, 117 S.Ct. 644; United States v. Varoudakis, 233 F.3d 113, 122 (1st Cir.2000).
Trial judges enjoy great latitude in making these balancing decisions (often under time pressure) and are normally overturned only where their judgment is egregiously wrong. See United States v. Rodriguez, 162 F.3d 135, 142 (1st Cir.1998). Many such decisions are simply close calls on which able judges may differ. The trial judge had the advantage in being on the spot and having a better sense than the appellate court of the courtroom dynamics in the case. See Udemba v. Nicoli, 237 F.3d 8, 15-16 (1st Cir.2001); United States v. Rodriguez-Estrada, 877 F.2d 153, 156 (1st Cir.1989).
Generalities about deference carry us only to the starting line. Here, the government says that the evidence of the sexual relationship was relevant for two reasons. The first is to support a link in the chain of evidence connecting Adams with the Sturm Ruger so as to prove his possession of the weapon pursuant to count I. Because the gun was in a lockbox under Chrissy’s bed, the fact that Adams had a sexual relationship with Chrissy tended to increase the likelihood that he spent time in that bed, supporting the inference that he put the lockbox there and controlled it.
*112There is one gliteh. Several witnesses testified without, objection that Adams slept in Chrissy’s bed, so the added information that they had a sexual relationship was of peculiarly limited value. The sexual relationship arguably made the same-bed story more credible and perhaps increased the likelihood that he viewed the bed as his own, but these reinforcing inferences — although making the evidence technically relevant — are hardly of great value.
The second argument for relevance, and apparently the one that prompted the ruling admitting the evidence (although we can affirm the admission of evidence on any valid basis, see United States v. Meserve, 271 F.3d 314, 327 (1st Cir.2001)), requires more background. When Adams testified he gave a (in some measure) more benign version of his encounter with Morales charged in count II. Adams said that he had gone to beat up Morales because Morales, who worked in the same restaurant as Chrissy, had been trying to give her drugs in order to seduce her and that he, Adams, had been seeking to protect her. Other defense cross-examination sought to support this supposed motive for the assault.
Arguing that the defense had sought to cast Adams as a gentleman-protector of the innocent, the government then sought leave to bring out through Wright (who had been cross-examined about Adams’ aspersions on Morales) that Adams had a sexual relationship with Chrissy. Thereafter, the government also got confirming testimony as to the sexual relationship from Chrissy herself. In both cases, the defense objected to the testimony but did not seek a limiting instruction as to the use of the testimony.
Of course, the government was entitled to discredit Adams’ story since he was denying that he had gone with the intention of robbing Morales of drugs;2 but it is not clear why Adams’ sexual relationship with Chrissy would make it less likely that he would be interested in attacking Morales as a would-be seducer. Perhaps the evidence had a slight tendency to counter Adams’ insinuation that he had attacked Morales for high-minded motives (he called himself her “guardian”) and so discredit further Adams’ denial of a plan to steal drugs.
Thus, we have two arguments for relevance; both may work and can be treated as cumulative justification, but in neither is the added information necessary or even very useful. As for prejudice, there was obviously some potential for prejudicing the jury by telling them that Adams had seduced a 15-year-old girl, but it should not be overstated. The jury already knew from other testimony that Adams slept in Chrissy’s bed and that they had sometimes slept in the bed at the same time. How much explicit confirmation of the sexual relationship added may be open to doubt.3
*113This is a perfect example of why district judges have latitude. Viewed in the cold light of post-trial reflection, the judges on this panel might well have excluded the sexual relationship evidence. But we have the advantage not only of ample time to reflect but also of all of the trial testimony. It is much easier now to put together all the pieces, see the full strength of the government’s case, and reflect on just how little the disputed testimony added. In this case, the trial judge’s call, although debatable, was not an egregious error.
Even if we found a violation of Rule 403, we would regard any error as harmless because this evidentiary ruling could not have affected the outcome. See United States v. McCann, 366 F.3d 46, 55-56 (1st Cir.2004). At least eight different witnesses testified that they had seen Adams in possession of a gun, usually one with a laser sight. This made almost beside the point Adams’ already thin story that his wife and Sarah Blake alone controlled the weapon while it resided in the lockbox under Chrissy’s bed. The idea that the jury would ever have acquitted Adams on the felon-in-possession charge is hard to take seriously.
As for Adams using the gun during the drug robbery of Morales, two witnesses (Morales and his girlfriend) testified to seeing him use it and a third (Wright) testified to Adams’ admission that he used it. And a bullet, shown by expert evidence to have been earlier loaded in the Sturm Ruger, was found in the motel room— supporting Morales’ claim that he had been hit with the gun by Adams. Three separate witnesses, the bullet, and Adams’ prior control of the gun made the conviction almost inevitable.
Adams relies heavily upon United States v. Aguilar-Aranceta, 58 F.3d 796 (1st Cir.1995), and Gov’t of the Virgin Islands v. Archibald, 987 F.2d 180 (3d Cir.1993). Both decisions reversed district court convictions where prejudicial evidence of slight probative value was admitted. But in both cases the incremental prejudicial effect of the disputed evidence was stronger and in neither case does it appear that untainted evidence of guilt virtually assured a conviction.
Adams makes two further and quite separate claims on appeal. One is that the felon-in-possession statute that underpins his conviction on count I is unconstitutional. Adams says that because the statute applies only where the weapon traveled in interstate commerce, he would have been safe in Maryland where the gun was manufactured and was convicted here only because of the “fortuity” that he lives in Maine. This, he says, makes the statute irrational under equal protection standards.
In accord with several other circuits, see United States v. Walker, 930 F.2d 789, 795 (10th Cir.1991); United States v. Wynde, 579 F.2d 1088, 1092-93 (8th Cir.1978), we reject this argument. The statute is not keyed to the defendant’s residence in one state rather than another; it applies wherever the gun traveled in interstate commerce. Adams could also have been convicted if he lived in the state of manufacture so long as the gun had been shipped out of the state and then brought back in. About all one can say is that a felon who lives in a gun manufacturing state has a better chance of avoiding violation.
Admittedly, odd results are possible: a felon who brought a Sturm Ruger in Maryland and kept it there is not intrinsically less dangerous than Adams. But travel of the gun in interstate commerce was the jurisdictional hook available to Congress and the prohibition on felons having guns is rational. See Lewis v. United States, *114445 U.S. 55, 65-66, 100 S.Ct. 915, 63 L.Ed.2d 198 (1980) (discussing 18 U.S.C.App. § 1202(a)). That Congress left unremedied like problems beyond its ready grasp does not make the statute irrational under equal protection standards. See Packer Corp. v. Utah, 285 U.S. 105, 110, 52 S.Ct. 273, 76 L.Ed. 643 (1932) (Brandeis, J.); Dunagin v. City of Oxford, 718 F.2d 738, 753 (5th Cir.1983).
Adams’ other argument is that the fruits of the search of the WhitmoreWright apartment should have been suppressed for lack of probable cause for the warrant. Wright’s statements to the officer, recounted in the warrant affidavit, described Adams’ role in the set of robberies recounted above and identified just where Adams’ Sturm Ruger was hidden in the apartment. The affidavit also noted Adams’ prior criminal record, a report by Laurie to the police that the guns had been taken, and information tending to confirm Adams’ participation in drug dealings (a police report) and a drug-related robbery (a witness interviewed by the officer).
This assemblage supplies several times over probable cause to believe that evidence of a felony (the gun) would be found in the apartment. Adams’ attacks on details and small discrepancies are not worth discussion. See United States v. Schaefer, 87 F.3d 562, 567 (1st Cir.1996). He has received vigorous and thorough assistance of counsel on this appeal, and no judge should begrudge the time needed to consider arguments by a man now serving a sentence of 204 months. That does not mean that proportionate time is needed to explain why the weakest of the arguments fails.
Affirmed.