
500 F.3d 629 (2007)
UNITED STATES of America, Plaintiff-Appellee,
v.
Saleem LAKE, Defendant-Appellant.
No. 05-4797.
United States Court of Appeals, Seventh Circuit.
Argued October 30, 2006.
Decided September 5, 2007.
*630 April M. Perry (argued), Office of the United States Attorney, Chicago, IL, for Plaintiff-Appellee.
Michael A. Duffy (argued), Kirkland & Ellis, Chicago, IL, for Defendant-Appellant.
Before KANNE, ROVNER, and WILLIAMS, Circuit Judges.
*631 ROVNER, Circuit Judge.
A jury convicted Saleem Lake of possessing crack cocaine with intent to distribute, see 21 U.S.C. § 841(a)(1), possessing a firearm as a felon, see 18 U.S.C. § 922(g)(1), possessing a firearm with an altered serial number, see 18 U.S.C. § 922(k), and possessing a firearm in relation to drug trafficking, see 18 U.S.C. § 924(c)(1)(A). He was sentenced to twenty years' imprisonment. On appeal Lake argues that the district court erred in denying his motion to suppress evidence, and that the government did not prove beyond a reasonable doubt that Lake possessed crack. We affirm.

I.
In September 2004, a "concerned citizen" informed Chicago police officer Stephen Del Bosque that he had known Saleem Lake for at least ten years, that Lake sold "rock," or crack, out of his apartment, and that he had bought crack from Lake the previous evening. The informant specified that Lake took the crack from a particular dresser drawer in his bedroom and that he saw a black pistol inside that drawer. He then drew a diagram of Lake's apartment and highlighted where Lake kept the contraband. Officer Del Bosque and another officer drove past Lake's apartment to confirm that the exterior matched the informant's description. It did, and Officer Del Bosque requested that an Illinois state-court judge sign a search warrant, which she did after listening to sworn statements from Officer Del Bosque, two other officers, and the informant. Upon executing the warrant, the officers found drugs and a gun, and they arrested Lake. In February 2005, the grand jury indicted Lake on the four previously-mentioned charges; he pleaded not guilty.
Before trial Lake moved to suppress the gun and drugs found in his bedroom, arguing that the search warrant was not based on probable cause. The district court held a hearing on Lake's motion. At the hearing, the government called two witnesses: the officer who obtained the warrant and the state-court judge who issued it. Officer Del Bosque testified that the informant told officers that Lake sold crack from his apartment and the informant specified the location of the drugs. Officer Del Bosque also testified to meeting with the state-court judge, other officers, and the informant to secure a search warrant. According to Officer Del Bosque, the judge only signed the warrant after swearing in and questioning both the informant and the officers. For her part, the state-court judge testified that, although she could not remember this particular warrant, her general practice was to speak with the officers as well as the individual supplying information for the warrant and to have all parties sign the warrant. She also testified that she always questioned informants who appeared before her. When asked why the warrant in this case was not signed by the informant, the judge admitted that she had made a mistake.
Lake began by calling the informant to the stand, but, asserting his Fifth Amendment privilege against self-incrimination, the informant refused to answer questions. The district court asked the government whether it would grant immunity to the informant, but the government refused because, it argued, the officers were available as witnesses and the only relevant question was whether the officers reasonably believed the informant's statements. Additionally (as we discuss below), the government had reason to doubt the veracity of the informant's testimony. Agent Raphael Uribe of the Bureau of Alcohol, Tobacco, and Firearms next testified that during a July 2005 meeting with an assistant U.S. attorney and various others, the informant changed his initial story. He *632 denied having told police that he bought crack from Lake and that he had seen a gun in Lake's apartment. But on cross-examination, Agent Uribe also testified that the informant apparently was beaten up after he told police about Lake's illegal activities. The government suggested that the beating may have affected the informant's willingness to cooperate.
Lake then renewed his motion to suppress the gun and drugs found in his bedroom. The district court acknowledged that the circumstances surrounding the issuance of the warrant were somewhat troubling because the informant changed his story and then asserted his Fifth Amendment rights, giving Lake no opportunity to cross-examine him, and because the state-court judge could not explain why the informant had not signed the warrant. Nonetheless, the district court found that the officers reasonably relied on the informant's statements and that a reasonable judicial officer would have found probable cause given the evidence presented to her.
The government charged Lake with possessing crack, which carries higher penalties than other forms of cocaine, so at trial it had to specifically prove that Lake possessed crack. To this end, the government called four witnesses. Both a forensic scientist who specialized in analyzing controlled substances and a forensic chemist testified that the "white rocky substance" found in Lake's bedroom tested positive for cocaine base. On cross-examination, the chemist admitted that Lake's drugs did not contain sodium bicarbonate (baking soda), which is often used to prepare crack. But he explained that a person could produce crack without leaving traces of sodium bicarbonate in the finished product. Next, a lieutenant from the Drug Enforcement Administration testified that the drugs found in Lake's possession were crack. Finally, a self-described "crack-head" testified that Lake gave him crack "from time to time."
At the close of trial in July 2005, the jury found Lake guilty on all counts. The jury also returned a special verdict finding that Lake possessed crack. In November 2005, the district court sentenced Lake to a total of twenty years' imprisonment.

II.
On appeal Lake advances three arguments: (1) the district court should have granted his motion to suppress the gun and drugs found in his bedroom, (2) the government violated his due process rights by refusing to grant immunity to the informant, and (3) the government did not prove beyond a reasonable doubt that the drugs were crack.

A.
Lake claims that the gun and drugs should have been suppressed because the search warrant used to enter his apartment was not supported by probable cause. We review the denial of a motion to suppress de novo for questions of law, but for clear error as to questions of fact. See United States v. Shoals, 478 F.3d 850, 852 (7th Cir.2007). The district court's probable cause determination is reviewed de novo. See United States v. Spry, 190 F.3d 829, 835 (7th Cir.1999). Probable cause for a search warrant exists where the known facts and circumstances are sufficient for a reasonably prudent person to form the belief that contraband or evidence of a crime will be found. See United States v. Olson, 408 F.3d 366, 370 (7th Cir.2005).
The known facts and circumstances in this case support a finding of probable cause. The informant told police that he had bought drugs from Lake in Lake's apartment the previous evening. *633 He also drew a diagram of the apartment and specified exactly where Lake kept the drugs. Officers then drove past Lake's apartment and verified the accuracy of at least some of the information the informant gave them. As an initial matter, the level of detail provided by the informant supports the probable cause finding. See United States v. Brack, 188 F.3d 748, 756 (7th Cir.1999). Additionally, the informant's admission that he had purchased crack is a statement against his penal interest and thus a weighty factor in establishing probable cause even if the statements have not been proven reliable. See United States v. Brown, 366 F.3d 456, 459-60 (7th Cir.2004). Lake makes much of the fact that this informant was previously unknown to police, but he had bought the crack from Lake the night before he spoke to police and, given the recency of the purchase, it was reasonable for the police to rely on his statements. Compare United States v. Harju, 466 F.3d 602, 603, 609-11 (7th Cir.2006) with Owens v. United States, 387 F.3d 607, 608 (7th Cir.2004). Finally, although the informant later changed his story, the validity of a warrant is judged on the basis of information available at the time the warrant was issued. See Maryland v. Garrison, 480 U.S. 79, 84-86, 107 S.Ct. 1013, 94 L.Ed.2d 72 (1987); United States v. White, 416 F.3d 634, 637-38 (7th Cir.2005).
The district court's probable cause finding was further supported by the fact that the informant was presented to the state-court judge before the warrant was issued, and the judge had the opportunity to assess his credibility. According to her testimony at the suppression hearing, the state-court judge's practice was to require officers and the informant to appear personally before her for questioning before she issued warrants. The judge's testimony was supported by Officer Del Bosque, who also described meeting with the judge, informant, and other officers to acquire the search warrant. Additionally, even though the informant later disavowed telling officers that he saw drugs in Lake's apartment, according to Agent Uribe's testimony, the informant acknowledged having met with the state-court judge and officers on the night the search warrant was signed, and the state-court judge testified that she always questioned informants who came before her. Accordingly, there was enough evidence to support a finding that the judge assessed the informant's credibility, which is an important factor in determining whether probable cause is established on the basis of an informant's tip. See United States v. McGaughy, 485 F.3d 965, 970 (7th Cir.2007). Because there was probable cause for the warrant, the district court properly denied Lake's motion to suppress.

B.
Lake next argues that the government's refusal to grant immunity to the informant during the suppression hearing prevented him from challenging whether probable cause existed for the search warrant, thus depriving him of due process. We will not review decisions regarding immunity unless substantial evidence shows that the government's action was a clear abuse of discretion that violated the due process clause. See United States v. Schweihs, 971 F.2d 1302, 1315 (7th Cir. 1992). Prosecutors have significant discretion to decline immunity to a witness, especially when it is likely that the witness will perjure himself. See, e.g., United States v. Burke, 425 F.3d 400, 411 (7th Cir.2005); United States v. Hooks, 848 F.2d 785, 802 (7th Cir.1988). In this case, the informant initially told the officers that he had seen drugs in Lake's apartment, but later retracted his statements. Not surprisingly, the government doubted that the informant's testimony would be truthful, and the government's "refusal to absolve witnesses *634 of their responsibility to testify truthfully does not impermissibly distort the fact-finding process." Burke, 425 F.3d at 412. We therefore conclude that Lake's due process rights were not violated by the government's decision not to grant immunity.

C.
Finally, Lake argues that the government did not prove beyond a reasonable doubt that he possessed crack. The jury that convicted Lake found that the substance was crack, and we will overturn that determination only if the record contains no evidence from which a rational jury could have returned the finding. See United States v. James, 464 F.3d 699, 705 (7th Cir.2006). In this case, in addition to the chemist and forensic scientist who testified that the substance contained cocaine base, a DEA lieutenant and, perhaps more importantly, a former crack user identified the drugs as crack. See United States v. Bradley, 165 F.3d 594, 595-96 (7th Cir. 1999) ("[T]hose who smoke, buy, or sell this stuff are the real experts on what is crack."). Lake cites United States v. Edwards, 397 F.3d 570, 572 (7th Cir.2005), to argue that the drugs found in his possession could not be crack because they did not contain sodium bicarbonate, but Lake misreads our precedent. Although we observed in Edwards that crack is "the street name for a form of cocaine base, usually prepared by processing cocaine hydrochloride and sodium bicarbonate, and usually appearing in a lumpy, rocklike form," id. (emphasis added), we did not mandate that a substance must contain those ingredients to be crack. We have previously held that the testimony of both a forensic chemist and a veteran police officer is sufficient proof that a substance is crack. See United States v. Buchanan, 362 F.3d 411, 413 (7th Cir.2004); United States v. Linton, 235 F.3d 328, 329-30 (7th Cir.2000). Accordingly, we conclude that the testimony of the officer and others in this case constituted enough evidence for a rational jury to conclude that Lake possessed crack.

III.
For the reasons stated above, the judgment of the district court is AFFIRMED.
