
582 F.3d 827 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Tracy A. CARSON, Defendant-Appellant.
No. 08-3625.
United States Court of Appeals, Seventh Circuit.
Argued May 6, 2009.
Decided October 6, 2009.
*829 Gayle Helart, Attorney (argued), Office of the United States Attorney, Indianapolis, IN, for Plaintiff-Appellee.
Gabriel B. Galloway, Attorney (argued), Oklahoma City, OK, for Defendant-Appellant.
Before EASTERBROOK, Chief Judge, and POSNER and WOOD, Circuit Judges.
WOOD, Circuit Judge.
Tracy Carson is a bank robber who, in April 2007, held up and robbed an Indianapolis branch of Chase Bank. Following a tip from an informant and an independent investigation, the police obtained a search warrant and arrested Carson at a local hotel. In the face of the damning evidence seized at the hotel, including more than $100,000 in cash wrapped in Chase Bank straps and stamped with information particular to the robbed facility, latex gloves, a firearm, cocaine, and marijuana, Carson immediately confessed to the robbery. He was later charged with, and convicted of, armed bank robbery, in violation of 18 U.S.C. § 2113(a) & (d), brandishing a firearm, in violation of 18 U.S.C. § 924(c)(1)(A)(ii), and being a felon in possession of a firearm, in violation of 18 U.S.C. §§ 922(g) & 924(e).
On appeal, Carson's primary argument is that evidence critical to his conviction should have been suppressed because probable cause did not support the issuance of the search warrant. In the alternative, he asserts that the affidavit supporting the application for the warrant contained material false statements. Finally, he argues that his confession should have been suppressed because the large quantities of drugs and alcohol that he ingested prior to his arrest and confession invalidated his waiver of his Miranda rights. We conclude that the district court correctly refused to suppress both the evidence and the confession, and we thus affirm its judgment.

I
At a little after one o'clock in the afternoon of April 25, 2007, a robber, later identified as Carson, entered a Chase Bank branch at 7001 South Madison Avenue in Indianapolis. Carson was wearing a mask over his face and latex gloves on his hands, and was carrying a firearm. He made away with more than $120,000. Indiana State Police learned of the robbery later that evening when, at around 11:15, an informant gave Sergeant Dean Wildauer and Detective Ronnie Shoemaker extensive information about the robbery. The informant's report included the following details: a bank robbery had occurred on the south side of Indianapolis; the robber's name was Tracy; Tracy was a white male between the ages of 35 and 38 and was approximately six feet tall; Tracy was at a hotel that had a swimming pool in the guest room; the room went for $500 per night; Tracy was accompanied by a woman named Amanda; he possessed money that the informant estimated as at least $100,000 (based on the informant's observation of Tracy's counting the money); Tracy also had a handgun, narcotics, and cocaine; Tracy and Amanda had been *830 dropped off at the hotel; and the hotel was located at 21st and Post Streets, on the east side of Indianapolis. While Sergeant Wildauer was aware that the Sybaris Hotel in Indianapolis had swimming pools in the rooms, he did not know of any such hotel located at 21st and Post. Sergeant Wildauer asked the informant to check his information, and the informant promptly confirmed that the hotel was indeed the Sybaris.
With this information in hand, Sergeant Wildauer contacted the FBI bank robbery detail and spoke with Agent Bervin White, who confirmed that a Chase Bank located at Southport Road and Madison Avenue in Indianapolis had been robbed on April 25, 2007, by a white male meeting the description Sergeant Wildauer had been given. Agent White also told Sergeant Wildauer that the robber was carrying a gun and had stolen approximately $125,000 from the bank. Sergeant Wildauer and Detective Shoemaker then went to the Sybaris Hotel and learned that a woman named Charlotte Ruby had rented Suite 12 for two people, Tracy Carson and Amanda Johnson, and that Carson and Johnson had both signed a waiver and release form. The officers also learned that the room was paid for in cash and had been rented for two nights.
After returning to the police station, Sergeant Wildauer ran a background check on Carson and learned that he had prior convictions for bank robbery, two handgun violations, and grand larceny and escape convictions. Sergeant Wildauer also discovered that Carson had an outstanding warrant from Marion County for possession of a controlled substance and public intoxication. Detective Shoemaker again contacted FBI Agent White, who advised him that the FBI had identified Carson as a suspect in a bank robbery within the previous twelve months. Sergeant Wildauer then memorialized all this information in an affidavit, and, at 3:34 a.m. on April 26, 2007, obtained a state search warrant for Suite 12 of the Sybaris Hotel; the warrant authorized the police to look for and seize Carson, the fruits of the bank robbery, and narcotics.
Warrant in hand, the police arrived at the Sybaris about an hour later. In Suite 12, they found Carson, Johnson, approximately $106,000 wrapped in straps with stampings from the victimized Chase Bank branch dated April 24, 2007, along with latex gloves, a firearm, cocaine, and marijuana. Officers also noted that a tall, gallon-sized bottle of vodka was in the room and had been opened, though very little appeared to have been consumed. After the room was secured, Sergeant Wildauer read Carson his Miranda rights. Carson immediately responded, "This is mine. It's all mine. She's [meaning Johnson] got nothing to do with it." Approximately 30 minutes later, Agent Eric Jensen of the federal Bureau of Alcohol, Tobacco, Firearms and Explosives again advised Carson of his Miranda rights. This time Carson said, "Yeah, been there." Carson did not sign the waiver form, purportedly because by that time he had been handcuffed.
But Carson then admitted that he had robbed the Chase Bank in question of $130,000, that he knew that his possession of the firearm made him an armed career criminal for the purposes of the Armed Career Criminal Act ("ACCA"), 18 U.S.C. § 924(e), and that he was facing a virtual life sentence. Carson described the clothes he wore during the robbery, mentioning his jeans, Nike tennis shoes, gloves, and mask. Carson confessed that he carried a .45 caliber handgun in the bank. He said that he bought the gun on the street and that it was not stolen (this was later confirmed). Carson recounted that he had driven to the target bank in a red Chrysler LeBaron that he had bought *831 for $250. Carson also revealed that on two prior occasions he had robbed the Chase Bank branch at Hanna and Keystone Avenues, obtaining $23,000 and $29,000, and also had attempted to rob a particular credit union. Carson recalled that the credit union attempt was unsuccessful because the employees shut him out using an automatic door system when they saw him approaching wearing a mask. Agent Jensen later corroborated this information.
Carson declined to answer any questions implicating anyone else or divulging his methodology. He explained that bank robbery methods are learned in prison and passed around confidentially, "sort of like a trade secret." Remarkably, he commented that he did not want to "screw it up" for anyone else in the bank robbery trade. The interview lasted for somewhere between 30 and 60 minutes, during which time Carson had to excuse himself at least twice to go to the restroom to vomit. Agent Jensen later testified that Carson walked normally, that he did not sit or fall during the interview, and that his speech and memory appeared to be clear, given his ability to offer a coherent account of the events relating to the robberies and to provide responsive answers.
Following Carson's arrest and indictment, he was provided with a supplemental case report. The supplemental report indicated that the information that Sergeant Wildauer and Detective Shoemaker had about Carson's whereabouts had not actually come from the informant directly, but instead had come from an unknown third party who first had conveyed these details to the informant. In light of this revelation, Carson filed two motions to suppress. The motions took the position that the district court should suppress the evidence obtained through the search warrant because the warrant application failed to demonstrate the reliability of the person upon which the officers actually relied (that third party who was the original source), that the issuing magistrate judge was misled by material omissions in the warrant, and that Carson had been incapacitated while he was being questioned by officers and therefore had been incapable of knowingly waiving his Miranda rights.
Following a hearing, the district court denied both motions. The court found that the affidavit in support of the search warrant contained enough information to support probable cause, that Sergeant Wildauer had not deliberately omitted anything from his affidavit, and that Carson was not too impaired to give an effective waiver of his Miranda rights.

II

A
We consider first Carson's argument that the district court erred by denying his motion to suppress the evidence seized in the search of Suite 12 at the Sybaris Hotel. When a search is executed pursuant to a facially valid warrant, we review a district court's findings of historical fact for clear error and its legal conclusions de novo. United States v. Garcia, 528 F.3d 481, 485 (7th Cir.2008). With respect to the question whether the facts add up to probable cause, while we give no special weight to the district court's decision, we give great deference to the conclusion of the judge who issued the warrant. United States v. McIntire, 516 F.3d 576, 578 (7th Cir.2008).
Probable cause is established when, based on the totality of the circumstances, the affidavit sets forth sufficient evidence to persuade a reasonably prudent person that a search will uncover evidence of a crime. Illinois v. Gates, 462 U.S. 213, 238, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983). If an affidavit is the only evidence presented *832 to the judge in support of a search warrant, and the issuing judge hears no live testimony, the validity of the warrant depends on the strength of the affidavit. United States v. Peck, 317 F.3d 754, 755 (7th Cir.2003). Where an informant supplies the information contained in the affidavit, this court considers several factors: first, "the extent to which police have corroborated the informant's statements"; second, "the degree to which the informant has acquired knowledge of the events through firsthand observation"; third, the amount of detail in the affidavit; and fourth, the interval between the time of the events that gave rise to the need for a search warrant and that of the police officer's application for the warrant. United States v. Koerth, 312 F.3d 862, 866 (7th Cir.2002). We also take into account whether the informant testified at the probable cause hearing. Peck, 317 F.3d at 756. None of these factors is determinative; "a deficiency in one factor may be compensated for by a strong showing in another or another indicator of reliability." United States v. Brack, 188 F.3d 748, 756 (7th Cir.1999).
Carson argues that the affidavit in his case did not establish probable cause, because it provided no way to assess the reliability of the underlying source and there was no indication that the informant's report was based on first-hand observations. The conclusory statement in the affidavit to the effect that the informant was a "reliable source" was, Carson argues, insufficient. In our view, Carson has missed the forest for the trees. We assess the affidavit as a whole. While Carson is correct that it did not say that the informant's information was the result of first-hand observations, the affidavit was ultimately sufficient to support the determination of probable cause.
In the first instance, the affidavit reported that the informant identified Carson by name, described his appearance, pinpointed where he was located, described the appearance of Carson's hotel room, named the woman with whom Carson was sharing the room, specified that he had seen the amount of money Carson had in his possession, said that Carson was in possession of a gun and drugs, and stated that Carson was a convicted bank robber. In addition, the affidavit outlined the independent efforts the police took to corroborate the information provided by the informant, including the fact that a bank robbery had occurred at the location identified by the informant, the appearance of the robber, the amount of money the robber had stolen, that Suite 12 of the Sybaris Hotel was occupied by Carson and Johnson (just as the informant had said), that their room came equipped with a personal swimming pool, that Carson had a prior conviction for bank robbery, and that Carson had outstanding arrest warrants for possession of a controlled substance. Finally, the time between the robbery (1:00 p.m. on April 25), the conversation with the informant (11:15 p.m. the same day), and the application for the warrant (3:34 a.m. on April 26) was minimal. The police also wasted no time executing the warrant: they arrived at Carson's room at 4:30 a.m. on April 26.
Carson attempts to counter all of this evidence by claiming that his case is just like Koerth, supra, in which we found probable cause to be lacking. 312 F.3d at 868. Koerth, however, is readily distinguishable. In Koerth, the supporting affidavit failed to explain the extent to which the informant had previously provided information leading to arrests or prosecutions. Indeed, the affidavit was devoid of detail, and the police failed to check out any of the information provided. Id. at 868. As we have already recounted at length, Carson's case could not be more different. In addition to the particulars we have already mentioned, the affidavit stated that the informant was reliable and *833 had previously provided accurate information leading to arrests on five separate occasions. Finally, the affidavit described the extensive efforts undertaken by the police to corroborate the informant's account. We have no trouble concluding that this affidavit supported the issuing judge's finding of probable cause for the warrant.
We have not overlooked the fact that the law also permits a challenge to an affidavit on the basis that material facts were omitted, where that omission was made intentionally or with reckless disregard for the truth. Franks v. Delaware, 438 U.S. 154, 155-56, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978); United States v. Sims, 551 F.3d 640, 645 (7th Cir.2008). Carson argues that, had the affidavit specified that the informant's tip that Carson could be found at the Sybaris Hotel came from an unidentified third party, no judge would have found the informant reliable and probable cause would have been lacking. Once again, we do not attach such great significance to that one detail. Even if the informant had not identified the hotel, there would have been enough information in the affidavit to establish probable cause to search Carson's room there. Sergeant Wildauer stated in the affidavit that he independently identified the Sybaris Hotel based on the informant's description, because the Sybaris is the only hotel in Indianapolis with in-room swimming pools. Moreover, the affidavit notes that the police did not blindly rely on the informant's word. Instead, they personally visited the hotel, requested the names of the hotel guests, and confirmed that Carson was there. There is no reason to conclude that the omission of the original source of the name of the Sybaris Hotel was made knowingly or with reckless disregard for the truth.
Nor was this omission material. Even if the informant's original source had been disclosed, we do not see a reasonable probability that the results of the proceeding before the issuing judge would have been different. Sims, 551 F.3d at 645. The issuing judge properly found probable cause on the basis of adequate information. The omission of the fact that the name of the hotel where Carson was arrested initially came from an independent third source, and not the informant, does not detract from this finding.

B
Carson also argues that his April 26 confession should have been suppressed pursuant to Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966), and Missouri v. Seibert, 542 U.S. 600, 124 S.Ct. 2601, 159 L.Ed.2d 643 (2004). A defendant may waive her Miranda rights only if that waiver was made "voluntarily, knowingly and intelligently." Moran v. Burbine, 475 U.S. 412, 421, 106 S.Ct. 1135, 89 L.Ed.2d 410 (1986). This court has held that a confession is voluntary if, under all the circumstances, it is the "product of a rational intellect and free will and not the result of physical abuse, psychological intimidation, or deceptive interrogation tactics that have overcome the defendant's free will." United States v. Dillon, 150 F.3d 754, 757 (7th Cir.1998). A finding that the police engaged in coercive activity is an essential predicate to a finding that a suspect's confession was involuntary. See Colorado v. Connelly, 479 U.S. 157, 167, 107 S.Ct. 515, 93 L.Ed.2d 473 (1986). We determine whether police coerced a suspect by examining things like "the defendant's age, education, intelligence level, and mental state; the length of the defendant's detention, the nature of the interrogations; the inclusion of advice about constitutional rights; and the use of physical punishment, including deprivation of food or sleep." United States v. Huerta, 239 F.3d 865, 871 (7th Cir.2001). When *834 the interrogating officers should reasonably have known that a suspect was under the influence of drugs or alcohol, "a lesser quantum of coercion may be sufficient to call into question the voluntariness of the confession." United States v. Haddon, 927 F.2d 942, 946 (7th Cir.1991).
Carson asserts that his confession was not voluntary because he had "overdosed on heroin . . . [and] other mind-altering substances" when the officers administered his Miranda rights. According to Carson, he had imbibed an astonishing amount of liquor: since noon on the day of his arrest, he had drunk three-quarters of a fifth of whiskey, a fifth of vodka, and half a bottle of champagne. As if that were not bad enough, he had also been using heroin and cocaine in tandem throughout the day. Carson elaborates that he had overdosed during the night of his arrest; he was so high that at one point he was crawling on all fours in the hotel room; he was vomiting; he continuously nodded off and woke up; he could not remember when the police came into the hotel room; his state of mind was "like a retarded kid" when he was talking to police officers; and he did not remember receiving his Miranda warnings. Carson argues that the officers must have known about his incapacitated state because he vomited a couple of times during the interrogation and there was cocaine on the table in the hotel room where he was arrested.
Just as in United States v. LeShore, 543 F.3d 935, 941 (7th Cir.2008), Carson is confronted by a threshold problem: the standard of review. The district court specifically found that Carson was alert and coherent, never complained about great pain, was given aspirin when he requested it, and gave no indication that he was seriously sleep-deprived or drug-induced at the time of the interrogation. Further, while Carson testified at the suppression hearing that he had injested copious amounts of alcohol, cocaine, and heroin, the district court was negatively impressed with this story for a number of reasons. First, the court found that Carson was cognizant enough of his whereabouts to order a battery charged for his electric shaver just before the police arrived. Second, both Carson and the police officers involved in his arrest testified that Carson's first reaction to the police entry into his room was the entirely rational thought that his gun possession would heighten any penalty he received for the bank robbery. Third, Carson commented to the police that he realized that if he were convicted for bank robbery, he would qualify for a heightened sentence under the ACCA. Fourth, Carson told the police that he knew that any statements he made about the bank robbery would not affect his probable life sentence. Fifth, Carson told the police that the gun and drugs were his alone in an effort to protect Johnson. Sixth, during the course of the interview, Carson chose to answer some questions and not others, because he said that he did not want to incriminate the people from whom he had purchased the gun and a stolen car. Finally, as we mentioned earlier, Carson told the police that he would not reveal the "trade secrets" of bank robbers because it was not appropriate to do so.
Based on these findings, the district court found that Carson's testimony about the crippling degree of his intoxication was incredible. If Carson was not under any influence that would diminish his capacity, there is no circumstance that would lead us to question the validity of his Miranda waiver, under any standard of review.
The judgment of the district court is AFFIRMED.
