WOLLMAN, Circuit Judge.

This appeal from an order suppressing evidence raises issues regarding the omission from a search warrant affidavit of information allegedly relevant to the judicial officer's determination of the reliability of the informants, and thus of the existence of probable cause.

Kirk C. Reivich was charged with possession with intent to distribute cocaine, see 21 U.S.C. § 841(a)(1) (1982), after police seized a large quantity of that drug and a substantial sum of money during a search of his alleged residence. The warrant authorizing the search had been based upon the identification of Reivich as a drug source by two persons who had just been arrested on drug charges. Reivich moved to suppress the evidence seized during the search, and the district court, citing the lack of assurances of reliability or of corroboration regarding the tip provided by the informants, granted the motion. United States v. Reivich, 610 F. Supp. 538 (W.D.Mo. 1985). The district court particularly asserted that the judicial officer issuing the warrant might have had greater doubts about the reliability of the identification of Reivich had the affidavit revealed that the informants spoke in response to promises of more lenient treatment regarding their arrests. Id. at 544. We reverse and remand.

The affidavit upon which the Reivich search was based set forth essentially the following information:

On the afternoon of August 30, 1984, Creg Burns engaged in a drug transaction in Johnson County, Kansas, with a confidential police informant. Police then followed Burns and a companion, Thomas Linsin, to the area of 59th Street and Troost, Kansas City, Missouri. After losing sight of Burns and Linsin for about thirty minutes, police located them again in Johnson County, Kansas, and arrested them, seizing approximately one ounce of cocaine from Burns' vehicle.

Linsin identified Reivich as the source of the cocaine, provided a phone number, and said that Reivich three days previously had moved to a house in the area of 59th and Troost. Linsin further stated that he had been purchasing cocaine from Reivich for three years, that Reivich had in the past gone to Florida for cocaine and had on one occasion had a pound of cocaine, and that Reivich was never out of cocaine.

Burns separately identified Reivich as the source of the cocaine, provided the same phone number for Reivich, and said that Reivich lived just west of 59th and Troost. Burns told police that about two months previously he had accompanied Reivich to Florida where they had purchased one kilo of cocaine and that Reivich at present had cocaine left and was expecting to obtain a further quantity of cocaine late the next morning.

A police detective determined that the phone number provided by Burns and Linsin was listed to a person residing at 5912 Harrison in Kansas City. A car observed at 7:30 a.m. in the driveway of that dwelling bore a Kansas license plate and was registered to Reivich.

I.

The sufficiency of a search warrant is in the first instance determined on the basis of the information before the issuing judicial officer. See Hunt v. Swenson, 466 F.2d 863, 864 (8th Cir. 1972) (on habeas, citing decision of state supreme court, State v. Hunt, 454 S.W.2d 555, 558 (Mo.), cert. denied, 400 U.S. 942, 91 S.Ct. 239, 27 L.Ed.2d 256 (1970)). On a motion to suppress, a district court should not make a de novo determination of probable cause; rather, the decision to issue the warrant is to be upheld if supported by substantial evidence in the record. Massachusetts v. Upton, 466 U.S. 727, 728, 104 S.Ct. 2085, 2086, 80 L.Ed.2d 721 (1984) (per curiam).

"Probable cause" to issue a search warrant exists when an affidavit sets forth sufficient facts to justify a prudent person in the belief that contraband will be found in a particular place. Illinois v. Gates, 462 U.S. 213, 238, 103 S.Ct. 2317, 2332, 76 L.Ed.2d 527 (1983); see Brinegar v. United States, 338 U.S. 160, 175, 69 S.Ct. 1302, 1310, 93 L.Ed. 1879 (1949). A determination whether probable cause has been established involves a "practical, common sense" evaluation of the "totality of the circumstances." Gates, 462 U.S. at 238, 103 S.Ct. at 2332. When an affidavit is based in substantial part on information from an informant, the informant's reliability, veracity, and basis of knowledge are relevant considerations — but not independent, essential elements — in finding probable cause. Id. at 230, 103 S.Ct. at 2328; United States v. Ross, 713 F.2d 389, 393 (8th Cir. 1983).

The probable cause determination in this case, in contrast to that in Gates and many other cases, does not involve evaluation of a tip from either an anonymous or a confidential informant. Furthermore, since the police had already seized cocaine from Burns and Linsin, the question was not whether a crime was being committed, but only where and by whom. Burns and Linsin obviously had firsthand knowledge of the facts they provided, and their identities and the bases of their knowledge were made clear in the affidavit. The Supreme Court in part specifically adopted the flexible "totality of the circumstances" test for probable cause so that, for example, an informant's clear basis of knowledge could be balanced against, rather than automatically overruled by, that informant's lack of a "track record" of reliability. Gates, 462 U.S. at 233-35, 103 S.Ct. at 2329-30.

The affidavit further was not totally devoid of indicia of reliability. First, Burns and Linsin each made statements against penal interest by admitting past and current drug dealings. See United States v. Harris, 403 U.S. 573, 583-84, 91 S.Ct. 2075, 2081-82, 29 L.Ed.2d 723 (1971). These statements were no less against penal interest because Burns and Linsin had already been arrested. As the Supreme Court reasoned in Harris, "People do not lightly admit a crime and place critical evidence in the hands of the police in the form of their own admissions. * * * That the informant may be paid or promised a `break' does not eliminate the residual risk and opprobrium of having admitted criminal conduct." Id. Statements against penal interest also should not be rigidly parsed into incriminating portions and portions which, because they identify other participants in the criminal acts, might be characterized as constituting mere finger-pointing or bald accusations. The seminal Harris case itself involved a statement by an informant admitting past and current purchases of illicit liquor and identifying the premises at which the transactions took place. 403 U.S. at 584, 91 S.Ct. at 2082. Burns and Linsin similarly admitted to past and current participation in illegal transactions, and we do not believe their credibility is less in that they identified a person or source, rather than a premises, in connection with their drug dealings. The concept of statements against penal interest should not be interpreted narrowly and grudgingly but should be applied consistently with the underlying concern of determining the reliability of tips from informants. See 1 W. LaFave, Search and Seizure § 3.3, at 527-29 (1978). As the District of Columbia Circuit has recognized, a person admitting a crime risks disfavor with the prosecution if he lies to the police: "`[O]ne who knows the police are already in a position to charge him with a serious crime will not likely undertake to divert the police down blind alleys.'" United States v. Davis, 617 F.2d 677, 693 (D.C. Cir. 1979) (quoting 1 W. LaFave, supra, § 3.3, at 528), cert. denied, 445 U.S. 967, 100 S.Ct. 1659, 64 L.Ed.2d 244 (1980).

Second, the information provided by Burns and Linsin was generally corroborated by police investigation. The neighborhood in which Burns and Linsin placed Reivich corresponded to the neighborhood to which the police previously had followed Burns and Linsin; the phone number provided by Burns and Linsin was listed to a residence in that same neighborhood; and police the next morning observed a car registered in Reivich's name parked in the driveway of that residence. Furthermore, the affidavit suggested that Burns and Linsin had independently told consistent stories. The theory connecting reliability and corroboration is that an informant who is correct about some things more likely will be correct about critical unverified facts Spinelli v. United States, 393 U.S. 410, 427, 89 S.Ct. 584, 594, 21 L.Ed.2d 637 (1969) (White, J., concurring), and it is not necessary to a finding of reliability that the corroboration extend to illegal activity as well as to innocent details. United States v. Thompson, 751 F.2d 300, 302 (8th Cir. 1985) (per curiam).

In arguing that these indicia still are not sufficient to show reliability, Reivich and the district court focus, for example, on the fact that Burns and Linsin were neither citizen informants nor informants with established records of reliability and on the fact that the information Burns and Linsin provided did not consist of predictions of future events that were ultimately corroborated by subsequent happenings. Such emphases typify the "excessively technical dissection of informants' tips" and the "judging [of] bits and pieces of information in isolation against * * * artificial standards" against which the Supreme Court cautioned in Gates and Upton. See Upton v. Massachusetts, 466 U.S. 727 at 732, 104 S.Ct. 2085 at 2088, 80 L.Ed.2d 721 (1984). The police knew of the presence of drug traffic because they had found cocaine on Burns and Linsin, and Burns and Linsin had first-hand knowledge of the identity of their own drug source and a tenuous incentive to lie since giving false information could have furthered their trouble with the police. These circumstances were set out in the affidavit with sufficient particularity that the judicial officer's decision to issue the warrant constituted an exercise of independent judgment and was not just a rubber-stamping of conclusory police statements. See Gates, 462 U.S. at 239, 103 S.Ct. at 2332. Granted that Burns and Linsin might not have qualified for an AAA rating on a Dun Bradstreet credibility scale, not having been shown to be Certified Public Informants, their motivation to speak the truth (it being a reasonably safe assumption that self-preservation ranks higher than honor in a drug dealer's hierarchy of values) and their information concerning Reivich were sufficient to support a finding of probable cause. Probable cause requires only a "fair probability," and not a certainty, that contraband will be found at the premises to be searched, and the affidavit here on its face provided a substantial basis for a conclusion that such a probability existed. See id. at 246, 103 S.Ct. at 2336.

II.

A facially sufficient affidavit, however, may be challenged on the ground that it includes deliberate or reckless falsehoods, Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978), and this rule has been extended to allow challenges to affidavits based on alleged deliberate omissions. E.g., United States v. Dennis, 625 F.2d 782 (8th Cir. 1980). Reivich asserts that the affidavit based on Burns' and Linsin's statements was fatally misleading because it did not reveal that, as the district court found, Linsin had cooperated with the police because they agreed to reduce the charge against him from a Class C to a Class E felony (with a promise of probation rather than a jail sentence), they led him to believe Burns was providing information, and they "put him on `a little guilt trip' by describing his family background and explaining to him if he wanted to get off he would have to provide information `now or never.'" Reivich, 610 F. Supp. at 541. In addition, Reivich asserts that the affidavit should have revealed that Burns, while not offered a reduced charge, was told that he could "`better his situation'" by cooperating. Id. The district court apparently concluded that the recklessness of the police in omitting this information could be inferred from the clear importance of knowledge of these "inducements" to an informed decision on probable cause. Id. at 545. Suppression was then required because disclosure "might have" undermined Burns' and Linsin's credibility and because the judicial officer who issued the warrant had been "unable to fully evaluate, on a proper understanding[,] the information provided him in the affidavit." Id. at 544.

Although absent clear error we are bound by the district court's findings of fact regarding the circumstances of Burns' and Linsin's statements, we may reverse if that court's ultimate ruling on suppression reflects an erroneous view of the applicable law. United States v. Lewis, 738 F.2d 916, 920 (8th Cir. 1984), cert. denied, ___ U.S. ___, 105 S.Ct. 1362, 84 L.Ed.2d 383 (1985); United States v. Ross, 713 F.2d 389, 392 (8th Cir. 1983). Adapting Franks to the situation involving omissions from affidavits, Reivich had to show (1) that the police omitted facts with the intent to make, or in reckless disregard of whether they thereby made, the affidavit misleading. United States v. Melvin, 596 F.2d 492, 499 (1st Cir.), cert. denied, 444 U.S. 837, 100 S.Ct. 73, 62 L.Ed.2d 48 (1979); e.g., United States v. Strini, 658 F.2d 593, 597 (8th Cir. 1981) (failure to reveal informant's identity not a false statement within the contemplation of Franks when the omission was intended not to enhance the contents of the affidavit but to protect the informant); and (2) that the affidavit if supplemented by the omitted information would not have been sufficient to support a finding of probable cause. United States v. Stanert, 762 F.2d 775, 782 (9th Cir.), amended, 769 F.2d 1410 (9th Cir. 1985); United States v. Martin, 615 F.2d 318, 328 (5th Cir. 1980); cf. Franks, 438 U.S. at 155-56, 171-72, 98 S.Ct. at 2676, 2684. We conclude that Reivich met neither of these burdens.

First courts have stated, as the district court implicitly found here, that recklessness may be inferred from the fact of omission of information from an affidavit. E.g., Martin, 615 F.2d at 329. Such an inference, however, is warranted only when the material omitted would have been "clearly critical" to the finding of probable cause, id., and existing precedents in fact generally have relied also on additional circumstances in support of their findings of recklessness. For example, in United States v. Rule, 594 F. Supp. 1223, 1340 (D.Me. 1984), order vacated on other grounds sub. nom United States v. Streifel, 781 F.2d 953 (1st Cir. 1986), cited by the district court, the affidavit not only failed to mention that the informant had continued serving as a drug courier contrary to the express instructions of the agents with whom he was working, but also was structured to imply falsely that the informant had come forward voluntarily to give information about the activities of a criminal organization of which he had been a part. The District of Columbia Circuit has suggested that recklessness should be inferred from the omission of information only in the face of flagrant police actions, as when officers take statements out of context or engage in particularly overbearing conduct. United States v. Davis, 617 F.2d 677, 694 (D.C. Cir. 1979), cert. denied, 445 U.S. 967, 100 S.Ct. 1659, 64 L.Ed.2d 244 (1980). In particular, the court made that statement in a case involving an affidavit, as here, based on a tip from an informant who allegedly had been coerced. Although the tactics used, including insinuations that harm might befall the informant's female companion, had not been noted in the affidavit, the court held an inference of recklessness unjustified because, again as here, the informant had spoken against penal interest and the police had made some efforts to corroborate the facts provided. Id.

Second, even if we accept the district court's implicit inference of recklessness in regard to the omissions from the affidavit, we must consider whether the affidavit, supplemented by the information regarding police promises to Burns and Linsin, still could have supported a finding of probable cause. The district court found only that the omitted facts and circumstances were material — i.e., that they might have changed the decision of the judicial officer issuing the warrant. Any misconception that such a finding is adequate to justify suppression springs in part from the two different ways in which courts have used the concept of "materiality" in Franks cases.

On one hand, courts concerned perhaps with a perceived boundlessness in extending Franks to include omissions as well as affirmative falsehoods limit the extension to cases where the omission is sufficiently material to cast doubt on the existence of probable cause; absent this degree of relevance, these courts suggest, omissions do not rise to the level of misrepresentations and thus do not implicate the concern with falsehood addressed in Franks. United States v. Dennis, 625 F.2d 782, 791 (8th Cir. 1980); see also Stanert, 762 F.2d at 781 (omissions must "tend to mislead"). On the other hand, some courts have labeled the Franks requirement that the affidavit, with the false portions set aside, be insufficient to establish probable cause, a requirement of "materiality." E.g., United States v. Ippolito, 774 F.2d 1482, 1485 (9th Cir. 1985); United States v. Williams, 737 F.2d 594, 604 (7th Cir. 1984), cert. denied, ___ U.S. ___, 105 S.Ct. 1354, 84 L.Ed.2d 377 (1985). Thus, a court finding "materiality" in the first sense may think it has made the second Franks finding and may invalidate a warrant after concluding only that the additional information might have affected the probable cause determination and not that the supplemented warrant could not have supported the existence of probable cause.

This erosion of the second Franks factor may be supported on the ground that police, by omitting information from the affidavit, act in a manner destructive of the warrant process. See Reivich, 610 F. Supp. at 545. Deliberate falsehoods in affidavits, however, would seem no less destructive, Franks, 438 U.S. at 165, 98 S.Ct. at 2681; yet Franks does not go so far as holding that otherwise sufficient affidavits may be challenged because of deceits in dispensable portions. Even the court in Rule, the case relied on by the district court, did not invalidate a warrant solely because of the relevance of certain omitted facts but instead proceeded to consider the existence of probable cause on the basis of a "corrected" affidavit. See 594 F. Supp. at 1241.

Applying Franks here, we conclude that an affidavit supplemented with the police promises of leniency to Burns and Linsin still would have supported a finding of probable cause. Such a result follows from our earlier analysis of the facial sufficiency of the affidavit and our conclusion that such "deals" are not inconsistent with continued recognition of the inferences of reliability that otherwise attach to statements against penal interest. Details of the exchanges between Burns and Linsin and the police particularly would add little to consideration of their reliability because the judicial officer issuing the warrant, presented as he was with the fact of the arrest, could easily have suspected and taken into account the typical kind of bargaining involved here. After all, we expect such judicial officers to be only neutral and detached — not naive and ingenuous. Cf. People v. Kurland, 28 Cal.3d 376, 392-94, 618 P.2d 213, 223-24, 168 Cal.Rptr. 667, 677-78 (1980) (affidavit adequate when it merely identified tip as coming from police informant because factors which might suggest that such informants were less reliable were common knowledge, making predictable details of the informant's criminal past cumulative), cert. denied, 451 U.S. 987, 101 S.Ct. 2321, 68 L.Ed.2d 844 (1981). Considering also the corroboration of some details and the firsthand bases of Burns' and Linsin's knowledge, the judicial officer still could have found, under the totality of the circumstances, that probable cause existed. Our touchstone is "probability," and not "certainty," and one-hundred-percent reliability on the part of Burns and Linsin was not crucial to issuance of the warrant. See Davis, 617 F.2d at 694; see also Marvin v. United States, 732 F.2d 669, 672 (8th Cir. 1984) (probable cause would not have been lacking had omitted information going to affiant's reliability been presented to the magistrate).

Reivich points to several other inaccuracies in the affidavit, but the correction of most, such as the misstatement regarding where Burns and Linsin were arrested, clearly would not change the probable cause determination. The informants' cross-corroboration is somewhat diminished by the district court's finding that only Linsin, and not Burns, gave the police a phone number for Reivich; but the informants still independently identified Reivich as their source of cocaine and placed his residence in the same general area; and to find that the error (assuming it was reckless) in the affidavit regarding the phone number negated the existence of probable cause would greatly exaggerate the role of cross-corroboration in the totality of circumstances on which we rely. Similarly, even if Burns did not tell the police that Reivich had cocaine left, it is not disputed that he told them that Reivich would be receiving more the morning of the search; nor is it fatal to the existence of probable cause that Burns and Linsin may have just affirmed police suggestions that Reivich was their source of cocaine or that Linsin had to call his wife to get Reivich's phone number (after all, Reivich had moved just three days previously). We need not determine whether the affidavit also established probable cause for the search of Reivich's car because a vehicle found on a premises (except, for example, the vehicle of a guest or other caller) is considered to be included within the scope of a warrant authorizing a search of that premises. United States v. Bulgatz, 693 F.2d 728, 730 n. 3 (8th Cir. 1982), cert. denied, 459 U.S. 1210, 103 S.Ct. 1203, 75 L.Ed.2d 444 (1983); see also United States v. Percival, 756 F.2d 600, 612 (7th Cir. 1985) (citing cases). Finally, we find no merit in Reivich's arguments that evidence from the search should be suppressed because of the alleged misconduct of and improper procedures used by police in drawing up the affidavit and executing the warrant.

Since there is no basis for excluding the challenged evidence in this case, we need not reach the district court's consideration, pursuant to United States v. Leon, 468 U.S. 897, 104 S.Ct. 3405, 82 L.Ed.2d 677 (1984), of the good faith exception to the exclusionary rule. United States v. Young, 745 F.2d 733, 758 (2d Cir. 1984), cert. denied, ___ U.S. ___, 105 S.Ct. 1842, 85 L.Ed.2d 142 (1985); United States v. Hendricks, 743 F.2d 653, 654 (9th Cir. 1984), cert. denied, ___ U.S. ___, 105 S.Ct. 1362, 84 L.Ed.2d 382 (1985).

We reverse the order of suppression and remand to the district court for further proceedings.