GOLDBERG, Circuit Judge:

Would you buy a used car from these men?

So defense counsel asked the jury, not entirely rhetorically, in his closing argument in this case, after having attempted to show that two important government witnesses, John Kral and Ismael Rodriquez, were not credible or reliable. Nevertheless, the jury bought; it convicted John Martin under 18 U.S.C. § 2113(a) for the robbery of the Atlantic Federal Savings and Loan in Boca Raton, Florida.

On appeal, Martin asks a related question: Did the affidavit which was submitted to the United States Magistrate and which consisted solely of hearsay accounts of information received from Kral, Rodriquez, and Martin's brother Jeffrey contain allegations from which the magistrate could constitutionally determine there was probable cause to believe that these men did in fact have a car to sell? That is, could the magistrate credit their information and determine that the affidavit established probable cause for Martin's arrest? On the basis of the affidavit submitted, the magistrate determined that there was probable cause to believe that Martin had committed the crime, and issued a warrant for his arrest. At the pretrial suppression hearing, the district court agreed that the affidavit established probable cause for arrest and held that the evidence seized pursuant to the warrant was admissible at trial. Martin raises both facial and subfacial challenges to the validity of the affidavit and argues that the evidence was wrongfully admitted. Because we believe that the tip from Rodriquez, read in the context of the entire affidavit, supported the magistrate's decision, we affirm the judgment of the district court.

I.

On June 14, 1978, a white male with dark, shoulder-length hair, wearing a ski mask and carrying a snub-nosed revolver, robbed the Atlantic Federal Savings and Loan in Boca Teeca Shopping Plaza in Boca Raton. After secreting approximately $4,293.00 in a brown paper bag, the robber left the bank and headed north. Several individuals testified at trial that they had seen a maskless white male with dark, shoulder-length hair, running from the direction of the bank and carrying a brown paper bag. While all the eyewitnesses to the activities of the robber/runner provided essentially consistent descriptions of his general physical characteristics (though estimates of his height, for example, ranged from 5'8" to 6'0"), none of them ever claimed to be able to identify him. Furthermore, the Government presented no information from these witnesses to the magistrate who made the probable cause determination.

The Government's evidence at the suppression hearing showed that in July 1979, while the F.B.I. was investigating charges against another individual in connection with the robbery of Atlantic Federal, it received information that John Martin's brother Jeffrey had told an undercover agent for the Boca Raton Police Department that John Martin had committed the robbery. Upon the request of the Boca Raton Police, the F.B.I. stayed its investigation of John Martin until the local undercover operation was over. On October 24, 1978, F.B.I. Agent Lee Kizer followed up the lead regarding John Martin by contacting and questioning Kral and Rodriquez, who, according to Jeffrey Martin, had firsthand knowledge of John Martin's activities. Agent Kizer then obtained from Kral and Rodriquez signed statements implicating John Martin in the robbery.

On October 24, 1979, Agent Kizer prepared an affidavit based on the statements from Kral and Rodriquez and on information he had received from the Boca Raton Police regarding a statement made to them by Jeffrey Martin. This affidavit, set out in the margin, he attached to a signed complaint which he presented to Magistrate Patricia Kyle in support of his request for an arrest warrant. He presented no other information. The arrest warrant issued and, pursuant to it, John Martin was taken into custody, and certain evidence procured.

At the suppression hearing in the district court, Martin argued that the affidavit would not support the issuance of the arrest warrant. He argued first that the affidavit was insufficient on its face to establish probable cause for his arrest because it contained no indication that the informants who supplied the hearsay information in the affidavit were reliable. Second, he argued that the affiant withheld from the magistrate information material to the determination of probable cause and thus that the affidavit could not support Martin's arrest. After hearing evidence and argument on both these theories, the court denied Martin's motion to suppress.

On appeal, Martin urges these same theories in his attack on the validity of the arrest warrant. We consider both the facial sufficiency of Agent Kizer's affidavit and the claim that information material to the determination of probable cause was omitted from the affidavit.

II.

The Fourth Amendment to the Constitution of the United States provides:

The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.

In this amendment resides one of the principle pillars of the liberty of the individual in the Republic: "the right to be let alone — the most comprehensive of rights and the right most valued by civilized men." Olmsted v. United States, 277 U.S. 438, 48 S.Ct. 564, 572, 72 L.Ed. 944 (1928) (Brandeis, J., dissenting). Yet this right is not absolute, as the limitation of the prohibition on searches and seizures to those which are "unreasonable" implies. The balance struck by the Framers between the need for protection of individual liberty and privacy and the need for effective enforcement of our laws is perhaps best reflected in the requirement that there be "probable cause, supported by Oath or affirmation," before a warrant may be issued. As has recently been affirmed, "[t]he bulwark of Fourth Amendment protection, of course, is the Warrant Clause, requiring that, absent certain exceptions, police obtain a warrant from a neutral and disinterested magistrate before embarking upon a search." Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 2681, 57 L.Ed.2d 667 (1978). Justice Jackson made clear the elemental values behind this requirement:

The point of the Fourth Amendment, which often is not grasped by zealous officers, is not that it denies law enforcement the support of the usual inferences which reasonable men draw from evidence. Its protection consists in requiring that those inferences be drawn by a neutral and detached magistrate instead of being judged by the officer engaged in the often competitive enterprise of ferreting out crime. Any assumption that evidence sufficient to support a magistrate's disinterested determination to issue a search warrant will justify the officers in making a search without a warrant would reduce the Amendment to a nullity and leave the people's homes secure only in the discretion of police officers. Crime, even in the privacy of one's own quarters, is, of course, of grave concern to society, and the law allows such crime to be reached on proper showing. The right of officers to thrust themselves into a home is also a grave concern, not only to the individual but to a society which chooses to dwell in reasonable security and freedom from surveillance. When the right of privacy must reasonably yield to the right of search is, as a rule, to be decided by a judicial officer, not by a policeman or Government enforcement agent.

Johnson v. United States, 333 U.S. 10, 68 S.Ct. 367, 369, 92 L.Ed. 436 (1948) (footnotes omitted).

The meaning of the Fourth Amendment's protections resides only in the individual decisions which implement them. The grand conceptions of "reasonableness" and "probable cause" acquire definition through their application to concrete sets of facts. When courts decide, as we must in this case, what police activities are proper and what are not; what circumstances are sufficient to subject an individual's privacy to the state's needs in the enforcement of its laws; then the accommodations they make signpost the boundaries of the rights of the citizenry to be "secure in their persons, houses, papers, and effects . . . ." The general terrain we must now cover has already been well-mapped. We proceed forthwith to our destination.

A. A Topographical Exercise: The Facial Sufficiency of the Affidavit

The affidavit supporting the arrest warrant in this case consisted solely of hearsay accounts of information given to police officials by Jeffrey Martin, John Kral, and Ismael Rodriquez. In Aguilar v. Texas, 378 U.S. 108, 84 S.Ct. 1509, 12 L.Ed.2d 723, the Supreme Court set out the standards for evaluating the sufficiency of hearsay affidavits to establish probable cause. In finding that the affidavit present there could not constitutionally support the magistrate's probable cause determination, the court held:

Although an affidavit may be based on hearsay information and need not reflect the direct personal observations of the affiant, . . . the magistrate must be informed of [1] some of the underlying circumstances from which the informant concluded that the narcotics were where he claimed they were, and [2] some of the underlying circumstances from which the officer concluded that the informant, whose identity need not be disclosed, . . . was "credible" or his information "reliable." Otherwise, "the inferences from the facts which lead to the complaint" will be drawn not "by a neutral and detached magistrate," as the Constitution requires, but instead, by a police officer "engaged in the often competitive enterprise of ferreting out crime," . . or, as in this case, by an unidentified informant.

Id. 84 S.Ct. at 1514. (emphasis supplied) (citations omitted).

The twin requirements of Aguilar provide the basis for evaluating the facial sufficiency of an affidavit based on a hearsay account of an informant's tip. The essence of Aguilar is that the affidavit must state facts which allow the magistrate to determine independently whether probable cause for the issuance of a warrant exists. These facts must enable the magistrate to make two distinct determinations. First, the magistrate must be presented with the facts from which the informant concluded that some criminal activity was taking, or had taken, place. He must then assess these underlying facts to determine whether or not the inference of criminal activity is warranted. Second, the magistrate must be presented with facts which establish the probable credibility of the informant or the reliability of his information. Even if the first requirement is satisfied, the affidavit cannot establish probable cause unless it establishes a factual basis for crediting the informant's conclusion. Thus, if either of Aguilar's requirements is not met, the affidavit cannot establish probable cause. See United States v. Harris, 403 U.S. 573, 91 S.Ct. 2075, 2079-80, 29 L.Ed.2d 723 (1971). We must now apply this two-pronged analysis to the affidavit before us.

1. Basis for the Informants' Conclusions

The affidavit adequately sets forth the factual underpinnings for Kral and Rodriquez' conclusions that John Martin committed the crime. The tip from Kral reveals itself to be the product of his personal observation of Martin on the day of the robbery. The affidavit shows that he saw Martin with a brown paper bag full of banded money in his possession and heard Martin and Rodriquez discuss the bank robbery. Furthermore, the affidavit reveals Rodriquez' own involvement in the robbery and his personal observations of Martin's activities. This court has held that information derived from personal observation satisfies the first prong of Aguilar, see, e.g., United States v. Williams, 603 F.2d 1168, 1171 (5th Cir. 1979); United States v. Tucker, 526 F.2d 279, 281 (5th Cir. 1976), cert. denied, 425 U.S. 958, 96 S.Ct. 1738, 48 L.Ed.2d 203 (1976), particularly when the tipster reveals his personal involvement in the criminal undertaking. See United States v. Ashley, 569 F.2d 975, 981 (5th Cir. 1978) cert. denied, 439 U.S. 853, 99 S.Ct. 163, 58 L.Ed.2d 159 (1978). Because these portions of the affidavit thus set forth facts which would support the conclusion that John Martin committed the robbery, each is independently sufficient to satisfy Aguilar's first prong.

The tip from Jeffrey Martin stands on a different footing. The affidavit reveals nothing about the source of his claimed knowledge. Standing alone, the information derived from him may represent nothing more than a "casual rumor circulating in the underworld." Spinelli v. United States, 393 U.S. 410, 89 S.Ct. 584, 589, 21 L.Ed.2d 637 (1969). Because of our disposition of this case, we need not determine whether it is saved by the corroboration it receives from the other tips. See id. 89 S.Ct. at 588-89.

2. The Reliability of the Informants' Tips

Aguilar's second requirement, as discussed above, is that the affidavit must set forth facts from which the magistrate can judge for himself the probable credibility of the informant or the reliability of his information. Martin argues that the affidavit does not state facts which would allow the magistrate to assess the credibility of any one of the informants or the reliability of his information.

A perusal of the affidavit discovers no affirmative allegation that any of the three informants was known to be reliable. This type of allegation is not necessary, however, and, if not accompanied by supporting facts, is irrelevant. See United States v. Farese, 612 F.2d 1376, 1378 n. 3 (5th Cir. 1980). There are several judicially-recognized methods of establishing the credibility of an informant and the reliability of his information. Perhaps the most intuitive and direct method has been to allege that the informant has previously given tips which proved to be correct. See, e.g., Jones v. United States, 362 U.S. 257, 80 S.Ct. 725, 736, 4 L.Ed.2d 697 (1960); United States v. Williams, supra, 603 F.2d at 1171; United States v. Tucker, supra, 526 F.2d at 281. But with first time informants, such as those involved here, this method is obviously not available; as this court has recognized, the reliability of first-time informants may thus be more difficult to establish. See, e.g., United States v. Ashley, supra, 569 F.2d at 981. To establish the credibility of such an informant or the reliability of his information, the affidavit may show other information within the affiant's knowledge to corroborate the tip, see, e.g., Spinelli v. United States, supra, 89 S.Ct. at 589-90; United States v. Squella-Avendano, 447 F.2d 575, 582 (5th Cir. 1971), cert. denied 404 U.S. 985, 92 S.Ct. 450, 30 L.Ed.2d 369 (1971); or it may show that the informant's tip was against his penal interest, although this alone is not sufficient to establish reliability. See United States v. Ashley, supra, 569 F.2d at 981-82. The Government contends that the magistrate could credit the tips recited in the affidavit because they corroborate each other and, in the case of Rodriquez' tip, because it constitutes a statement against his penal interest.

Rodriquez' statement to Agent Kizer is against his penal interest. The affidavit reveals that Rodriquez admitted that he had been a party to the planning of the robbery, had planned to drive the getaway motorcycle, and later had met Martin at Kral's house and discussed the robbery. We have held, however, that, standing alone, a statement against penal interest is "not enough to justify a finding of probable cause;" rather it is "one of many cumulating factors to be considered." United States v. Ashley, supra, 569 F.2d at 982.

The facts of our case demonstrate even more clearly than those in Ashley why statements against penal interest cannot satisfy Aguilar's second requirement without more. Whereas the court in Ashley noted that the declarant voluntarily came forward to supply information to the F.B.I., a factor which served to "discount any inference that [the informant] was not reliable because he gave information to lessen any pressure on himself," id., in this case, the affidavit itself reveals nothing of the circumstances under which the admission was made. In fact, Martin showed in the suppression hearing that the F.B.I. sought Rodriquez out and initiated the interview, and Rodriquez testified at trial that he had been given immunity from prosecution. See Part B infra. Under these circumstances, there exists a danger that the informant sought to implicate another in order to curry the favor of the police and perhaps gain immunity for himself. While such motivations do "not eliminate the residual risk and opprobrium of having admitted criminal conduct," United States v. Harris, supra, 91 S.Ct. at 2082, they certainly make the declaration less reliable. Cf. United States v. Gonzalez, 559 F.2d 1271, 1273 (5th Cir. 1977) (excluding statement against penal interest under Fed.R.Evid. 804(b)(3) because declarant had been granted immunity from prosecution and because pressures from the prosecution and grand jury made it his "best interest" to make the statement). Thus, under Ashley, Rodriquez' statement against penal interest, although it is entitled to some weight, cannot alone establish his reliability under Aguilar.

Since Rodriquez' tip alone does not pass Aguilar, we turn to the Government's claim that the informants' tips sufficiently corroborate each other to establish their reliability. Spinelli provides the framework within which we evaluate this claim:

The informer's report must first be measured against Aguilar's standards so that its probative value can be assessed. If the tip is found inadequate under Aguilar, the other allegations which corroborate the information contained in the hearsay report should then be considered. At this stage as well, however, the standards enunciated in Aguilar must inform the magistrate's decision. He must ask: Can it fairly be said that the tip, even when certain parts of it have been corroborated by independent sources, is as trustworthy as a tip which would pass Aguilar's tests without independent corroboration? . . . A magistrate cannot be said to have properly discharged his constitutional duty if he relies on an informer's tip which — even when partially corroborated — is not as reliable as one which passes Aguilar's requirements when standing alone.

Spinelli v. United States, supra, 89 S.Ct. at 588-89.

No one of the three tips recounted in the affidavit can stand alone under Aguilar's second test since no one statement provides sufficient internal indicia of reliability. We must thus determine whether, when the tips are cumulated and the degree of their corroboration assessed, any one of the three "is as trustworthy as a tip which would pass Aguilar's tests without independent corroboration." Id.

Normally, when corroborative evidence is relied upon to validate a tip which is not alone sufficient, that evidence consists of independent verification by the police of details of the tip through their own investigation. See, e.g., Draper v. United States, 358 U.S. 307, 79 S.Ct. 329, 3 L.Ed.2d 327 (1959); United States v. Squella-Avendano, supra. This court has held, however, that where informers give tips that substantially corroborate each other that factor helps establish the reliability of the tips. See United States v. Farese, supra, at 1379; United States v. Barham, 595 F.2d 231, 246 (5th Cir. 1979); United States v. Scott, 555 F.2d 522, 527 (5th Cir. 1977), cert. denied, 434 U.S. 985, 98 S.Ct. 610, 54 L.Ed.2d 478 (1977). But in the above-cited cases the government agents also reported that they had corroborated the tips by independent investigation. In contrast, in this case the affidavit discloses only the corroboration between the tips. Thus, here, we think it important under Spinelli to examine the degree of corroboration between the tips to determine whether it is sufficient to make any one of the tips reliable. We question, for example, whether or not this affidavit would be sufficient if it consisted solely of the statements from Kral and Jeffrey Martin. Certainly these accounts corroborate each other, but only in the most general terms. Jeffrey Martin's tip is devoid of any substance other than his bald conclusions that John Martin committed the crime and that Kral and Rodriquez had "first-hand knowledge" of that fact. We doubt that Kral's more factual statement could be made sufficiently reliable by its proximity to these merest of conclusions without other indicia of trustworthiness.

There are, however, strong reasons for crediting the tips from Kral and Rodriquez when they are considered in the full context of the affidavit. Rodriquez and Kral corroborated each other in close detail; both men independently recounted to Agent Kizer essentially identical descriptions of events which, they stated, occurred in their joint presence. Further, Jeffrey Martin's tip does give some additional weight, however slight, to their information. This degree of corroboration of Kral and Rodriquez' stories clearly "reduced the chances of a reckless or prevaricating tale." Jones v. United States, supra, 80 S.Ct. at 736.

We need not determine whether this corroboration is of itself sufficient to establish the reliability under Aguilar of the information given by Kral and Rodriquez. Rather, we hold that when the affidavit is read as a whole the tip from Rodriquez is sufficiently reliable to satisfy Aguilar's second prong. First, we give some weight to Rodriquez' statement against his penal interest. Second, the substantial corroboration of his tip by the other informants provides "strong ground for crediting" his story. United States v. Farese, supra, at 1379 n. 4. Taken together, these factors are enough to allow the magistrate to credit his information and thus to establish his trustworthiness under the second prong of Aguilar. As we have already shown, the affidavit adequately sets out the underlying facts from which Rodriquez concluded that Martin had committed the crime, thus satisfying the first prong of Aguilar. Because Rodriquez' tip thus satisfies both of Aguilar's requirements, it establishes probable cause for Martin's arrest.

B. A Subterranean Excursion: The Subfacial Challenge to the Affidavit

Martin next argues that Agent Kizer failed to disclose to the magistrate certain material facts within his knowledge which would have affected her assessment of the informants' reliability and thus her determination that the affidavit established probable cause for Martin's arrest. Specifically, he argues that Agent Kizer should have disclosed that he initiated the interviews with Kral and Rodriquez, that he used a "yes and no" questioning format which did not ensure the informants' truthfulness, and that Rodriquez had been granted immunity from prosecution based on the information he gave. He at least implies that these omissions were intentional. The district court, at the suppression hearing, allowed Martin to present evidence regarding omissions from the affidavit. Having examined the evidence at that hearing, we believe the district court was correct in finding that the omissions from the affidavit did not vitiate the magistrate's finding of probable cause.

In Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978), the Supreme Court for the first time recognized the viability of subfacial challenges to affidavits presented in support of a warrant and defined the circumstances in which such an attack could prevail. The court summarized its holding as follows:

[W]e hold that, where the defendant makes a substantial preliminary showing that a false statement knowingly and intentionally, or with reckless disregard for the truth, was included by the affiant in the warrant affidavit, and if the allegedly false statement is necessary to the finding of probable cause, the Fourth Amendment requires that a hearing be held at the defendant's request. In the event that at that hearing the allegation of perjury or reckless disregard is established by the defendant by a preponderance of the evidence, and, with the affidavit's false material set to one side, the affidavit's remaining content is insufficient to establish probable cause, the search warrant must be voided and the fruits of the search excluded to the same extent as if probable cause was lacking on the face of the affidavit.

Id. 98 S.Ct. at 2676-77. While Franks dealt only with misstatements, Judge Coleman in United States v. Park, 531 F.2d 754, 758-59 (5th Cir. 1976), recognized that allegations of material omissions were to be treated essentially similarly to claims of material misstatements. Accord United States v. House, 604 F.2d 1135, 1141 n. 9 (8th Cir. 1979); United States v. Collins, 549 F.2d 557, 561 (8th Cir. 1977), cert. denied, 431 U.S. 940, 97 S.Ct. 2656, 53 L.Ed.2d 259 (1977); United States v. Lewis, 425 F. Supp. 1166, 1173 (D.Conn. 1977); Morris v. Superior Court, 57 Cal.App.3d 521, 129 Cal.Rptr. 238 (1976).

Since the district court allowed Martin to present evidence regarding the omissions at the suppression hearing, we do not face the issue of whether or not a hearing on the omissions was required. Rather, we must examine the record of the suppression hearing to determine whether or not Martin proved by a preponderance of the evidence, first, that the omissions were in fact made, and, second, that they were made intentionally or with a reckless disregard for the accuracy of the affidavit. If Martin carried this burden, we would be required to determine whether, if the omitted material had been included in the affidavit, the affidavit would still establish probable cause for Martin's arrest. If it would not, we would be required to void the warrant and suppress the evidence seized pursuant to it. See Franks v. Delaware, supra, 98 S.Ct. at 2676-77; United States v. House, supra, 604 F.2d at 1141.

The record of the hearing establishes both that Agent Kizer initiated the interviews with Kral and Rodriquez and that he used the "yes and no" questioning format of which Martin has complained. It does not establish, however, that Rodriquez had been granted or promised immunity at the time he made his statement to Agent Kizer. In fact, Martin never contended at his hearing that Rodriquez had been promised immunity; apparently he discovered the promise only at trial (Trial Transcript at 173), and did not at that time renew his motion to suppress in light of this information. Furthermore, at oral argument the Government stated that it was not certain that Rodriquez had been promised immunity until after he made the statement upon which the affidavit was based. Thus, since the record at the hearing does not establish that Agent Kizer failed to disclose that Rodriquez had been promised or granted immunity, we cannot further consider this alleged omission.

Under Franks, a proven misstatement can vitiate an affidavit only if it is established that the misstatement was the product "of deliberate falsehood or of reckless disregard for the truth . . . . Allegations of negligence or innocent mistake are insufficient." 98 S.Ct. at 2685. By analogy, it must be proven that the omissions were made intentionally or with a reckless disregard for the accuracy of the affidavit; negligent omissions will not undermine the affidavit. See United States v. House, supra, 604 F.2d at 1141.

Here, there is no evidence in the record directly illuminating the state of mind of the affiant, Agent Kizer, when he omitted from the affidavit the facts that he had initiated the interviews with Kral and Rodriquez and had used a "yes and no" questioning format, for Martin proved little more than that these omissions were made. Doubtless it will often be difficult for an accused to prove that an omission was made intentionally or with reckless disregard rather than negligently unless he has somehow gained independent evidence that the affiant had acted from bad motive or recklessly in conducting his investigation and making the affidavit. Nevertheless, it follows from Franks that the accused bears the burden of showing by a preponderance of the evidence that the omission was more than a negligent act. It is possible that when the facts omitted from the affidavit are clearly critical to a finding of probable cause the fact of recklessness may be inferred from proof of the omission itself. Ours, however, is not that case.

Agent Kizer's failure to reveal the fact that he initiated contact with Kral and Rodriquez and the nature of his questioning format does not, in the circumstances of this case, give rise to the inference that he acted with reckless disregard for the accuracy of the information he presented to the magistrate. As is clear from our analysis of the facial sufficiency of the affidavit, these facts were not so central as to warrant the inference that Agent Kizer's actions were reckless. For this reason, we hold that Martin failed to carry his burden of showing that the omissions were more than negligent.

III.

In analyzing the claims involved in this case, we have tried to be true to the

recognition that the Fourth Amendment's commands, like all constitutional requirements, are practical and not abstract. If the teachings of the Court's cases are to be followed and the constitutional policy served, affidavits . . . must be tested and interpreted by magistrates and courts in a commonsense and realistic fashion.

United States v. Ventresca, 380 U.S. 102, 85 S.Ct. 741, 746, 13 L.Ed.2d 684 (1965). Because the affidavit here was sufficient to support Martin's arrest, we affirm the judgment of the court below.

AFFIRMED.