MANSFIELD, Circuit Judge:
On this appeal from a decision of the United States District Court for the Eastern District of New York ordering the suppression of certain evidence and testimony as obtained in violation of appellees’ Fourth Amendment rights, the government asks us to reverse a decision by Judge James L. Watson that there was no probable cause to issue the search warrant in question or, alternatively, to restrict the operation of the exclusionary rule in this case. Since we find that the warrant was improperly issued, and are unpersuaded by the government’s arguments regarding the exclusionary rule, we affirm the decision below.
The case involves a search of Steve’s Pier One Restaurant in Bayville, N.Y.; appellee Steve Karathanos is the president and sole shareholder of the corporation which owns the restaurant, while appellee John Karathanos, his brother, works there as a chef. The search was conducted under authority of a search warrant issued by a United States Magistrate after Neil Jacobs, an investigator for the Immigration and Naturalization Service (“INS”) swore in an affidavit that he had reason to believe illegal aliens were on the restaurant’s premises. The affidavit reads, in pertinent part, as follows:
“Upon information and belief, there are a number of aliens who are not lawfully entitled to enter or reside within the United States, employed at and present within the premises known and operated as STEVE’S PIER I RESTAURANT, 33 BAYVILLE AVENUE, BAYVILLE, NEW YORK, within the Eastern District of New York. The presence of said aliens is a violation of Title 8, United States Code, Section 1325.1 Moreover, such aliens are subject to arrest pursuant [29]*29to Title 8, United State Code, Section 1325, for having unlawfully entered the United States.
“The source of your deponent’s information and the grounds for his belief are:
“1. During the past five years at least eleven illegal aliens have been apprehended on the premises known as STEVE’S PIER I RESTAURANT, 33 BAYVILLE AVENUE, BAYVILLE, NEW YORK, including but not limited to the following individuals: MICHAEL KATSIGIORGIS, DIMITRIOUS STROUPAS, EMANUEL ARETINES, VELIRIS KOSTAS, VICTOR LLANOS, KOAS-TANTINOS VOULGARIDIS, ROBERTO BARRENCHEA-CAMACHO, VICTOR ALEXANDRO LLANO S-ATUNEA, LADIGLAO VENEGAS-FLORES, HUGO LAGOS, and KIKOLOS TISSANOS.
“2. On May 15, 1975, one ATHANASIOS ATHANASIOU, an admitted illegal alien, holding Greek citizenship, surrendered himself to agents of the Immigration and Naturalization Service at 20 West Broadway, New York, New York. After being advised of his rights, Mr. Athanasiou advised that he had been employed at STEVE’S PIER I RESTAURANT, 33 BAYVILLE AVENUE, BAY-VILLE, NEW YORK from October of 1973 till Sunday, May 11,1975; that as of May 11, 1975 at least eight other persons known to him to be illegal aliens were employed at STEVE’S PIER I RESTAURANT, 33 BAYVILLE AVENUE, BAY-VILLE, NEW YORK. That during the last year and a half he has resided in the basement of said restaurant with eleven other individuals in six (6) foot by six (6) foot cubicles. That at least six of the eleven individuals residing in the basement at 33 Bayville Avenue, Bayville, New York are known to him to be illegal aliens.”
Having obtained the warrant, INS agents searched the restaurant and arrested seven illegal aliens on the premises. The Karathanos brothers were then indicted for harboring and concealing these aliens in violation of 8 U.S.C. § 1324.2 The appellees moved to exclude from their trial any evidence of the presence of the aliens obtained during the search, and the testimony of the aliens themselves, on the ground that the affidavit for the search warrant failed to state probable cause to search. After a hearing, Judge Watson granted the motion, and the government, deeming the excluded evidence essential to its prosecution of the Karathanos brothers, appealed pursuant to 18 U.S.C. § 3731.
DISCUSSION
Though fine judgments are often required to determine whether an affidavit states facts sufficient to show probable cause for issuance of a search warrant, the basic standard for the decision is well-settled. When an affidavit relies on an informant’s time to establish probable cause, the affidavit must, first, set forth “some of the underlying circumstances” forming the basis of the informant’s conclusion that there is illegal activity or evidence thereof on the premises, and, second it must state facts which give some assurance that the informant is a credible person. See Spinelli v. United States, 393 U.S. 410, 89 S.Ct. 584, 21 L.Ed.2d 637 (1969); Aguilar v. Texas, 378 U.S. 108, 84 S.Ct. 1509, 12 L.Ed.2d 723 (1964). The purpose of the “two-pronged” test thus enunciated in Aguilar and Spinelli is, of course, to assure that the magistrate will not function merely as a rubber stamp but will issue search warrants only when [30]*30the facts are sufficient to satisfy a reasonably prudent detached and neutral person that a crime is being committed or evidence of it kept on the premises to be searched and that the informant’s information has been obtained by him in a reasonably reliable way rather than through neighborhood gossip, conjecture, or mere suspicion. See Spinelli v. United States, supra, 393 U.S. at 416, 89 S.Ct. 584, 21 L.Ed.2d 637. Then only is a limited invasion of a person’s privacy sanctioned by the Fourth Amendment.
With this basic framework in mind, we turn our attention to whether the requirements of the first phase of the Aguilar-Spinelli test have been met. The only information presented in the Jacobs affidavit3 to indicate how the informant Athanasiou reached his conclusion that there were illegal aliens at the restaurant is the statement that he had lived on the premises with these aliens. The government, recognizing that the mere presence of aliens (assuming that Athanasiou had a basis for concluding they were aliens) would not provide a basis for concluding that they had entered the United States illegally or otherwise violated immigration laws, strenuously argues that his statement gives rise to a reasonable inference that the other aliens must have admitted to him their illegal status, and thus provides sufficient assurance that he reached his conclusion in a reliable way.
Unquestionably statements to the informant by the other aliens that they were illegally in the United States would have been sufficient to support a holding that the information was reliably obtained by the informant. See, e.g., United States v. Sultan, 463 F.2d 1066, 1068 (2d Cir. 1972). But the affidavit’s bald statement that Athanasiou had lived with the other aliens is an insufficient basis for inferring that they made such incriminating admissions. While co-workers and bunkmates may exchange considerable amounts of information, it can hardly be assumed that, living in fear of arrest and deportation, illegal aliens would have revealed their illegal status to a stranger such as Athanasiou. On the contrary, one would expect this subject to rank high on the list of topics too sensitive to be casually revealed. The unlikelihood that the information was directly revealed by any of the aliens to Athanasiou is heightened by the fact that in depositions taken later in the present proceeding the deposition of Athanasiou was taken in the Greek language whereas the depositions of six out of seven of the seized aliens were taken in the Spanish language, indicating that any communication between him and them would have been handicapped by a language barrier.
Rather than hearing any such admissions by the aliens, Athanasiou may simply have concluded that his co-workers were illegal aliens by observing their physical appearance, language characteristics and the fact that they lived in cramped quarters on the premises where they worked. Such observations would be an insufficient basis, however, for determining that the person observed is an illegal alien, since there is no necessary connection between a person’s physical, linguistic characteristics, and living arrangements, on the one hand, and the legality of his status, on the other. See United States v. Brignoni-Ponce, 422 U.S. 873, 885-87, 95 S.Ct. 2574, 45 L.Ed.2d 607 (1975);4 United States v. Mallides, 473 F.2d 859, 860 (9th Cir. 1973). The fact that the co-workers were boarded in the basement is not inconsistent with traditional employers’ [31]*31past treatment of low-paid lawfully admitted immigrants. It is equally consistent to infer that, in tipping the INS that eight illegal aliens were employed on the premises, Athanasiou was simply passing along rumors about various employees which he had collected in the course of his employment at the restaurant; rumors, however, are patently insufficient to provide a sufficient basis for probable cause. If, indeed, Athanasiou obtained his information by direct statements from the aliens rather than by rumor, the Jacob affidavit should have so stated. Its failure to do so is a fatal deficiency.
To infer that the informant reached his conclusion in a reliable manner (e.g., through admissions by the aliens) rather than in an unreliable manner (e.g., through rumor or assumptions based on observations of physical appearance and the like) would be to permit a warrant to issue on the basis of a degree of speculation proscribed by the Aguilar-Spinelli test. While an affidavit supporting a search warrant should not be read in a grudging or technical manner, United States v. Ventresca, 380 U.S. 102, 108-09, 85 S.Ct. 741, 13 L.Ed.2d 684 (1965), neither should it require the magistrate, or a reviewing court, to use imagination to supply essential details critical to determining probable cause. See Aguilar v. Texas, supra, 378 U.S. at 114-15, 84 S.Ct. 1509; Giordenello v. United States, 357 U.S. 480, 486, 78 S.Ct. 1245, 2 L.Ed.2d 1503 (1958). The affidavit in the present case requires precisely that. We do not mean to imply that in all cases an affidavit must detail precisely how the informant reached his conclusion, but “[i]n the absence of a statement detailing the manner in which the information was gathered, it is especially important that the tip describe the accused’s criminal activity in sufficient detail that the magistrate may know that he is relying on something more substantial than a casual rumor circulating in the underworld or an accusation based merely on an individual’s general reputation.” Spinelli v. United States, supra, 393 U.S. at 416, 89 S.Ct. at 589. The present affidavit completely lacks such supporting detail. The alleged illegal aliens are never named or even described. It furnishes no indication of their nationality, of how they came into the country, or indeed any statement about them other than their number and the conclusion about their illegality.
Our recent decision in United States v. Pond, 523 F.2d 210 (2d Cir. 1975), on which the government relies, does not suggest that such an undetailed affidavit would be sufficient. In Pond, the affidavit specifically described the baggage which allegedly contained marijuana, and averred that an informant, experienced in smelling marijuana, had detected marijuana fumes coming from the luggage in question. Id. at 211-13. The Pond affidavit thus made clear what is in the present case still an object of conjecture: the manner in which the informant reached his conclusion about illegal activity.
The affidavit’s statement that during the past five years 11 illegal aliens had been arrested at the restaurant does not remedy its failure to set forth how the informant obtained his information. To be sure, Chief Justice Burger’s opinion in United States v. Harris, 403 U.S. 573, 91 S.Ct. 2075, 29 L.Ed.2d 723 (1971), relied on a constable’s knowledge of a person’s reputation as a moonshiner and on a prior seizure of non-taxpaid whiskey at the person’s house to help establish probable cause to search for illegal liquor. However, in Harris there was no doubt that the affidavit met the first prong of the Aguilar-Spinelli test — the requirement that the affidavit show how the informant secured his information; it recited that the informant had personally purchased non-taxpaid whiskey and had observed others doing so. The prior history of criminal activity in Harris was held sufficient, when considered along with other evidence, to allow the affidavit to pass the second prong of the Aguilar-Spinelli test: the requirement that the credibility of the informant be established, or, put another way, that the affidavit must give the magistrate a “ ‘substantial basis’ for crediting the hearsay” account by the [32]*32informant of how he obtained the information. See 403 U.S. at 579-80, 91 S.Ct. 2075 at 2080. In our view, the Harris opinion does not suggest that when an affidavit clearly fails to pass the first prong of the test, the addition of a recital of past criminal activity may serve as an acceptable substitute for probable cause standards that have not been met. Cf. United States v. McNally, 473 F.2d 934, 938-39 (3d Cir. 1973) (holding that Harris did not overrule two-pronged test).5 If such a recital were sufficient to remedy the deficiency, any tip, no matter how unreliably obtained, would suffice to allow a search, provided it could be shown that the owner of the premises had a record of prior similar criminal offenses. While past involvement in criminal activity carries some weight, it will not supplant the necessity of showing how the informant obtained his information. We thus hold that the affidavit fails to state facts sufficient to indicate probable cause to search, and that the search warrant was therefore improperly issued.6
Upon this appeal the government seeks for the first time to avoid the sanction which would normally follow as a matter of course from our holding that the warrant was issued without probable cause, i.e., the exclusion of the evidence obtained as a result of the search from the trial of the appellees. We are asked to modify the exclusionary rule so as to make it inapplicable whenever law enforcement agents have followed the preferred course of going to a magistrate to obtain a search warrant, even though the warrant turns out to have been improperly issued. The basic contention, which was not made before Judge Watson, is that in such a case the rule does not serve to deter unconstitutional searches because the unconstitutionality of the search is due only to a mistake in judgment on the part of the magistrate, and not to any bad faith on the part of the officers. There the rule does not serve any deterrent function, the argument continues, its use should be avoided since it then serves only to exclude probative evidence.
In response appellees challenge the good faith of the INS agents who obtained the warrant in the present case, contending that material representations in the Jacobs affidavit were false and that two warrant-less searches simultaneously made by the agents of the home of John Karathanos and of a nearby resident indicate that the agents were engaged in a general dragnet operation. Since an issue was thus raised as to whether the magistrate was misled, it is argued that the government should at this stage be precluded from assuming that the agents acted in good faith. If the agents’ good faith should turn out to be material, appellees argue that they are at least entitled to an evidentiary hearing on the issue. See United States v. Dunnings, 425 F.2d 836, 840 (2d Cir. 1969), cert. denied, [33]*33397 U.S. 1002, 90 S.Ct. 1149, 25 L.Ed.2d 412 (1970).
Were we considering the advisability of adopting an exclusionary rule prior to definitive landmark Supreme Court decisions on the subject, the government’s thesis would provide an intriguing suggestion for possible formulation of a somewhat different version of the rule. See Oaks, Studying the Exclusionary Rule in Search and Seizure, 37 U.Chi.L.Rev. 665 (1970); Amsterdam, Search, Seizure and Section 2265: A Comment, 112 U.Pa.L.Rev. 378 (1964). But see Amsterdam, Perspectives on the Fourth Amendment, 58 Minn.L.Rev. 349, 476 n.598 (1974). However, no purpose is served by pursuing the government’s suggestion, since decisions of the Supreme Court outlining the scope of the exclusionary rule offer no support for limiting it in this manner. The landmark discussions of the rule clearly regard it as a remedy to be applied whenever the search in question does not comply with Fourth Amendment standards, regardless of the presence or absence of a warrant and the good or bad faith of the police officers. See Mapp v. Ohio, 367 U.S. 643, 81 S.Ct. 1684, 6 L.Ed.2d 1081 (1961); Weeks v. United States, 232 U.S. 383, 34 S.Ct. 341, 58 L.Ed. 652 (1914). The Supreme Court has specifically ordered the exclusion of evidence even when the unconstitutionality of the search resulted only from what might be termed a magistrate’s error of judgment in determining probable cause. See Aguilar v. Texas, supra; Giordenello v. United States, supra; Byars v. United States, 273 U.S. 28, 47 S.Ct. 248, 71 L.Ed. 520 (1927). In the face of such an unvarying application of the rule by the Supreme Court, even if we were convinced that the rule should be modified as suggested by the government, it would be inappropriate for this court to do so since, as we said in Salerno v. American League of Professional Baseball Clubs, 429 F.2d 1003, 1005 (2d Cir. 1970), cert. denied, 400 U.S. 1001, 91 S.Ct. 462, 27 L.Ed.2d 452 (1971), with rare exceptions not here applicable, “we continue to believe that the Supreme Court should retain the exclusive privilege of overruling its own decisions it
Moreover, we are unpersuaded by the arguments of policy underlying the government’s position. Given the fragmentary empirical evidence regarding the actual effectiveness of the exclusionary rule in deterring unconstitutional searches,7 any discussion of its deterrent effects must be undertaken with considerable humility. However, there is no reason to assume that the rule does not help to deter unconstitutional searches even when applied in cases such as the present one, where the evidence was seized pursuant to a warrant issued without probable cause. While we do not assume that United States magistrates or state officials authorized to issue search warrants are necessarily prone to act as the “rubber stamp[s] for the police” condemned in Aguilar v. Texas, supra, 378 U.S. at 111, 84 S.Ct. 1509, the exclusionary rule’s effect of making them aware that their decision to issue a search warrant is a matter of importance not only in regard to the constitutional rights of the person to be searched, but also in regard to the success of any subsequent criminal prosecution, may well induce them to give search warrant applications the scrutiny which a proper regard for the Fourth Amendment requires, see id.
The suggested modification of the exclusionary rule might also have a significant, albeit indirect, effect on the behavior of [34]*34police officers. If a magistrate’s issuance of a warrant were to be, as the government would have it, an all but conclusive determination of the validity of the search and of the admissibility of the evidence seized thereby, police officers might have .a substantial incentive to submit their warrant applications to the least demanding magistrates, since once the warrant was issued, it would be exceedingly difficult later to exclude any evidence seized in the resulting search even if the warrant was issued without probable cause. The suggestion that “magistrate-shopping” or patronization by the police of lenient or “rubber stamp” justices of the peace could be remedied by removal of the offenders ignores the fact that many state officials entitled to issue search warrants are elected to office.8 For practical purposes, therefore, the standard of probable cause might be diluted to that required by the least demanding official authorized to issue warrants, even if this fell well below what the Fourth Amendment required. By contrast, the present universal application of the exclusionary rule to all unconstitutional searches gives law enforcement officers no comparable incentive to seek out the most lenient magistrates. In sum, while any appraisal of the effectiveness of the exclusionary rule cannot claim to be conclusive, we cannot accept the view that the rule patently lacks any deterrent function in cases such as the present one.9
The final contention advanced by the government is that the exclusionary rule should be applied here only to bar introduction of the evidence obtained during the search — primarily the INS agents’ testimony about the presence of the illegal aliens on the premises — but not to exclude the testimony of the arrested aliens about their relationships with the Karathanos brothers. It is urged that the combination of circumstances in this case — the INS agents’ obtaining of a warrant and the aliens’ decision voluntarily to testify against the Karathanos brothers — is sufficient to break the connection between the original illegal search and the testimony. We must, of course, appraise this question under the principles set out in Wong Sun v. United States, 371 U.S. 471, 487-88, 83 S.Ct. 407, 417, 9 L.Ed.2d 441 (1963):
“We need not hold that all evidence is ‘fruit of the poisonous tree’ simply because it would not have come to light but for the illegal actions of the police. Rather, the more apt question in such a case is ‘whether, granting establishment of the primary illegality, the evidence to which instant objection is made has been come at by exploitation , of that illegality or instead by means sufficiently distinguishable to be purged of the primary taint.’ Maguire, Evidence of Guilt 221 (1959).”
Mapping all the distinctions between such “fruits of the poisonous tree” and a healthy harvest fit for court consumption is a task which has recently led even one distinguished commentator to throw up his hands in despair, see Amsterdam, Perspectives on the Fourth Amendment, 58 Minn.L. Rev. 349, 361 (1974). However, our previous decision in United States v. Tane, 329 F.2d 848 (2d Cir. 1964), provides some guidance. In Tane, where a witness had agreed to testify after his identity had been discovered by an illegal wiretap and he had been [35]*35confronted with transcripts of the wiretapped conversations, we rejected the argument that his decision to testify was a sufficient intervening act to allow the testimony to be used at trial, and held that the testimony must be excluded because “[t]he road from the tap to the testimony may be long, but it is straight.” 329 F.2d at 853. From Tane, it is clear that the fact that a living witness, rather than inanimate evidence, is derived from an illegal search does not necessarily render the witness’ testimony admissible at trial. See also United States v. Garcilaso de la Vega, 489 F.2d 761, 763 (2d Cir. 1974).
The government seeks to distinguish Tane on the ground that Tane involved a deliberate violation of Fourth Amendment rights, while here the INS agents acted in good faith by obtaining a search warrant. Our opinion, however, did not rest on the nature of the police officers’ conduct, but rather on the closeness of the connection between the original illegality and the witness’ testimony. See 329 F.2d at 853. Moreover, while the “purpose and flagrancy of the official misconduct” are indeed relevant considerations in determining how far the taint of the original illegality extends, Brown v. Illinois, 422 U.S. 590, 603-04, 95 S.Ct. 2254, 45 L.Ed.2d 416 (1975); see United States v. Edmons, 432 F.2d 577, 584-85 (2d Cir. 1970), the fact that the agents obtained a warrant is far from conclusive in resolving the admissibility of the aliens’ testimony since, for reasons already stated, the exclusionary rule still performs a significant function in such a case. Indeed, Brown v. Illinois itself, in holding that the giving of Miranda warnings to an illegally arrested person did not, by itself, suffice to make a confession admissible, warned against adopting any such “talismanic test[s]” to resolve the question of the scope of the taint of an illegal search. 422 U.S. at 603, 95 S.Ct. 2254.
In the present case, there is a close connection between the initial illegal search and the testimony which the government seeks to use at trial. The purpose of the search, as described in the application for the warrant, was to seize the illegal aliens; it is these same aliens who are now the government’s prospective witnesses. Once the aliens were arrested, the INS agents had obtained considerable leverage over them, since it was within the government’s discretion to prosecute and deport them, or to allow them to leave the United States voluntarily. See 8 U.S.C. § 1252(b). If deported, the aliens would be permanently ineligible to receive visas to re-enter the country, see 8 U.S.C. § 1182(a)(17), while voluntary departure at one’s own expense carries no similar penalty of permanent exclusion. The government concedes that the aliens’ testimony was prompted by the use of this leverage; their agreement to testify came only after a promise to allow them to voluntarily depart without prosecution. In these circumstances, we think their decisions to testify cannot accurately be characterized as intervening “act[s] of free will” of sufficient independence “to purge the primary taint of the unlawful invasion.” Wong Sun v. United States, supra, 371 U.S. at 486, 83 S.Ct. at 417. The testimony is the not unpredictable result of the influence which the government possessed over the aliens once they had been arrested during the initial illegal search, and if such reasonably foreseeable fruits of the search were deemed admissible, it might help induce similar future searches without probable cause in the hope that they would uncover aliens who could be similarly prompted to testify.
Accordingly, we affirm the decision below and remand the case for further proceedings consistent with this opinion.