The government appeals under 18 U.S.C. § 3731 from the district court’s order suppressing Dennis Mahoney’s post-arrest confession “as the fruit of an unlawful arrest.” Finding that the actions of the state law enforcement agents, though assumed here to be illegal, were taken in a reasonable and good faith belief that they were legal, we apply the “good faith exception” to the exclusionary rule explicated in United States v. Williams, 622 F.2d 830 (5th Cir. 1980) (en banc), and reverse.
On February 24, 1982, a federal grand jury in Austin, Texas, returned an indictment charging twelve defendants with violations of the Racketeer Influenced and Corrupt Organizations Act, 18 U.S.C. § 1962(d). One of the defendants was named in the indictment as “JOHN DOE, a/k/a ‘DENNIS’ (last name unknown).” Although state and federal law enforcement officers and government prosecutors involved in the investigation had learned from a co-defendant of the race, height, weight, and hair color of “Dennis,” an arrest warrant issued the next day pursuant to the order of a federal magistrate described its subject only as “JOHN DOE a/k/a DENNIS (LNU).” Later that day, law enforcement officers in El Paso arrested another co-defendant who told them that the “Dennis” named in the indictment was Dennis Mahoney and that he worked at a supermarket in Houston. Around 4 p.m., the El Paso officers relayed this information to the Houston Police Department Homicide Squad.
The Houston officers then called the supermarket and obtained Mahoney’s home address. Using the same arrest warrant issued earlier that day, five plainclothes officers from the Houston Police Department Homicide Squad and the Texas Department of Public Safety proceeded to Mahoney’s home at around 6 p.m. A friend of Mahoney, in response to a knock, opened the door and then stepped back. An officer stepped across the threshold and asked “Who is Dennis?” A man seated about fifteen feet from the door and in sight when the door was opened responded by rising from the sofa. That individual, who proved to be Mahoney, matched the description given before the warrant had been issued. The officers then arrested him without resistance, advised him of his constitutional rights, and drove him to the police station. At the station, the officers again advised him of his rights and began to interrogate him. Several horn’s later, Mahoney signed an eight-page statement, in which he described his role in a drug-dealing organization and confessed to participating in the execution and burial of two potential drug purchasers.
Mahoney moved before trial to suppress this confession, arguing that the arrest warrant was invalid, that the warrantless entry into Mahoney’s apartment and the subsequent arrest violated the fourth amendment, and that the confession was the product of the illegal arrest. The district court granted this motion. It first held that the arrest warrant was invalid because it did not identify Mahoney with “sufficient particularity.” Noting that the validity of the arrest by the state officers must be judged under Texas law, the court held that the *958officers’ warrantless entry into the apartment to make the arrest violated both Texas law and the fourth amendment because the government had not shown either exigent circumstances or consensual entry. See Payton v. New York, 445 U.S. 573, 100 S.Ct. 1371, 63 L.Ed.2d 639 (1980). It also held that the confession was the “fruit” of the illegal arrest and therefore must be suppressed. Finally, it found that the officers “executed the arrest warrant in the belief that it was valid” but refused to apply a good faith exception to the exclusionary rule because “under Texas law, an arresting officer’s good faith does not suffice to purge an unlawful arrest of its illegality insofar as the exclusion of evidence is concerned....”
The government now appeals from this decision. While it characterizes the questions regarding the warrant’s validity and the arrest’s legality as “close,” it does not challenge the district court’s conclusions on these points. Instead, it first argues that Mahoney’s confession was not “obtained by the exploitation of the illegal police conduct” and thus was not a “fruit” of any fourth amendment violation in the sense of Wong Sun v. United States, 371 U.S. 471, 83 S.Ct. 407, 9 L.Ed.2d 441 (1963). It also argues that the good faith exception to the exclusionary rule adopted in United States v. Williams, 622 F.2d 830 (5th Cir.1980) (en banc), cert. denied, 449 U.S. 1127,101 S.Ct. 946, 67 L.Ed.2d 114 (1981), is applicable here. Because we agree that the exclusionary rule is not applicable, we need not and do not reach the question whether the confession was the “fruit” of the illegal arrest.
In arguing that the good faith exception of Williams is not applicable, Mahoney echoes the district court’s conclusion that the involvement of state officers triggers the application of state law to this issue and that Texas recognizes no exception to the federal exclusionary rule.1 The source of this conclusion is United States v. Garcia, 676 F.2d 1086 (5th Cir.1982). In Garcia, this court noted that when state officers arrest#, for a federal crime, the legality of the arrest is determined by the law of the state in which the arrest takes place, subject to federal constitutional standards. Id. at 1089. See also United States v. Bowdach, 561 F.2d 1160, 1168 (5th Cir.1977). Because an arrest’s legality depends on state law, it followed for the Garcia panel that application of the good faith exception to the exclusionary rule also depends on state law and that Texas, where the arrest occurred, recognizes no such exception.2
*959That recent decisions of the Texas courts put in question whether Garcia’s interpretation reflects present Texas law does not require that we repair to an Erie -like exercise. The government’s petition for certiorari in Garcia urged error in the application of Texas law to a federal prosecution. On June 21, 1983, the Supreme Court granted the petition, vacated the decision, and remanded to the panel for reconsideration in light of United States v. Ross, 456 U.S. 798, 102 S.Ct. 2157, 72 L.Ed.2d 572 (1982). See United States v. Garcia, 676 F.2d 1086 (5th Cir.1982), vacated and remanded,-U.S. -, 103 S.Ct. 3105, 77 L.Ed.2d 1360 (1983). The relevance of Ross to Garcia is plain. Ross determined the scope of a warrantless search of a container in an automobile. In Garcia, a Texas game warden stopped a truck outside of a state park, searched its tank, arguably a container, found marijuana, and arrested its occupants. Bypassing the fourth amendment question, the Garcia panel had analyzed the validity of the game warden’s warrantless arrest under state law and held that he lacked statutory authority to arrest for non-game law violations occurring outside of state parks. By remanding Garcia for reconsideration in light of the fourth amendment standards announced in Ross, the Court perforce instructed that state law did not control the case and that the admissibility of evidence depends on the legality of the search and seizure under federal law.
Even if the brevity of the Court’s order vacating Garcia garbles its message, it frees this panel to question whether application of the good faith exception to the exclusionary rule in a federal criminal proceeding depends on state law and not federal law. Assuming the threshold proposition that the legality of a state officer’s conduct may be measured by state law, a proposition that we do not here decide,3 it does not follow that state law should govern a federal court’s decision whether to admit evidence that is tainted by illegal conduct. In Garcia, the court applied the state’s interpretation of the exclusionary rule because it seemed to regard the existence of good faith as integral to the legality of the arrest. We view the inquiry as a distinct inquiry into the utility in a given case of the remedial device of exclusion, a creature of the federal courts. As the Supreme Court recently stated in Illinois v. Gates, -U.S.-,-, 103 S.Ct. 2317, 2324, 76 L.Ed.2d 527 (1983), “The question whether the exclusionary rule’s remedy is appropriate in a particular context has long been regarded as an issue separate from the question whether the Fourth Amendment rights of the party seeking to invoke the rule were violated by police conduct.” Because it is a creature of the federal courts and because it ought to be applied in a manner that promotes uniformity in federal cases, federal law must guide our decision whether to apply the exclusionary rule whether or not the legality of the underlying arrest or search turns on state law.
Having determined that federal law is the source of any remedial response to an illegal arrest in a federal prosecution, we turn to that law. The en banc court in *960 Williams held that “evidence is not to be suppressed under the exclusionary rule where it is discovered by officers in the course of actions that are taken in good faith and in the reasonable, though mistaken, belief that they are authorized.” 622 F.2d at 840. We reasoned:
[T]he exclusionary rule exists to deter willful or flagrant actions by police, not reasonable, good-faith ones. Where the reason for the rule ceases, its application must cease also. The costs to society of applying the rule beyond the purposes it exists to serve are simply too high — in this instance the release on the public of a recidivist drug smuggler — with few or no offsetting benefits. We are persuaded that both reason and authority support this conclusion.
Id. Noting that the justifications for the exclusionary rule cease to exist when an officer makes a “good faith mistake” regarding operative facts or commits a “technical violation,” we applied the good faith exception in that case because the officer had committed both a good faith mistake regarding an element of the crime of bail jumping and a good faith technical violation of a statute that later was reconstrued. Id. at 846.
While the court described the good faith exception in broad terms, it nonetheless noted that because “no warrant is involved here ... nothing that we say applies to factual situations where one has been obtained.” Id. at 840 n. 1. Despite the precision of its confinement to warrantless contexts, nothing suggests that the good faith exception is necessarily inapplicable when, as here, a police officer acts pursuant to a warrant issued after an unchallenged finding of probable cause. To the contrary, a recent decision suggests that the good faith exception may be applicable in this context. In United States v. Cady, 651 F.2d 290 (5th Cir.1981), cert. denied, 455 U.S. 919, 102 S.Ct. 1274, 71 L.Ed.2d 459 (1982), defendants argued that the trial court should have suppressed evidence because the search warrant in question, though indisputably supported by probable cause, was invalid for failing to specify a reasonable time limit on the monitoring that it authorized. Before rejecting this contention, the court noted that the government did not contend, “as it well might have, that the reasonable good faith of these police officers, who obtained a warrant and complied with its terms explicitly, would insulate the evidence in question from suppression.” Id. at 291 n. 2 (citing Williams ). Based on Cady, we are persuaded that the existence here of a warrant founded on probable cause does not remove this case from the reasoning of Williams,4
Having determined that Williams applies to this case in principle, we now decide whether it applies in fact. The first inquiry under Williams is whether Mahoney’s arresting officers had a subjective, good faith belief that their actions were legal. Though the district court found that the arrest warrant executed by the officers was invalid because it did not identify Mahoney with “sufficient particularity,”5 the court *961also found that the officers “executed the arrest warrant in the belief that it was valid.” We cannot conclude that this finding of good faith is clearly erroneous. Ken-, neth Williamson, a homicide detective with the Houston Police Department, testified that he knew an arrest warrant for Mahoney had been issued by a federal magistrate pursuant to a grand jury indictment and that he regarded the description of Mahoney provided by his co-defendants as reliable. As such, he testified that he thought the arrest warrant was valid even though it named only “John Doe a/k/a Dennis LNU.” Because the arresting officer thus believed the warrant to be valid, it follows that he also believed his entry into Mahoney’s apartment was lawful.
Our inquiry cannot end here, however, because Williams requires that we also decide whether the officers’ subjective good faith was “grounded in objective reasonableness” and “based upon articulable premises sufficient to cause a reasonable, and reasonably trained, officer to believe that he was acting lawfully.” 622 F.2d at 841 n. 4a. We conclude that Mahoney’s arresting officers have met this test and note that Mahoney has made no argument to the contrary. We do not demean the fourth amendment by noting that its violation assumed to have occurred here was virtually esoteric. It resulted only with the synergistic intersection of the extremities of two doctrines. Though the federal arrest warrant executed by the Houston officers was issued after Mahoney’s indictment and thus was presumptively supported by probable cause, it was held to be constitutionally deficient because it inadequately described Mahoney and did not provide his last name. Thus armed with an invalid warrant, the officers’ arrest was illegal under Payton v. New York, 445 U.S. 573, 100 S.Ct. 1371, 63 L.Ed.2d 639, because stepping across the plane of the open door was a warrantless entry into Mahoney’s apartment without consent or acceptable exigent circumstances even though the officers had probable cause to make the arrest without a warrant.
We cannot, however, charge these adequately trained and properly motivated officers with knowledge that their actions would fall along this cutting edge of two legal doctrines. The officers dutifully obtained an arrest warrant whose deficiency was attributable primarily to the prosecutors’ failure to fully describe Mahoney in the indictment. Though the officers quickly learned Mahoney’s last name and could have sought a new warrant, their belief that they were not required to do so was reasonable under the circumstances. The officers were entitled to believe that any deficiency in the arrest warrant could be “cured” by their independent personal knowledge that the person they arrested was indeed the one for whom the warrant was intended. At the time of Mahoney’s arrest, only the Second Circuit had held that extrinsic evidence may not be used to validate an otherwise invalid “John Doe” warrant. See United States v. Jarvis, 560 F.2d 494, 497 (2d Cir.1977), cert. denied, 435 U.S. 934, 98 S.Ct. 1511, 55 L.Ed.2d 532 (1978). The Third Circuit recently followed Jarvid approach in United States v. Doe, 703 F.2d 745 (3d Cir.1983). This conclusion of objective reasonableness is buttressed, and arguably independently sustainable, by an additional circumstance. Though the district court concluded that the entry into Mahoney’s apartment was without consent, the officers reasonably could have believed that Mahoney’s friend consented to their entry when he opened the door and took a step back. For example, in United States v. Turbyfill, 525 F.2d 57 (8th Cir.1975), the court found that a person who opened the door and stepped back impliedly invited the police to enter. That Payton v. New York may have eroded the full force of Turbyfill does not answer our inquiry. Consensual entry remained legal. In sum, the arresting officers were mistaken in their belief that the warrant was valid, a legal error, and mistaken in their belief that, regardless, consent to enter was given, an error of both factual and legal dimension. The law was not so clear and the officers’ interpretation of the facts so wrong as to foreclose the objective reasonableness of their belief.
*962 Williams teaches that the exclusionary rule is not to be applied “in those contexts where it does not effectively deter official misconduct.” 622 F.2d at 842. We are persuaded that this is such a case. As we explained, because the officers neither knew nor should have known that their actions later would be invalidated, there is no specific deterrent value in suppressing this confession. We also are persuaded that any contribution to the general deterrence of future police action caused by suppressing this confession will be minimal because it is probable that the set of facts that occurred here will only rarely intersect and sum to illegality. More specifically, if these officers have acted in good faith measured both objectively and subjectively, we are uncertain what suppression of Mahoney’s confession is calculated to deter the officers from doing in the future. Arguably the officers would have the incentive to learn more. That explanation will not wash, however, because we have posited that their conduct was objectively Reasonable. If the violated principle was so bright lined as to be the subject of police lecture, finding the good faith to have been objectively reasonable would be sorely taxed. - As we stated in Williams, we do not reward ignorance. Here, only a sophisticated lawyer could have then known with confidence both that the warrant was defective and that the officer could not step through the open door when the person who opened it stepped back without comment.
We question on these facts the claimed teaching value of the exclusionary rule. Suppression would teach, but the lesson would be one of cynicism and disrespect for a rule of law so wooden as to require application even when its purpose is not served. Such reasoning transforms the rule from servant to master and becomes the end itself. In short, the marginal increment in deterrence that could be achieved by applying the exclusionary rule does not justify the societal costs of denying the jury access to Mahoney’s confession. Of course, there may be benefit in uniformly applying the exclusionary rule such that legality is the sole index of exclusion. Those benefits bear in our view too great a price. Regardless, we crossed that bridge in Williams. We find the exclusionary rule to be inapplicable here and reverse the district court’s decision to suppress Mahoney’s confession.
REVERSED.