Section 527.040 of the Kentucky Revised Statutes makes it a crime for a convicted felon to possess a handgun. David E. Jennings, who is serving a term of imprisonment in the Kentucky State Reformatory for violation of that statute, petitioned the United States District Court for release on a writ of habeas corpus. It was and is Mr. Jennings’ contention that the handgun he was convicted of possessing was seized illegally and should not have been admitted in evidence at his trial. The federal district court held that the seizure was legal and denied the writ of habeas corpus. We agree that the seizure was legal, and we believe that it would have been necessary to deny the writ in any event because of the fact that before convicting Mr. Jennings, Kentucky provided him an opportunity for full and fair consideration of his claim that the handgun should have been excluded from evidence as the fruit of an illegal seizure.
I
In July of 1982 an apartment occupied by Mr. Jennings came under the surveillance of two Covington, Kentucky, police officers. Noticing a dozen or so people entering the building and leaving after a very short time, the policemen arranged to have a confidential informant go to the apartment and see if he could buy drugs there. He did, returning to the police with five tablets of controlled substances that he said he had bought from David (“Day Day”) Jennings.
On the strength of an affidavit executed by a Covington police lieutenant, a warrant was then issued authorizing the search of Mr. Jennings’ apartment for drugs and for the marked currency used by the informant in making his purchase. The affidavit, which described the circumstances of the purchase in some detail, stated that “Jennings is a known (and convicted) trafficker of controlled substances____”
When the police executed the search warrant (at 1:15 in the morning) they found *74Mr. Jennings and two other people in the apartment, along with a quantity of drug tablets, syringes, and a loaded handgun. The gun was hidden between the mattress and box springs of Mr. Jennings’ bed. (Illicit drugs are often hidden under mattresses, according to Mr. Jennings’ prosecutor, and it is standard procedure for the Coving-ton police to look there when searching for drugs.) Although no gun had been specified in the search warrant, the police chose not to leave Mr. Jennings’ loaded weapon behind; it was removed from the apartment, and so, we presume, was Mr. Jennings.
Mr. Jennings was indicted on four counts, the first of which was possession of a handgun by a convicted felon. The handgun count was severed for trial, and on the day before the trial was to begin in Kenton County Circuit Court the trial judge conducted a hearing on the motion filed by Mr. Jennings’ lawyer “to suppress certain physical evidence.” Counsel confirmed, at the hearing, that he was talking about the handgun, and suggested that the motion to suppress be granted for two reasons: because the seizure of the gun had not been authorized by the warrant, and because the warrant was invalid. Counsel presented extensive argument on the latter point, but none on the former.
The circuit court expressed the view that the issuance of the warrant was justified by the affidavit, but asked the prosecutor to explain how the gun could be considered contraband and how its seizure could be justified when the weapon had not been named in the warrant. The prosecutor replied:
“He is a convicted felon. It is against the law for him to own a handgun. That is the basis of the search against him, Your Honor. * * * Also while in execution of the search warrant, the officers would normally not let a handgun sit there for someone else to grab and use against a police officer.”
Mr. Jennings’ counsel asked the court, in the middle of this explanation, “would you listen to arguments on that?” The court said “Yes.” Counsel offered no such arguments, however, stating instead that “I would like to go back and make a brief argument about the structural integrity of the affidavit.” The court declined to hear additional argument on the latter point, and after preserving for the record his “position that there is not enough reliable independent information,” counsel stated “that’s all I have at this time.” The court then announced that the trial would begin the next morning and that the weapon would not be suppressed because its seizure was “acceptable.”
The jury returned a verdict of guilty and made a recommendation pursuant to which Mr. Jennings was sentenced to a five year term of imprisonment. The conviction was affirmed on appeal. (The separate trial of the remaining counts also resulted in a guilty verdict, but only the conviction on a count charging Mr. Jennings with drug possession was upheld on appeal.)
On September 28, 1984, Mr. Jennings applied to the United States District Court for permission to proceed in forma pauper-is. A petition for a writ of habeas corpus was tendered at the same time. The petition asserted that the conviction (on all counts) had been obtained by use of evidence gained pursuant to an unconstitutional search and seizure. On April 22, 1985, after the drug conviction had been affirmed on appeal and the convictions on two other counts had been overturned, Mr. Jennings (represented, once again, by counsel) sought leave to amend the habeas corpus petition to bring in the drug conviction. The motion to amend noted that the original petition “appears to address only issues related to [Mr. Jennings’] conviction for possession of a handgun by a convicted felon.”
The motion for leave to amend was denied. Mr. Jennings then filed a second habeas petition, this one dealing solely with the drug conviction. In his second petition Mr. Jennings answered “no” to the question “have you previously filed any petitions, applications, or motions with respect to this judgment ... ?”
*75On recommendation of a magistrate, both habeas petitions were denied by the district court. The order denying the first petition was properly appealed. No appeal was taken from the denial of the second petition. We are now asked to reverse the denial of the first petition not only on the ground that the handgun conviction was secured through evidence obtained in an unconstitutional seizure, but also on the ground that the district court failed to address, in the first proceeding, the constitutionality of the drug conviction. We decline to reverse on either ground.
II
Taking the subsidiary issue first, it does not seem to us that Mr. Jennings was improperly deprived of an opportunity to challenge the constitutionality of his drug conviction. If, as he now contends, he was entitled to brief that issue in the original habeas case without amending his petition, he should have briefed it. If, as he thought earlier, it was necessary to file a second petition after failing to obtain leave to amend, he was free to file such a petition — and, of course, he did so, and thus had every opportunity to attack his drug conviction in the second habeas proceeding. Having lost there, and having elected not to appeal, he is not entitled to another bite at that apple here.
With respect to the seizure of the handgun, the federal district court rested its denial of habeas relief on “public safety” considerations of the kind held in New York v. Quarles, 467 U.S. 649, 104 S.Ct. 2626, 81 L.Ed.2d 550 (1984), to have justified the New York police in seizing a suspected rapist’s loaded handgun before reading him his “Miranda rights.” Recognizing the potential for mischief that loaded handguns tend to present, we cannot quarrel with the district court’s judgment. Neither can we find fault with the proposition, advanced by the state, that the police were entitled to take Mr. Jennings’ gun under the “plain view” exception to the warrant requirement. See Coolidge v. New Hampshire, 403 U.S. 443, 91 S.Ct. 2022, 29 L.Ed.2d 564 (1971), which, as explained in United States v. Szymkowiak, 727 F.2d 95 (6th Cir.1984), permits police officers to seize “intrinsically suspicious” evidence inadvertently discovered during a lawful search as long as the officers had probable cause, upon discovery of the evidence, to consider it incriminating. Mr. Jennings argues here that the police had no probable cause to believe that the loaded gun found under his mattress was evidence of the crime of illegal handgun possession: he bases that argument on the fact that the affidavit that the police used to get their search warrant said only that “Jennings is a known (and convicted) trafficker of controlled substances,” without specifying that his drug trafficking conviction was for a felony and not merely a misdemeanor.
The argument is more ingenious than persuasive. The question is whether the police officers had probable cause to believe, when they found the gun, that it constituted evidence of a crime. The affidavit was prepared by a Covington policeman, not by a Philadelphia lawyer, and it provided ample support for an affirmative answer to the probable cause question. Given the context of the statement that Mr. Jennings was a convicted drug trafficker, and given the nature of the other evidence found by the police (i.e., syringes and drug tablets), we think the loaded gun could properly have been treated as evidence both of the crime of illegal handgun possession and of the crime of drug trafficking. The loaded handgun may fairly be viewed as a tool of the drug trafficker’s trade, and it is hard for us to understand how the police could have been expected to leave the gun in the apartment even if they had not been concerned about what might be done with it were it to be left there.
Be that as it may, Stone v. Powell, 428 U.S. 465, 96 S.Ct. 3037, 49 L.Ed.2d 1067 (1976), would require us to affirm the denial of habeas relief even if the “public safety” and “plain view” doctrines could somehow be considered inapplicable here.
Unlike the unloaded weapons in United States v. Szymkowiak, 727 F.2d 95, *76supra, which were seized upon the advice of an agent of the federal government and were used in evidence in a federal prosecution for violation of a federal statute, Mr. Jennings’ loaded handgun was seized by local police and was used as evidence in a trial conducted in a state court on a charge brought under state law. Ours is a federal system, and the rule adopted by the United States Supreme Court in 1914 precluding the use in federal trials of evidence seized improperly by federal officials (Weeks v. United States, 232 U.S. 383, 34 S.Ct. 341, 58 L.Ed. 652 (1914)) may not be invoked in federal habeas corpus proceedings “where the State has provided an opportunity for full and fair litigation of a Fourth Amendment claim____” Stone v. Powell, supra, 428 U.S. at 494, 96 S.Ct. at 3052. When persons convicted in state court of having violated state criminal laws are asking a federal court to turn them loose, as the Supreme Court explained in Stone, “the contribution of the exclusionary rule, if any, to the effectuation of the Fourth Amendment is minimal and the substantial societal costs of application of the rule persist with special force.” Id. at 494-95, 96 S.Ct. at 3052-53 (footnote omitted).
Application of the exclusionary rule, as the Supreme Court said elsewhere in Stone, “deflects the truthfinding process and often frees the guilty. * * * Thus, although the rule is thought to deter unlawful police activity in part through the nurturing of respect for Fourth Amendment values, if applied indiscriminately it may well have the opposite effect of generating disrespect for the law and administration of justice.” Id. at 490-91, 96 S.Ct. at 3050-51 (footnotes omitted). The court went on to observe that “[tjhese long-recognized costs of the rule persist when a criminal conviction is sought to be overturned on collateral review on the ground that a search-and-seizure claim was erroneously rejected by two or more tiers of state courts.” Id. at 491, 96 S.Ct. at 3051 (footnote omitted). Quoting from Justice Powell’s concurring opinion in Schneckloth v. Bustamonte, 412 U.S. 218, 259, 93 S.Ct. 2041, 36 L.Ed.2d 854 (1973), the court (speaking now through Justice Powell) noted that the “important” values on which resort to habeas corpus “intrudes” include “(i) the most effective utilization of limited judicial resources, (ii) the necessity of finality in criminal trials, (iii) the minimization of friction between our federal and state systems of justice, and (iv) the maintenance of the constitutional balance upon which the doctrine of federalism is founded.” Id. 428 U.S. at 491, n. 31, 96 S.Ct. at 3051, n. 31. It was considerations such as these that led the Supreme Court to conclude that state prisoners “who have been afforded the opportunity for full and fair consideration of their reliance upon the exclusionary rule with respect to seized evidence by the state courts at trial and on direct review [may not] invoke their claim again on federal habeas corpus review.” Id. at 489, 96 S.Ct. at 3050.
When read in light of Stone v. Powell, we think the record of the suppression hearing conducted by the Kentucky trial court establishes beyond question that Mr. Jennings was provided an opportunity for full and fair litigation of his Fourth Amendment claim. Citing Riley v. Gray, 674 F.2d 522 (6th Cir.), cert. denied sub nom. Shoemaker v. Riley, 459 U.S. 948, 103 S.Ct. 266, 74 L.Ed.2d 207 (1982), Mr. Jennings now asserts that even though the state provided a procedural mechanism for adjudicating his suppression claim, there was a “failure” of that mechanism because the trial court was laboring under a misapprehension as to who had the burden of proof at the suppression hearing. We find no indication of any such misapprehension.
At the outset of the hearing the prosecutor suggested (correctly, we believe) that the defendant would have the burden of proving the search warrant invalid if the gun were to be suppressed on the ground that there was no lawful warrant authorizing any search at all. Mr. Jennings’ counsel made a determined effort to demonstrate that the search warrant was invalid, but left it to the court itself to raise with the prosecutor the question of whether, if the warrant was valid, there was justifica*77tion for seizure of a weapon not named in the warrant. After the affidavit on which the warrant had been issued was read into the record, the court asked the prosecutor for an explanation of why the weapon was subject to seizure as contraband, and the court explicitly offered Mr. Jennings’ counsel an opportunity to respond to the prosecutor’s answer. Mr. Jennings’ counsel never took advantage of the court’s invitation to respond. Counsel’s failure to answer is no reflection on the mechanism provided by Kentucky for adjudication of suppression claims. All that Stone v. Powell requires is an “opportunity” for full and fair consideration of the claim for suppression; it is up to the claimant and his counsel to decide what use, if any, is to be made of the opportunity. If Mr. Jennings’ lawyer could not think of any rejoinder to the prosecutor’s argument that the handgun was subject to seizure as evidence that Mr. Jennings had violated KRS § 527.040, that is hardly a reason for the federal courts to compel Kentucky to set Mr. Jennings free.
The judgment denying Mr. Jennings’ petition for a writ of habeas corpus is AFFIRMED.