BAUER, Chief Judge.

Alonzo Rice, Jr. was convicted of two counts of possession of a firearm as a convicted felon in violation of 18 U.S.C. § 922(g)(1), and possession of an unregistered firearm in violation of 26 U.S.C. § 5861(d). Rice received a 96-month prison sentence, with a five-year term of supervised release. Rice appeals his conviction. For the reasons set forth below, we affirm.

I. Facts

Because Rice’s encounter with the Milwaukee Sheriffs Department on January 6, 1992 is the focus of one of his arguments on appeal, we will review that encounter in some detail. Michael Pautz and Donald Hurley, two detectives from the Milwaukee County Sheriffs Department, went to the Knight’s Inn motel in Oak Creek, Wisconsin (which is just south of Milwaukee) on January 6, 1992 to investigate a report of illegal drug activity. The report indicated the activity was occurring in room 401. The detectives arrived at the motel around noon. Transcript of Evi-dentiary Hearing (“Tr. E.H.”) of 4/13/92 at 3. A man and woman occupied room 401, and the detectives found drugs and drug paraphernalia in the room. While Detective Pautz was investigating in room 401, he looked through the window and saw a yellow ear pull up outside. A man got out of the car, and Pautz left room 401 to speak to him. Hurley remained in room 401. Although Pautz did not learn his identity until later, the driver was Alonzo Rice. Pautz believed that Rice might be involved in the activities in 401 because he drove up close to the room, the motel rooms opened directly on to the parking lot, and the rest of the lot was empty.

Pautz told Rice who he was, and asked Rice where he was staying. Rice said he was staying in room 402, and asked what Pautz was doing. Pautz said they were investigating drug activity in room 401 and asked if Rice knew the occupants. Rice said he did not know them, but had seen them come and go. The men talked in front of the door to room 402. During the conversation, Rice knocked on the door to room 402, and Doris Solomon opened it. Without asking for or receiving permission, Pautz followed Rice into his room as they talked. Rice made no objection, and Pautz characterized his manner as “very cordial.” Id. at 8. Neither Rice nor Solomon objected to his entry or asked Pautz to leave.

Pautz asked Solomon and Rice if they had anything illegal in their room. Both said they had nothing illegal. Pautz asked if he could look around, and said that if there was no problem, he would leave. Tr. E.H. at 9-10. Both people said to go ahead, and Pautz looked around. Pautz saw some roaches (marijuana cigarette butts) in an ashtray and a small bag which he believed contained mar *721 ijuana. He asked the couple what was in the bag, and opened it at the same time. It contained marijuana. He asked the couple if they had been smoking. The woman told him she had smoked some marijuana the night before.

Pautz asked Rice if he had any identification, and Rice showed him his birth certificate. Pautz also asked the woman for identification. Pautz asked Rice if he had any other identification, and asked him to empty his pockets. Among other things, Rice produced a set of keys and two envelopes containing crack cocaine from his pockets. At some time during the interview, Pautz admit ted Sheriffs Deputy Kenneth Kujawa to the room. Kujawa asked Rice if it was okay to look around the room; Rice told him to go ahead. Kujawa found some crack pipes and other drug paraphernalia in a shaving kit.

Pautz asked Rice if the keys fitted the car outside. Rice said they did; Pautz asked whether anything illegal was in the car. Rice said no, and Pautz asked whether it was okay to search the car. According to Pautz, Rice said to go ahead because he had nothing to hide. Id. at 13. Before he left the room to search the car, Pautz told Rice and Solomon that they were under arrest for possession of the drugs in the room.

Pautz discovered a loaded, short-barreled shotgun in the trunk of the car. Pautz took Rice to the Milwaukee County Sheriffs Detective Bureau, and then gave Rice Miranda warnings. Pautz read the warnings from a card which he routinely uses to advise arres-tees of their rights. After he gave Rice the warnings, Pautz questioned Rice about the shotgun. Rice said that he received the gun from an acquaintance in exchange for $65.00 and that he knew the gun was loaded, but had not used it.

Rice and Solomon were arrested again on January 24,1992. (The record does not indicate the circumstances of their release after the first arrest.) They were in the same car involved in the January 6 arrest; Rice was driving, and Solomon was in the front passenger seat. The police were responding to a citizen’s complaint about the car’s presence outside her home. The police removed them from the car after one officer saw what she believed was a gun on the front seat. The police found a loaded .44 magnum revolver protruding from under the front passenger seat of the car. (The object on the seat was not a gun.) Rice and Solomon were arrested. Solomon said she knew nothing about the gun; Rice said the gun might belong to his friends Rick and Dave.

Rice was indicted by a grand jury on March 3,1992. He was charged with possession of an unregistered shotgun with a barrel less than 18 inches long, and with two counts of knowing possession of a firearm as a convicted felon.

Rice moved to suppress the shotgun and his statements about it. The trial court referred his motion to a Magistrate. At the hearing before the Magistrate, Rice’s version of the events surrounding the January 6 arrest differed from Pautz’s version. Rice testified that three or more officers entered room 402. He said he did not agree to Pautz’s search of his room or pockets. Rice denied that he consented to the search of the car. According to Rice, Pautz did not ask to search the car, he just picked up the keys and went out to search. He also testified that he and Solomon were in handcuffs at that time. Finally, Rice denied that he was ever given Miranda warnings, or that he was questioned or made a statement about the shotgun. E.H. Tr. of 4/14/92 at 23-25.

The Magistrate recommended that the district court grant Rice’s motion to suppress the shotgun and related statements. The Magistrate found that Rice voluntarily admitted Pautz to room 402, but he found Rice’s consent to the search of his pockets and car were tainted by coercion. Only the search of the car is at issue here. The Magistrate found that Pautz’s presence and statements about searching the room created “subtle coercion” because Pautz did not expressly inform Rice of his right to refuse the search. Magistrate Recommendation of April 29, 1992, R. Doc. 14 at 9. The magistrate ruled that his finding of subtle coercion was supported by the presence of the roaches in the ash tray. Rice and Solomon could not have believed that Pautz might search and find nothing, he reasoned, so they would not have *722 consented voluntarily. Id. Kujawa’s presence in the room, together with the discovery of the cocaine, according to the Magistrate, added to the coercive atmosphere. Based on the circumstances, the Magistrate ruled that reasonable people would not believe they were free to refuse Pautz’s requests, and for that reason their consents were not voluntary. 1 But his analysis was not unequivocal:

It is difficult to point to any single factor which, standing alone, would make a person in Rice’s position feel that he had no choice but consent. However, the combination of subtle, and perhaps not so subtle, coercions, in the absence of any warnings or disclaimers such as those suggested in [United States v.] High, 921 F.2d 112, 115 (7th Cir.1990), leads this court to conclude that Rice’s consent was not voluntary.

Id. at 10.

The Magistrate also recommended that Rice’s statements about the shotgun be suppressed because the Government presented insufficient evidence that Pautz gave Rice the appropriate Miranda warnings before questioning him. Pautz could not repeat the warnings at the evidentiary hearing and had not produced his “standard card” as evidence. Id. at 13. Because of these failures, the Magistrate recommended that the court grant Rice’s motion to suppress his statements about the shotgun.

The government objected to the Magistrate’s recommendations. After hearing testimony from Pautz and reviewing the transcripts of the hearing before the Magistrate, the district court ruled that Rice’s consent was voluntary, and denied Rice’s motion to suppress the shotgun. It ruled that the facts presented did not support the Magistrate’s conclusion that Rice’s consent was tainted by coercion from the detectives. The court also found that the Government had proven adequately that Pautz gave Rice the appropriate Miranda warnings after his arrest and denied Rice’s motion to suppress his statements about the shotgun.

After a two-day jury trial, Rice was convicted of all three counts charged in the indictment. He appeals his conviction on two grounds. First, he argues the district court erred in denying his motion to suppress the shotgun. Second, he argues the district court improperly refused to give a proffered jury instruction regarding his possession of the revolver during his second arrest.

II. Analysis

A. Motion to Suppress

We review a district court’s factual and legal determinations on a motion to suppress for clear error. United States v. Kelly, 991 F.2d 1308 (7th Cir.1993) (citing United States v. Spears, 965 F.2d 262, 271, 277 (7th Cir.), cert. denied, — U.S. -, 113 S.Ct. 502, 121 L.Ed.2d 438 (1992)); United States v. Somers, 950 F.2d 1279, 1283 (7th Cir.1991), cert. denied, — U.S. -, 112 S.Ct. 1959, 118 L.Ed.2d 561 (1992). A finding is clearly erroneous when although there is evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed. United States v. Soria, 965 F.2d 436, 439 (7th Cir.1992).

Rice complains of the district court’s handling of the motion to suppress. He asserts that the parties stipulated before the suppression hearing that “no further hearing be held to develop the testimony concerning the issues raised in the Government’s objection.” Appellant’s Brief at 7. Rice then complains that the district court improperly rejected the Magistrate’s credibility determinations without an evidentiary hearing. Rice is mistaken, however, because the court did not reject the Magistrate’s credibility determinations. The Magistrate found that Rice consented to the search of the car, despite Rice’s testimony to the contrary. He ruled that the consent was involuntary. The district court disagreed with the Magistrate’s conclusion that the consent was involuntary — his application of the law to the facts. We believe the court’s management of the suppression hearing was entirely appropriate.

The court noted that the Government was unaware that the adequacy of the Miranda *723 warnings was to be considered by the Magistrate, and so was not prepared at the eviden-tiary hearing to litigate the issue. Suppression Hearing Tr. at 3-4; 18. For that reason, all the facts surrounding the warnings were not presented to the Magistrate. To remedy this inadequacy, the court questioned Pautz, who had his warning card with him. Rice’s counsel did not object to this procedure. After Pautz testified, the court asked counsel: “Are there any other matters of a factual nature that either side wishes to have the court consider in light of the testimony that’s been developed this morning?” Suppression Hearing of May 19, 1992, Tr. at 13. Counsel declined the invitation. The court gave the parties another opportunity to supplement the record: “Is there any other evidence that either side wishes to have the court consider?” Id. at 14. Counsel replied: “Not from Mr. Rice either. We will rely on the transcript from this point.” Id. Rice’s counsel argued briefly in support of Rice’s motion at the court’s invitation, but chose to rely on the transcripts of the witnesses’ testimony at the evidentiary hearing. Id. at 14-16. After the argument, the court reviewed the transcripts in chambers and then issued its ruling.

The district court ruled that Rice’s consent was voluntary and that he had received Miranda warnings. It did not reject the credibility findings of the Magistrate. We find no merit in Rice’s argument on appeal that this procedure violated due process or requires that we conduct a more searching review of the district court’s conclusions. Rice did not object to the district court’s management of the hearing either before or after the court issued its ruling, and the court afforded him more than ample opportunity to present evidence and arguments.

The district court also correctly denied Rice’s motion to suppress. “[Cjourts have developed three categories for analyzing police-citizen encounters under the Fourth Amendment.” United States v. Adebayo, 985 F.2d 1333, 1337 (7th Cir.1993) (citing United States v. Withers, 972 F.2d 837, 841 (7th Cir.1992)). The first category is an arrest supported by probable cause; the second is a brief investigatory stop. See Terry v. Ohio, 392 U.S. 1, 20-22, 88 S.Ct. 1868, 1879-81, 20 L.Ed.2d 889 (1968). Both of these categories are seizures under the Fourth Amendment. Withers, 972 F.2d at 841; United States v. High, 921 F.2d 112, 115 (7th Cir.1990). The third category, in which a police officer seeks a “citizen’s voluntary cooperation through non-coereive questioning,” does not implicate the Fourth Amendment. Withers, 972 F.2d at 841.

Rice voluntarily spoke with Pautz and admitted him to his hotel room. This initial contact falls within the third category and does not implicate the Fourth Amendment. Cf. United States v. Dickerson, 975 F.2d 1245, 1249 (7th Cir.1992) (naked man “voluntarily consented” to warrantless entry by four police officers who appeared, weapons drawn, at his front door), cert. denied, — U.S. -, 113 S.Ct. 1316, 122 L.Ed.2d 703 (1993). The interview ripened into an investigatory “stop” once Pautz discovered the drugs in Rice’s room. See Adebayo, 985 F.2d at 1339 (consensual encounter with suspected drug courier evolved into Terry stop); United States v. Borys, 766 F.2d 304, 311 (1985) (when officers explained they suspected defendant of transporting drugs and asked permission to search luggage, consensual questioning ripened into investigative stop), cert. denied, 474 U.S. 1082, 106 S.Ct. 852, 88 L.Ed.2d 893 (1986). A reasonable person would not have felt free to leave once a police officer discovered drugs in his hotel room. Pautz’s discovery of the cocaine and marijuana in Rice’s room was sufficient to permit him to detain Rice to investigate. The issue becomes, then, whether Rice voluntarily consented to- the extension of Pautz’s search to his automobile once the consensual encounter ripened into a Terry stop.

“A warrantless search conducted pursuant to consent which is ‘freely and voluntarily given’ does not violate the Fourth Amendment.” United States v. McGuire, 957 F.2d 310, 314 (1992) (quoting Schneckloth v. Bustamonte, 412 U.S. 218, 222, 93 S.Ct. 2041, 2045, 36 L.Ed.2d 854 (1973)). “[WJhether a consent was voluntary, as opposed to the product of duress or coercion, is a question of fact to be determined from the totality of the circumstances.” United States v. Duran, 957 *724 F.2d 499, 502 (7th Cir.1992). The government must prove the consent was voluntary by a preponderance of the evidence. Id. The district court found that Rice consented to the search of his room and his automobile. We will reverse this determination only if it is clearly erroneous. Id. at 502.

Rice has failed to show that the district court’s holding is clearly erroneous. We agree with the Government’s observation that any encounter between police officers and citizens in which the citizen is aware of the officers’ identity will involve some degree of “subtle coercion.” Hearing of 5/19/92 at 15. The Magistrate was unable to quantify what precise circumstances created the “subtle coercion” in this case, so we are a bit mystified by his conclusion. Rice was not subject to harsh interrogation. See United States v. Nafzger, 965 F.2d 213, 216 (7th Cir.1992) (discussing mode of questioning); United States v. High, 921 F.2d 112, 116 (7th Cir.1990) (same). Pautz and his officers did not overwhelm Rice with their physical presence — there were only two officers, and Solomon was present when Rice consented to the search. See High, 921 F.2d at 116 (discussing mitigating effect of another citizen’s presence, and non-intimidating police-citizen ratio of 3 to 2); Borys, 766 F.2d at 311 (ratio of 2 to 1 not intimidating). The officers did not display weapons or physically touch Rice, and the encounter occurred during the day. See Duran, 957 F.2d at 503 (weapon display and time of encounter); United States v. Fryer, 974 F.2d 813, 819-20 (7th Cir.1992) (weapon display), cert. denied, — U.S. - — , 113 S.Ct. 2418,124 L.Ed.2d 641 (1992); Adebayo, 985 F.2d at 1340 (physical contact). Finally, Rice was not an overawed youngster being confronted with law enforcement for the first time. He was 38 years old when the search occurred, and had at least four prior criminal convictions. Magistrate Recommendation at 8. There is simply no evidence that Pautz coerced Rice, subtly or otherwise. Accordingly, we do not find that the district court’s determination that Rice voluntarily consented to the search of his automobile was clearly erroneous.

B, Jury Instruction

Rice also argues that the district court committed reversible error in refusing to give proffered jury instructions on possession. “On review of a challenge to the sufficiency of the jury instructions, the question is not the correctness of a single phrase, but whether the ■ instructions as a whole were sufficient to inform the jury correctly of the applicable law and the theory of defense.” United States v. Villarreal, 977 F.2d 1077, 1079 (7th Cir.1992), cert. denied, - U.S. --, 113 S.Ct. 1350, 122 L.Ed.2d 731 (1993); United States v. Durades, 929 F.2d 1160, 1167 (7th Cir.1991) (instructions must cover issues “fairly and adequately”). A district court has substantial discretion with respect to the specific wording of jury instructions, and need not give a proposed instruction if the essential points are covered by the instruction given. United States v. Penson, 896 F.2d 1087, 1090 (7th Cir.1990).

Rice was charged in counts two and three of the indictment with possession of the shotgun and the revolver recovered in the January 6, and January 24, 1992 arrests. To defend the revolver charge, Rice argued that the gun belonged to Solomon and that he was unaware of its presence under the seat of the car. Although her testimony was impeached with the statement she gave after the January 24 arrest, Solomon testified that she brought the revolver into the ear and Rice knew nothing about it.

The district court gave the following possession instruction:

The law recognizes two kinds of possession: actual possession and constructive possession. A person who knowingly has direct physical control over a thing, at a given time, is then in actual possession of it.

A person who, although not in actual possession, knowingly has both the power and intention at a given time, to exercise dominion or control over a thing, either directly or through another person or persons, is then in constructive possession of it.

The law recognizes also that possession may be sole or joint. If one person alone has actual or constructive possession of a *725 thing, possession is sole. If two or more persons share actual or constructive possession of a thing, possession is joint. You may find that the element of possession as that term is used in these instructions is present if you find beyond a reasonable doubt that the defendant has actual or constructive possession, either jointly or with others.

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When the word “knowingly” is used in these instructions, it means that the defendant realized what he was doing and was aware of the nature of the conduct, and did not act through ignorance, mistake or accident. Knowledge may be proved by the defendant’s conduct, and by all the facts and circumstances surrounding the ease.

Jury Instructions, R.Doc. 29 at 13-14. We approved this possession instruction in United States v. Stockheimer, 807 F.2d 610, 616 (7th Cir.1986), cert. denied, 481 U.S. 1018, 107 S.Ct. 1899, 95 L.Ed.2d 506 (1987). The instruction on the meaning of knowingly is the Seventh Circuit Federal Criminal Jury Instruction § 6.04 (1980).

Rice requested that the district court supplement the possession instruction with the following language:

On the other hand, mere presence in the vicinity of a firearm, or mere knowledge of its physical location, does not constitute possession under the statute. It is even possible for a defendant to touch a firearm, and not have possession of it.

Defendant’s Proposed Jury Instructions, R.Doc. 29. The district court refused to give the instruction. Rice derived the additional language from United States v. Hamilton, 420 F.2d 1096, 1098 (7th Cir.1970), and United States v. Beverly, 750 F.2d 34, 36-37 (6th Cir.1984). Hamilton involved an unsuccessful appeal by a defendant convicted of mail fraud. In Beverly, the defendant argued successfully that the Government had failed to prove that he possessed a firearm found in a wastebasket in a friend’s kitchen with his fingerprint on it. We have found no cases (and Rice has cited none) which rely on either Hamilton or Beverly to formulate instructions on possession. We acknowledged Beverly’s holding in United States v. Wilson, 922 F.2d 1336, 1339 (7th Cir.), cert. de nied; — U.S. -, 112 S.Ct. 155, 116 L.Ed.2d 120 (1991), and noted that merely touching a gun would not be possessing it. Despite Beverly, however, we found the evidence sufficient to affirm the defendant’s conviction for possession of a firearm found under his girlfriend’s mattress with his fingerprint on it. Id. at 1339 n. 1.

But Rice does not challenge the sufficiency of the evidence; he argues that the given instructions inadequately covered his theory of defense. A defendant is entitled to have the jury instructed on a theory of defense if (1) the defendant proposes a correct statement of the law; (2) the defendant’s theory is supported by the evidence; (3) the defendant’s theory of defense is not part of the charge; and (4) the failure to include an instruction on the defendant’s theory in the jury charge would deny the defendant a fair trial. United States v. Briscoe, 896 F.2d 1476, 1512 (7th Cir.1990) (citing United States v. Douglas, 818 F.2d 1317, 1320-21 (7th Cir.1987)), cert. denied sub nom., Usman v. United States, 498 U.S. 863, 111 S.Ct. 173, 112 L.Ed.2d 137 (1990). After reviewing the instructions given, we conclude that Rice has failed to meet the third and fourth prongs of the test. The theory of defense outlined in the tendered instruction was adequately covered by the instructions given. The district court gave complete instructions to the jury. We have rejected the contention that possession instructions must include a qualifier that “mere proximity” is not possession. United States v. Saunders, 973 F.2d 1354, 1361 (7th Cir.1992), cert. denied, - U.S. -, 113 S.Ct. 1026, 122 L.Ed.2d 171 (1993); United States v. Durades, 929 F.2d 1160, 1168 (7th Cir.1991). As we noted in Durades, district courts are not required to give alternative explanations of every term defined in the instructions. Id.

Giving the supplemental instructions Rice requested would have been supererogatory, and perhaps confusing to the jury. As the district court noted, there was no evidence presented about Rice touching either gun, so the Beverly case is inapposite. Tr. Instruction Conference 5/20/92 at 207. Further, the district court permitted Rice’s counsel to ar *726 gue his theory to the jury. This argument coupled with the district court’s instruction adequately presented Rice’s theory of defense to the jury. See Saunders, 973 F.2d at 1361 (additional points defendant requested were appropriate for argument); United States v. Borkenhagen, 468 F.2d 43, 50-51 (7th Cir.1972) (instructions coupled with argument adequately presented defense theory), ce rt. denied, 410 U.S. 934, 93 S.Ct. 1386, 35 L.Ed.2d 597 (1973).

III.

For the foregoing reasons, the judgment of the district court is

AFFIRMED.

. The judiciary is constantly amazed at the stupidity of criminals. The fact is, most smart peo-pie avoid lives of crime. That is to say, reasonable people do not commit crimes.