Norman C. Griffiths was taken into custody when he could not prove his immigration status to officials. While he was in custody, officials searched Griffiths’ duffel bag and discovered cocaine hidden inside a container. Griffiths was charged with unlawful possession and possession with intent to distribute five grams or more of cocaine, in violation of 21 U.S.C. §§ 841(a)(1), (b)(1)(B), and 844(a). He moved to suppress the cocaine. The United States District Court for the Western District of New York (Richard J. Arcara, Judge) granted the motion, rejecting the government’s argument that the search was consensual, or, in the alternative, that the cocaine would inevitably have been discovered by lawful means, 845 F.Supp. 105. The government appeals under 18 U.S.C. § 3731. We vacate and remand.
BACKGROUND
On July 14, 1993, defendant arrived at the Niagara Frontier Transportation Authority bus station in Buffalo, New York on a bus from New York City. On duty at the bus station was Deputy Sheriff Randall Fry of the Niagara County Sheriffs Department. Fry was acting as a plainclothes Task Force Officer with the Drug Enforcement Administration. Also on duty, but in uniform, was Border Patrol Agent Daniel Allman.
According to the government, Griffiths was the first person to leave the bus. He looked around repeatedly before he went into the bus terminal, and he changed direction after noticing Allman in uniform. His suspicion aroused, Fry followed Griffiths through the terminal. Along the way, Fry told Allman what he had seen, and they decided to follow Griffiths in Allman’s marked patrol ear. Griffiths, who was still on foot, turned and looked at the marked vehicle several times as it stalked him.
After a couple of blocks, Allman parked his vehicle. Fry approached Griffiths, identified himself as a police officer, and asked Grif-fiths if he could talk to him. Griffiths answered yes. Fry asked Griffiths where he was coming from, and Griffiths replied “New York.” Griffiths said he was going to Busti Street in Buffalo to visit someone named Earl, whose last name he had forgotten. Griffiths added that he was staying in the city for about two weeks and that he was thinking about relocating permanently in Buffalo.
Fry then asked Griffiths for identification. Griffiths produced a Florida driver’s license and a social security card. He said he was still, living in Florida and that he had flown to New York from Florida. After examining and returning Griffiths’ identification, Fry explained that he was a narcotics officer, and asked Griffiths whether he was carrying any drugs. Griffiths said no. Fry asked if he *76could look inside the duffel bag Griffiths was carrying. According to Fry, he explicitly told Griffiths that, because he was not under arrest, he did not have to consent. Griffiths said “go ahead.”
Before Fry could look in the bag, however, Allman approached and identified himself as an immigration officer. Noticing that Grif-fiths spoke with a West Indies accent, All-man asked him where he was born. Griffiths replied that he was born in Jamaica. Allman then asked whether Griffiths had a passport or alien registration card. Griffiths answered that he did not have his registration card (commonly called a “green card”) with him. Failure to carry the card is a misdemeanor under 8 U.S.C. § 1304(e).
Allman and Fry decided to take Griffiths back to the police office at the bus terminal to verify his immigration status. Griffiths, who was still in sole possession of the duffel bag, sat in the back of the police car, but was not restrained. During the trip to the bus station, Allman radioed for a check on Grif-fiths’ citizenship and criminal record, if any.
Arriving at the bus station, Griffiths, Fry and Allman entered the police office. Special Agent Bruce Johnson of the DEA was present. Allman called his office to follow-up his earlier request for information concerning Griffiths’ immigration status and criminal record. While Allman was on the phone, Fry again asked Griffiths if he could search his bag. According to Fry, Griffiths consented by saying “go ahead” and by placing the bag on the desk where Johnson was seated.
Fry removed a Minute Maid juice container from the bag, shook it, and placed it on the desk. Johnson noticed that the container had been opened and re-glued shut. His curiosity piqued, Johnson opened the container and saw a plastic bag containing beige chunks that looked like cocaine base. Grif-fiths said that he bought the container of juice at a store, and knew nothing about the chunks. At that point, Griffiths was arrested for suspected drug possession. A subsequent examination of the chunks confirmed that they were 56 grams of cocaine base.
While the search of the duffel bag was in progress, Allman completed his phone call. He was told that a check of immigration records had revealed that an individual named “Norman Constantine Griffiths, Jr.,” whose date and place of birth matched Grif-fiths’, was a legal resident alien. With regard to criminal history, Allman learned that an individual named “Norman Griffiths” had prior arrests in New York and New Jersey. Because one of the arrests was for criminal possession of a loaded weapon, “Norman ^Griffiths” was deportable.
After hanging up the phone, Allman asked Griffiths his middle name, and Griffiths responded, “Constantine.” Allman then asked Griffiths whether he had ever been arrested. Griffiths responded that he had not.
Griffiths, now under arrest for drug possession, was taken to the local DEA office for processing. Allman went along and sent fingerprints and photographs of Griffiths to the FBI to resolve definitively whether he was the “Norman Griffiths” who had an arrest record. As it turned out, Griffiths was “Norman Constantine Griffiths, Jr.,” the legal resident alien, but was not “Norman Griffiths,” the convicted felon. This determination took five days to make.
Griffiths was indicted for unlawful possession and possession with intent to distribute 5 grams or more of cocaine base, in violation of 21 U.S.C. § 841(a)(1), (b)(1)(B), and 844(a). He was not charged for failing to have his green card in his possession or for any other immigration offense.
Griffiths’ version of the events differed from the government’s in several respects. The most significant disagreement concerned the consent issue: Griffiths testified that at no time — neither on the street corner nor in the police office — did he consent to a search of his duffel bag.
Lower court proceedings
The district court designated all pretrial matters for determination by United States Magistrate Judge Carol E. Heckman. Thereafter, Griffiths moved to suppress the cocaine discovered in the juice container. The government opposed the motion. In an unpublished report, the magistrate judge recommended that the cocaine be suppressed. She found that the cocaine was not *77discovered pursuant to a consensual search, as the government had argued. She also rejected the government’s alternative argument that the evidence would inevitably have been discovered during an “inventory” of defendant’s possessions pursuant to his detention until his immigration status could be verified. The district court adopted the magistrate judge’s report in its entirety, and suppressed the cocaine.
The government appeals pursuant to 18 U.S.C. § 3731.
DISCUSSION
On appeal, the government has abandoned its quest to prove that the search of Griffiths’ bag was consensual. Instead, the government pursues two other arguments: the search was incident to a lawful arrest; the search was an inventory pursuant to a lawful detainer.
(1) Search incident to arrest
The government first contends that the encounter involving Fry, Allman, and Griffiths on the street two blocks from the bus terminal constituted a de facto arrest. The argument runs that Griffiths had violated 8 U.S.C. § 1304(e) by failing to produce his green card, and, consequently, the officers would not have permitted him to leave if he had refused to cooperate. Under this theory, according to the government, the cocaine would be admissible because it was discovered during a search of Griffiths’ belongings incident to his lawful arrest. We reject this argument, without reaching its merits, because the government failed to pursue it below.
In the proceedings before the magistrate judge and the district court, the government invoked the mantra “search incident to arrest” only twice: (1) in its response to Grif-fiths’ suppression motion; and (2) in its opposition to the magistrate judge’s recommendation that the cocaine be suppressed. In neither instance, however, did the government argue or even explain the point. Instead, it merely incanted the phrase “search incident to arrest” and then immediately proceeded to argue a different theory: that Griffiths had been detained (but not arrested) pending verification of his immigration status, and the cocaine would inevitably have been discovered during a routine inventory of his personal belongings. Significantly, neither the magistrate judge nor the district court made any reference to the “search incident to arrest” theory in ruling on Griffiths’ suppression motion.
In our view, merely typing out the words “search incident to arrest” at the district court level was insufficient to preserve'the issue for appeal. The government was required to offer some argument or development of its theory. It failed to do so, and has therefore waived the issue. Cf. United States v. Braunig, 553 F.2d 777, 780 (2d Cir.), cert. denied, 431 U.S. 959, 97 S.Ct. 2686, 53 L.Ed.2d 277 (1977) (“[Wjhere a party has shifted his position on appeal and advances arguments available but not pressed below ... and where that party has had ample opportunity to make the point in the trial court in a timely manner ... waiver will bar raising the issue on appeal.”).
(2) Inventory incident to detainer
The government has another arrow in its Fourth Amendment quiver. It argues that the district court should have admitted the cocaine pursuant to the “inevitable discovery” doctrine. Under that doctrine, evidence otherwise obtained in violation of the Fourth Amendment is, nevertheless, admissible if the government establishes that the evidence would inevitably have been discovered by lawful means. Nix v. Williams, 467 U.S. 431, 104 S.Ct. 2501, 81 L.Ed.2d 377 (1984); United States v. Whitehorn, 829 F.2d 1225 (2d Cir.1987), cert. denied, 487 U.S. 1237, 108 S.Ct. 2907, 101 L.Ed.2d 939 (1988).
The government argues that, despite the illegal search, Griffiths would still have been “detained” until his immigration status could be established. See Ojeda-Vinales v. Immigration and Naturalization Service, 523 F.2d 286, 287 (2d Cir.1975) (citation omitted) (alien may be detained upon reasonable suspicion of illegal status). Because it took days, not minutes, to check Griffiths’ background, property in his possession would have been taken from him and inventoried *78for safe-keeping. (Griffiths does not argue that the government lacked authority to detain him. See id.) According to the government, that inventory would have resulted in the discovery of the cocaine in the juice container.
The magistrate judge rejected this argument because the government “failed to show how an inventory search of defendant’s bag would have inevitably permitted the officers to open the juice container in search of identification documents.” The magistrate judge was also skeptical as to whether the immigration officials would have detained Griffiths at all, noting that “no immigration law violation was ever charged, and no order to show cause for a deportation hearing was ever served on defendant.” The district court adopted these findings without comment. For the reasons stated below, we vacate and remand for further proceedings.
At the outset, we are satisfied that the government carried its burden of establishing by a preponderance of the evidence that Griffiths would have been detained. The government offered the testimony of Allman, who explained that resident aliens who cannot produce a green card are routinely detained until their immigration status can be determined. Particularly in light of the information Allman received about “Norman Griffiths,” we accept the government’s conclusion that Griffiths would have been held. We also believe, based on Allman’s testimony, that Griffiths’ possessions would have been inventoried because of the length of time he was in custody.
The question, then, is whether the police would have discovered the cocaine pursuant to a valid inventory of Griffiths’ possessions. The magistrate judge never reached this issue, apparently in the belief that the container could only be opened to search for immigration documents, which it was highly unlikely to hold. This view misapprehends the purpose and scope of inventory searches, which “serve to protect an owner’s property while it is in the custody of the police, to insure against claims of lost, stolen, or vandalized property, and to guard the police from danger.” Colorado v. Bertine, 479 U.S. 367, 372, 107 S.Ct. 738, 741, 93 L.Ed.2d 739 (1987).
The police thus had authority to inventory Griffiths’ possessions for safe-keeping while he was in custody. Our inquiry is not over, however, because the right to inventory a suspect’s belongings does not carry in its wake unlimited discretion. Instead, the inventory must be conducted pursuant to “established inventory procedures.” Illinois v. Lafayette, 462 U.S. 640, 648, 103 S.Ct. 2605, 2610, 77 L.Ed.2d 65 (1983) (footnote omitted). Particularly when closed containers are involved, the police are required to have an established policy regarding the containers, so that the inventory does not become “a ruse for a general rummaging in order to discover incriminating evidence.” Florida v. Wells, 495 U.S. 1, 4, 110 S.Ct. 1632, 1635, 109 L.Ed.2d 1 (1990). Although the policy need not be in writing, there must be a standardized procedure. United States v. Thompson, 29 F.3d 62, 65-66 (2d Cir.1994).
Neither the magistrate judge nor the district court reached this issue. Accordingly, we remand for the district court to determine whether the cocaine would have been discovered pursuant to an established inventory policy, written or otherwise, including a specific procedure dealing with closed containers.
CONCLUSION
The decision of the district court is Vacated, and the case is Remanded for further proceedings.