ORDER

FBI agents uncovered drugs and a handgun in Miguel Bustamante’s car, and he was sentenced to 123 months’ imprisonment-on the charges that followed. Busta-mante asked the district court to vacate his sentence, 28 U.S.C. § 2255, claiming, as relevant here, that his attorney was ineffective for not moving to suppress his admission that the car was his, a statement he made without the benefit of Miranda warnings. The district court denied the motion but granted Bustamante a certificate of appealability. We affirm the judgment.

Bustamante, a suspected player in a cocaine conspiracy, was arrested at the home of a female companion. Before giving him Miranda warnings, agents asked Busta-mante if a car parked behind the building belonged to him, and he admitted that it did. Later, after he had invoked his right to counsel, agents obtained his consent to search the vehicle and found cocaine and a handgun inside its console. Bustamante was Charged for his role in the drug conspiracy, 21 U.S.C. §§ 846, 841(a)(1), as well as possession with intent to distribute cocaine, id. § 841(a)(1), unlawful possession of a firearm after a felony conviction, 18 U.S.C. § 922(g)(1), and carrying a firearm in relation to a drug offense, id. § 924(c)(1). He moved to suppress the evidence found inside his car, asserting only that his consent to search was obtained in violation of Miranda; he said nothing about suppressing his related admission that he was the car’s owner. The district court denied the motion, and Bus-tamante later pleaded guilty to all but the conspiracy charge. On direct appeal he challenged the district court’s ruling on his suppression motion, but we affirmed the judgment, concluding that there had been no constitutional violation because a request for consent to search a vehicle is not “interrogation” for purposes of Miranda. United States v. Bustamante, 493 F.3d 879, 892 (7th Cir. 2007).

In his § 2255 motion, Bustamante argued that his attorney provided ineffective assistance by not moving to suppress his admission that he was the owner of the vehicle parked outside his girlfriend’s *710 apartment. To establish that he received ineffective assistance of counsel, Busta-mante was required to prove that his lawyer’s performance was deficient and that, but for the alleged deficiency, he would not have pleaded guilty. See Hill v. Lockhart, 474 U.S. 52, 59, 106 S.Ct. 366, 88 L.Ed.2d 203 (1985); Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984); United States v. Peleti, 576 F.3d 377, 383 (7th Cir. 2009). When a claim of ineffective assistance is premised on an attorney’s failure to file a motion to suppress, the defendant must prove that the motion would have been meritorious. United States v. Cieslowski, 410 F.3d 353, 360 (7th Cir. 2005).

The government concedes that Busta-mante would have prevailed if his attorney had moved to suppress his admission of ownership. As we have held, where the police do more than ask for consent to search and inquire “as to ownership of that which is searched, the inquiry crosses the threshold into testimonial incrimination and is therefore barred unless the safeguards of Miranda have been put in place.” United States v. Smith, 3 F.3d 1088, 1098-99 (7th Cir. 1993); see also United States v. Henley, 984 F.2d 1040, 1042^43 (9th Cir. 1993); United States v. Monzon, 869 F.2d 338, 341-42 (7th Cir. 1989).

But that is not enough to demonstrate that counsel’s performance was constitutionally deficient. Even assuming that the district court would have granted a motion to suppress Bustamante’s admission, the government’s case against him would have remained the same because his consent to search the car and the physical evidence that was discovered would still be admissible. See United States v. Patane, 542 U.S. 630, 633-34, 124 S.Ct. 2620, 159 L.Ed.2d 667 (2004) (plurality opinion); United States v. Renken, 474 F.3d 984, 988 (7th Cir. 2007). Bustamante has never asserted, and there is no reason to believe, that the government would have been unable to connect him to the vehicle without his admission of ownership. Cf. Henley, 984 F.2d at 1044-45; see also Gentry v. Sevier, 597 F.3d 838, 851-52 (7th Cir. 2010) (concluding that counsel’s performance was constitutionally deficient where motion to suppress evidence would have been meritorious and government could not have convicted defendant without the excluded evidence). For example, although the record is silent about whether the car was registered to Bustamante, his girlfriend told agents that the keys to the ear found during a search of her bedroom belonged to him. An attorney is not required to pursue an argument that can lead only to a dead end for his client. Cf. United States v. Harris, 394 F.3d 543, 555-56 (7th Cir. 2005); United States v. Rezin, 322 F.3d 443, 446 (7th Cir. 2003). Bustamante had nothing to gain from having his admission of ownership excluded, and thus his lawyer’s decision to forego a motion to suppress was a sound strategic decision that cannot give rise to a claim of ineffective' assistance of counsel. See Cieslowski, 410 F.3d at 360-61.

AFFIRMED.