WASHINGTON (AP) — The Supreme Court on Wednesday seemed ready to strike down a restrictive New York gun permitting law, but the justices also seemed worried about issuing a broad ruling that could threaten gun restrictions on subways, bars, stadiums, and other gathering places.

The court was hearing arguments in its biggest guns case in more than a decade, about the right to carry a gun outside the home. Supreme Court decisions in 2008 and 2010 established a nationwide right to keep a gun at home for self-defense.

During two hours of arguments conservative members of the court, where they have a 6-3 majority, suggested New York’s law and perhaps others like it in half a dozen other states go too far. Why, Chief Justice John Roberts asked, does a person seeking a license to carry a gun in public for self-defense have to show a special need to do so. “The idea that you need a license to exercise the right, I think, is unusual in the context of the Bill of Rights,” he said.

Justice Amy Coney Barrett told Clement that there’s a history of states outlawing guns in “sensitive places.” “Can’t we just say Times Square on New Year’s Eve is a sensitive place…people are on top of each other…so we’re making a judgment, it’s a sensitive place.”

Paul Clement, arguing on behalf of New York residents who want an unrestricted right to carry concealed weapons in public, acknowledged that might be fine. In response to other questions, he said restrictions on guns in the New York City subway system and Yankee Stadium might also be okay.

Justice Brett Kavanaugh suggested that difficult questions about where exactly guns can be prohibited might be left for another day. “We don’t have to answer all the sensitive places questions in this case, some of which will be challenging, no doubt. Is that accurate?” he asked Clement, who agreed.

Arguing for the federal government, Brian H. Fletcher called New York’s law “consistent with the Second Amendment because it is firmly grounded in our nation’s history and tradition of gun regulations.”

The court’s liberal justices seemed willing to allow the state law to remain in place. Justice Elena Kagan called it “completely intuitive” that different states would have different gun laws, and that it is harder to get a license to carry a gun for self-defense in New York City than in a more rural area of the state. And Justice Sonia Sotomayor said that in her view, looking at the history and tradition of the Second Amendment, “states get a lot of deference” on restrictions.

Justice Stephen Breyer asked what kind of license the law’s challengers were asking for. Is the license “supposed to say you can carry a concealed gun around the streets or the town or outside just for fun? I mean, they are dangerous, guns,” he said.

But the court’s conservatives suggested New York’s requirements are unduly restrictive. Justice Samuel Alito asked whether New York’s law would allow a person to get a license to carry a gun if they get off work late and have to travel through a high crime area to get to a subway or bus. New York Solicitor General Barbara D. Underwood, arguing for the state, said no; that person has no specific need for a weapon that’s different from the general public.

“How is that consistent with the core right to self-defense, which is protected by the Second Amendment?” Alito asked. He said there are many people with illegal guns “walking around the streets” in New York while “the ordinary, hard-working, law-abiding people I mentioned—no, they can’t be armed?”

Underwood said that there’s no right “to be armed for all possible confrontations in all places.” She also said that allowing New York only to limit the carrying of guns in sensitive places would be inadequate. “In principle, it has an attractive quality to it, but in implementation, I think it would be unsuccessful,” she said.

Clement, arguing for the law’s challengers—including the New York State Rifle and Pistol Association, headquartered in East Greenbush—said the nation’s founders envisioned people making their own decisions about carrying a firearm outside the home for self-defense. “In 43 states, people are able to do that,” he said, adding “it doesn’t mean that those 43 states have any more problems with violent crimes” than the states like New York.