Senate lawmakers are exploring whether a gun control compromise might be reached that bans weapons sales to "smaller lists" of people who national security and law enforcement experts believe are connected to terrorism, instead of some of the much larger lists of people that the government maintains.

"There's beginning to be a coalescing around smaller lists, I think," Sen. Lindsey Graham, R-S.C., told the Washington Examiner. "Maybe, hopefully."

Such a policy prescription would be the product of a behind-the-scenes conversation about how the government tracks suspected terrorists, one that is more precise than the political fight that dominated Congress over the past week.

The public debate pits Democratic proponents of the ban against Republicans who worry about depriving people of their right to buy a gun without due process. In private, lawmakers understand that the government maintains a variety of lists, some of which might be more useful than others for targeting terror suspects.

"There are, I think, somewhere on the order of 11 lists, and each list represents something else," said Sen. John Thune, R-S.D.

FBI Director James Comey and Department of Homeland Security Secretary Jeh Johnson conducted a classified briefing with senators of both parties on Wednesday. Convened in response to the Orlando attack, Comey ended up providing the lawmakers with an extended explanation of the criteria for being placed on the various lists, several senators who attended the meeting told the Examiner.

"That was most of the discussion of the lists — how do they get on, how do they get off, and that category is all classified," one GOP senator, who like others discussed the briefing on condition of anonymity, said following the meeting.

That briefing took place while Sen. Chris Murphy, D-Conn., and several of his colleagues staged a talking filibuster in order to force a vote on an amendment that would ban the sale of weapons to anyone whose name appears on a "terror watch list," as he put it.

But Comey's briefing fed a conversation about whether one of the "smaller lists," to use Graham's term, could be used to ban or delay gun sales to individuals who are perceived as being particularly dangerous. Another senator indicated smaller lists exist that are made up of people with more specific evidence against them, as opposed to the larger lists that include anyone who might be broadly suspected.

"Fingerprints on an IED [improvised explosive device] are different than your neighbor reporting you," said another senator.

Such a proposal could still meet with opposition in both parties. Democrats could insist upon a ban that covers every list. And, whether the list is large or small, many Republicans will oppose depriving someone of the right to purchase a weapon unless the government can prove to a judge that they are dangerous.

"A lot of our members want to ensure that whatever is done creates due process for people," Thune said.