The House Intelligence Committee’s Republican and Democratic leaders said Thursday they’re nearing agreement on legislation that would end the National Security Agency’s bulk collection of U.S. citizens’ telephone data.

Negotiations on some key details remain fluid, but Ranking Member Dutch Ruppersberger (D-Md.) said in an interview that he’s “very close” to a deal with Chairman Mike Rogers (R-Mich.) on a plan that would allow phone companies to hold telephone records now collected by the NSA and conduct individual searches needed to pinpoint suspicious activity.

“We’ve got to have legislation that will take away the concern and perception that people are being listened to,” Ruppersberger said. He added that he hoped to reach an agreement before the end of this month.

Rogers avoided specifics in a separate interview, though he did confirm that talks with Ruppersberger and White House officials have been productive on a bill that would try to address some of the fallout from former NSA contractor Edward Snowden’s stolen secret documents.