WASHINGTON (AP) — In an overwhelming vote, the House moved the U.S. closer to ending the National Security Agency’s bulk collection of Americans’ phone records Thursday, the most significant demonstration to date of leaker Edward Snowden’s impact on the debate over privacy versus security.

But the final version of the legislation, “watered down” in the words of one supporter, also showed the limits of that impact. The bill was severely weakened to mollify U.S. intelligence agencies, which insisted that the surveillance programs that shocked many Americans are a critical bulwark against terror plots.