Both Democratic and Republican intelligence committee leaders have fallen over themselves to denounce National Security Agency (NSA) leaker Edward Snowden. But other members of Congress are using the opportunity of a renewed debate over surveillance to push for restrictions on the NSA’s ability to collect intelligence on Americans.

Senator Patrick Leahy (D-VT) has introduced a bill that would put an earlier end to provisions in the FISA Amendments Act that authorized the Internet surveillance program known as PRISM. His bill, called the FISA Accountability and Privacy Protection Act, would sunset the authorization to June 2015, two years sooner than the current law. That would force an earlier examination of the law allowing the Internet surveillance program that authorized the U.S. government to request user data from technology companies.

Other parts of the Leahy bill include an amendment to the Patriot Act that would restrict the NSA’s ability to collect phone data. The Guardian revealed that the U.S. government was collecting millions of Americans’ phone metadata, the first scoop that sparked the debate over surveillance. Leahy’s bill stipulates that the phone data would only be collected if it was an authorized investigation and, most importantly, if there was a definite link to a foreign terrorist group or power.

“The recent public revelations about two classified data collection programs have brought renewed attention to the use of government surveillance powers, which deserve close scrutiny by Congress,” said Leahy in a statement, according to the Washington Post. “The comprehensive legislation that I am introducing today will not only improve the privacy protections and accountability provisions associated with these authorities, but also strengthen oversight and transparency provisions in other parts of the USA Patriot Act.”

Leahy’s legislation would also sunset the Patriot Act provisions that allow “national security letters”–letters that are sent to phone and Internet companies that request data about Americans’ activity but that cannot be disclosed. Leahy’s bill would end the current law authorizing “national security letters” in 2015 as well–and force the letters to be made public unless the government gets a court order keeping them secret.

Furthermore, Leahy’s legislation would require inspector general audits of on use of the laws that authorize the NSA’s surveillance programs.

The bill is co-sponsored by four Senate Democrats–Richard Blumenthal, Mark Udall, Ron Wyden and Jon Tester–and one Republican, Mike Lee.

A coalition of Democrats and Republicans introduced similar legislation in the House earlier this month.