Dozens of civil liberties groups are calling on Congress not to stop short in reforming the National Security Agency.

The Bill of Rights Defense Committee led other organizations in a letter on Tuesday warning Congress against stopping with the USA Freedom Act, a bill currently in the Senate that would end the NSA’s bulk collection of Americans’ phone records.

{mosads}Lawmakers should pass that bill “and then immediately turn your attention to more meaningful and comprehensive reform of the [NSA’s] overreaching and unconstitutional surveillance practices,” the groups wrote.

The USA Freedom Act is “an important first step in curtailing the NSA’s abuses of fundamental constitutional rights, but it would not be enough,” they added.

For instance, the bill does not address so-called “backdoor” searches in which the NSA uses a legal authority meant to target foreigners to spy on Americans. It also does not address a contentious executive order that is the “primary source” for most of the agency’s spying, nor does it require the government to disclose its legal interpretations about contested laws.

“While we hope the USA Freedom Act would impose restraints on mass violations by the NSA and FBI, we recognize that, as currently drafted, [the Senate bill] fails to address these vital concerns,” the groups wrote.

The Libertarian Party, Council on American-Islamic Relations and Open The Government are among the organizations that signed the letter.

The USA Freedom Act passed the House earlier this year, but critics contended that it had been overly watered down and made toothless by the time it hit the floor.

Now the focus is on the Senate, where Judiciary Committee Chairman Patrick Leahy (D-Vt.) has been trying to get the bill passed by the end of the year. A broad coalition of lawmakers from both sides of the aisle as well as tech companies, privacy advocates and the Obama administration have signed on in support, but its prospects are still uncertain given congressional leaders’ reluctance to debate controversial matters during the lame duck period.

Critics of the bill have warned that it would jeopardize American national security right when the country is launching a military campaign against the Islamic State in Iraq and Syria (ISIS).