A bipartisan group of lawmakers is trying to bring the U.S. one step closer to finalizing a privacy-rights agreement with the European Union that’s been in the works since 2011. And in doing so they aim to boost sales for U.S. tech firms that have suffered in the wake of the Edward Snowden leaks.

The Judicial Redress Act of 2015, S. 1600, introduced by Sen. Chris Murphy (D-Conn.) last week and cosponsored by Sen. Orrin Hatch (R-Utah), would extend the core benefits enjoyed by Americans under the Privacy Act of 1974 to European allies, something EU officials have been demanding ever since revelations of National Security Agency spying programs in 2013.

“The passage of this bill will provide a clear signal to our allies that we value the transatlantic relationship and seek to fully rebuild trust in U.S.-EU data flows,” Chris Harris, a spokesman for Sen. Murphy, said in an email Friday.

Under the legislation, the Attorney General, with the approval of the Secretary of State, the Secretary of the Treasury and the Secretary of Homeland Security, would have the power to extend judicial redress to a foreign country’s residents.

The Privacy Act allows U.S. citizens to contest misuse of data collected on them by law enforcement in a court, a right that non-U.S. citizens currently don’t have, but is afforded to American citizens in many European countries.

Rep. Jim Sensenbrenner (R-Wis.) introduced a similar measure H.R. 1428, in March.

The legislation has taken on renewed importance in the aftermath of top-secret documents WikiLeaks released on Wednesday that allege the NSA spied on three successive French presidents. While President Barack Obama assured French President François Hollande that the U.S. is no longer spying on him, the relationship between the U.S. and its European allies remains strained.

Both bills were introduced as part of a large negotiation going on between the U.S. and the European Commission, which is representing the EU on this matter, and was specifically requested for from the European Union as part of the so-called Data Protection Umbrella Agreement.

“Adoption of the Judicial Redress Bill will allow for the conclusion of the umbrella agreement, which ensures a high level of data protection and greater legal certainty for our law enforcement data exchanges,” European Commission Vice-President Viviane Reding said in a March statement, referring to the Umbrella Agreement. “I remain committed to finalise the text of the agreement and initial it as soon as possible. We are not yet fully there – but I can tell you – we are not far. We would then conclude it once the Judicial Redress Bill has become law.”

The negotiations between the EC and U.S. began in 2011. But in 2013, when the NSA documents were released, the European Commission was less enthusiastic about the agreement. The EU has repeatedly said that until a “right to judicial redress” for its citizens is preserved in law, they will not sign the agreement.

The agreement, which would extend to private companies and law enforcement groups, looks to create an international framework to protect personal data transfers between the U.S. and EU, including cases in which personal data are sent from Europe to the U.S. for investigating and prosecuting crimes such as terrorism.

Sensenbrenner, a key architect of the 2001 Patriot Act and more recently the USA Freedom Act, said it is the responsibility of Congress to act in the best interest of America and its trusted allies.

“If the bill does not pass, bilateral agreements with the European Union could be negatively affected,” he said in an email. “But with the recent, bipartisan introduction of the legislation in the Senate, I’m optimistic that it will be brought to a vote and passed.”

While the Snowden revelations caused anger and debate among American citizens and nations worldwide, it had major blowback for one group in particular that has a large stake in EU citizens’ trust: U.S. businesses.

Thursday, a group of advocates sent a letter to Senate leaders calling for the swift passage of Murphy’s bill, whose supporters include the U.S. Chamber of Commerce, the Trans-Atlantic Business Council, Computer & Communications Industry Association, Google and Yahoo.

“The last two years have seen a significant erosion of global public trust in both the U.S. government and the U.S. technology sector,” the letter states. “As a result, U.S. companies across all sectors are suffering negative commercial consequences abroad. To help restore the public trust necessary for the continued success of U.S. industry, the Judicial Redress Act will extend certain rights to the citizens of our designated allies, particularly European Union Member States.”

A similar letter was sent in April to House leaders urging passage of Sensenbrenner’s bill.

Passage “would be very helpful for rebuilding trust with data transfers between law enforcement agencies in Europe and the Untied States, which in large part really colors how general data transfer are perceived by the European public,” Bijan Madhani, public policy and regulatory counsel at the CCIA, an advocacy group for free trade and open markets, said in an interview.

No congressional committee has taken action on either measure.

The Information Technology and Innovation Foundation, which advocates for policies that advance tech productivity, released a report this month showing the negative side effects on U.S. business as a result of the Snowden leaks.

“It has become clear that the U.S. tech industry as a whole, not just the cloud computing sector, has under-performed as a result of the Snowden revelations,” the June report states. “In the short term, U.S. companies lose out on contracts, and over the long term, other countries create protectionist policies that lock U.S. businesses out of foreign markets.”

In 2014, the German government announced it would terminate its internet contract with Verizon, in part due to the NSA revelations.

“How data is accessed and used both at home and abroad is one of the most pressing issues confronting us today,” Hatch said in a June 17 statement. “In today’s global economy, it is vital that we maintain strong relationships with our international partners, and the Judicial Redress Act will help us accomplish that.”