The National Security Agency has said it will stop snooping on American citizens’ private emails that mention foreign individuals targeted for surveillance, the New York Times reported.

Citing a U.S. official familiar with the decision, the Times said Friday that the NSA will no longer collect or analyze emails that mention identifying terms – such as names or email addresses – of foreigners the agency is spying on.

That surveillance was made possible under section 702 of the 2008 Foreign Intelligence Surveillance Act. The law specifies that the NSA can search through American’s private emails, phone calls and other communications if the content mentions an investigated foreigner in some way. Congress last rubber-stamped those powers in 2012, and they are up for renewal later this year.

Following the New York Times’ report, the NSA later published a statement confirming the decision. “After considerable evaluation of the program and available technology, NSA has decided that its Section 702 foreign intelligence surveillance activities will no longer include any upstream internet communications that are solely ‘about’ a foreign intelligence target,” the agency said. “Instead, this surveillance will now be limited to only those communications that are directly ‘to’ or ‘from’ a foreign intelligence target.”

Although it continued to defend the legality of its surveillance, the NSA admitted it had inadvertently violated some constraints it had agreed to during a secret surveillance court hearing. It said the decision to stop gathering emails was an optional measure aimed at protecting American’s privacy, though it denied accusations that the practice had violated American’s constitutional rights. The NSA added that it will delete the “vast majority of its upstream internet data.”

The change of policy was celebrated by privacy advocates, who argue that the NSA is too broad in its data collection campaigns.

“The content of our emails and texts contains incredibly personal information about our work, our families, and our most intimate thoughts,” said Michelle Richardson, the deputy director of the Freedom, Security, and Technology Project at the Center for Democracy and Technology, in a statement. “The NSA should never have been vacuuming up all of these communications, many of which involved Americans, without a warrant.”

Another rights champion, Sen. Ron Wyden (D-Ore.), told the Times that he plans to introduce new legislation that make the new limitations a law, rather than an “optional measure.”

“This change ends a practice that allowed Americans’ communications to be collected without a warrant merely for mentioning a foreign target,” Wyden told the Times. “While we welcome the voluntary stopping of this practice, it’s clear that Section 702 must be reformed so that the government cannot collect this information in the future.”

Despite the decision, The Register noted that the NSA still has plenty of other legal means by which it can collect more or less the same kind of data. One of those includes Executive Order 12333, issued during President Ronald Reagan’s administration and still used by intelligence agencies to justify their surveillance programs.

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