Senate Intelligence Chairwoman Dianne Feinstein said something Thursday afternoon that might have defense contractors cringing.

Speaking after a closed briefing for senators about the National Security Agency’s surveillance activities, the California Democrat signaled she would move to restrict the ability of contractors to access particularly sensitive classified information in the aftermath of the leaks by 29-year-old Edward Snowden, who was an employee of Booz Allen Hamilton.

“We will certainly have legislation, which would limit or prevent contractors from handling highly classified technical data and we will do some other things,” Feinstein said when asked what comes next.

Sen. Saxby Chambliss, R-Ga., vice chairman of the Intelligence Committee, said he was unsure that legislation for contractors was needed, but he said that other steps could be taken.

“I don’t know whether what we need to do needs to be done legislatively or not, but I think it’s pretty clear that we have to do a better job of making sure that our top-secret clearances go to only those individuals that deserve it and that we monitor all of those people who have a top-secret clearance from time to time, and we review their cases to determine whether or not there is any reason to suspect that they may have compromised U.S. intelligence in some way,” Chambliss said.

“I have tasked Director Clapper to consider the program, to present some changes if he feels it necessary,” Feinstein said, in an apparent reference to the NSA operations disclosed following reporting on Snowden’s leaks by The Guardian and The Washington Post. “We would consider changes.”

Feinstein said new information about terrorist acts thwarted by NSA programs could be released June 17.

Chambliss said special care will be taken if any information about thwarted plots were to be declassified.

“We would like to declassify as much information [as] we can about specific instances, but the problem you have is that declassifying almost always leads to the acknowledging of sources and methods and if we divulge sources and methods then we give the enemy a lot of our information that we use to watch them,” Chambliss said. “So the White House, and they haven’t told us exactly what they are going to do, but based on what we heard again today, they are going to be very careful on making a decision on declassifying any information.”

According to Feinstein, the seven briefers included Director of National Intelligence James R. Clapper Jr., NSA Director Gen. Keith Alexander and a former chief judge of the Foreign Intelligence Surveillance Court.  She also said that 47 senators attended.

“The privacy of Americans is protected under these procedures,” Florida Democratic Sen. Bill Nelson said. “It is misunderstood that Americans’ private information — telephone calls and emails — are being rummaged through by the government. That is not true.”

Nelson said he has found himself “just amazed to see the misunderstanding that people have that they think Americans’ private information is open to the government.”

Foreign Relations ranking member Bob Corker, R-Tenn., said that he already knew about the PRISM program, which pertains to collection of electronic communications before the public release.

“I can’t imagine any United States senator sitting in a briefing like we just had and not feeling thankful for the efforts that NSA and others put forth,” Corker said. “At the same time, there’s a question that … to keep these things in balance, the Senate has to do its job also as a place for oversight.”

Sen. Mike Johanns, R-Neb., came away from the briefing more comfortable with the programs.

“They kind of walked through the parameters of the program, the checks and the balances, and I am not sure I came out with a master’s degree understanding of it but it was a step in the right direction,” Johanns said. “I wouldn’t say [my concerns] were 100 percent resolved, but I think some very good steps were taken.”

Not all senators were talking, however. Sen. Rand Paul, R-Ky., who has criticized the NSA programs, declined to speak about the briefing with a gaggle of reporters and TV crews assembled nearby.