By Patricia Zengerle and Thomas Ferraro

WASHINGTON (Reuters) – Some members of the Congress say that getting straight answers from intelligence agencies about top-secret surveillance is like playing the game “20 Questions,” where answers come only if a questioner knows exactly what to ask.

They say quality of closed briefings depends largely on who conducts the sessions and whether members go in with a working knowledge of programs and pointed questions.

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Intelligence officials have scheduled several such briefings this week amid the furor over data collection by the National Security Agency after secrets were leaked to news outlets by Edward Snowden, an employee at an NSA contractor.

Although President Barack Obama insisted the Congress was “fully briefed,” many lawmakers said they were unaware of two programs exposed by Snowden that involved collecting billions of telephone records and monitoring Internet data through companies such as Google Inc and Facebook Inc.

“We, here, Congress needs to be informed of what’s going on, and we’re not, and that’s very disturbing to me,” said Democratic Senator Jon Tester, a sponsor of new legislation to force more disclosure to Congress.

A confidential briefing for the full Senate is set for Thursday to discuss details of the NSA surveillance. But a similar briefing Tuesday by officials from the Department of Justice, FBI, NSA and the office of the Director of National Intelligence for all 435 members of the House of Representatives left many lawmakers unsatisfied.

“I think there are still more questions than answers,” Republican Representative Tom Price said after the session.

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Administration officials noted that members of Congress were filled in on the programs 22 times in the 14 months ending in December 2012. Those sessions included hearings, meetings with individual members and meetings of the Judiciary and Intelligence committees, a senior administration official said.

‘TELLING US AS LITTLE AS THEY COULD’

Former U.S. Representative Jane Harman, a Democrat who served on every major House security committee before resigning from Congress in 2011, said getting the right briefer can make a big difference in how much lawmakers learn.

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“Sometimes these briefings are a game of 20 questions. If you don’t ask exactly the right question, you don’t get the answer,” said Harman.

Senators are generally provided with more information than members of the House. Staffers said high-tech intelligence issues also are particularly difficult because computer-savvy staffers – on whom busy lawmakers rely – are often barred from classified sessions.

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Lawmakers said oversight is made more difficult when spy agencies guard the truth.

“One of the most important responsibilities a senator has is oversight of the intelligence community. This job cannot be done responsibly if senators aren’t getting straight answers to direct questions,” said Democratic Senator Ron Wyden.

Wyden pressed James Clapper, the director of national intelligence, during a March hearing on whether the government collected data about millions of Americans.

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Clapper said it did not do so deliberately. After the Snowden leak, he said on NBC that his answer to Wyden was the “least untruthful” he could give at the time.

Former Senator Bob Graham, who chaired the Senate intelligence committee from 2001-2003, said spy agencies have always balanced what they see as the need for secrecy with the need to inform Americans.

“In the aftermath of 9/11, I got the impression that they were telling us as little as they could without perjuring themselves,” he said.

(Additional reporting by Roberta Rampton; Editing by Marilyn W. Thompson and Cynthia Osterman)

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[Photos of Snowden, a contractor at the NSA, and U.S. President Obama are printed on the front pages of local English and Chinese newspapers in Hong Kong in this illustration photo]