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The documents add that “airflow is restricted for 20 to 40 seconds and the technique produces the sensation of drowning and suffocation.” The session was not supposed to last more than 20 minutes.

The psychologists also waterboarded USS Cole bombing plotter Abd al-Nashiri twice in Thailand, according to former intelligence officials.

The role of Mr. Mitchell and Mr. Jessen in the interrogation of confessed Sept. 11 mastermind Khalid Sheikh Mohammed is a bit murkier.

At least one other interrogator was involved in those sessions, with the company providing support, a former official said. Mohammed was waterboarded 183 times in Poland in 2003, according to documents and former intelligence officials.

The CIA inspector general concluded in a top secret report in 2004 that the waterboarding technique used by the CIA deviated from the rules outlined by the Justice Department and the common practice at SERE school. CIA interrogations involved far more water poured constantly over the prisoner, investigators said.

“One of the psychologists/interrogators acknowledged that the agency’s use of the technique differed from that used in SERE training and explained that the agency’s technique is different because it is ‘for real’ and is more poignant and convincing,” the inspector general’s report said.

It was not clear whether Mr. Mitchell or Mr. Jessen made that remark.

Justice Department prosecutor John Durham is investigating whether any CIA officers or contractors, including Mr. Mitchell and Mr. Jessen, should face criminal charges.

In at least two instances, Mr. Mitchell and Mr. Jessen pushed back. During Zubaydah’s interrogation, the psychologists argued he had endured enough waterboarding, believing they had reached the point of “diminishing returns.” But CIA superiors told them to press forward, two former officials said.

In another case, Mr. Mitchell and Mr. Jessen successfully argued against waterboarding admitted terrorist Ramzi Binalshibh in Poland, the official said.

On top of the waterboarding case, Mr. Mitchell and Mr. Jessen also needed lawyers to help navigate the Justice Department’s investigation into the destruction of CIA interrogation videos.

Mr. Mitchell and Mr. Jessen were recorded interrogating Zubaydah and al-Nashiri and were eager to see those tapes destroyed, fearing their release would jeopardize their safety, former officials and others close to the matter said.

They often contacted senior CIA officials, urging them to destroy the tapes and asking what was taking so long, said a person familiar with the Durham investigation who insisted on anonymity because the case’s details remain sensitive. Finally the CIA’s top clandestine officer, Jose Rodriguez, made the decision to destroy the tapes in November 2005.

Mr. Durham investigated whether that was a crime. He subpoenaed Mitchell, Jessen & Associates last year, looking for calendars, e-mails and phone records showing contact between the contractors and Rodriguez or his chief of staff, according to a federal subpoena. They were ordered to appear before a grand jury in northern Virginia in August 2009.

Last month, Mr. Durham closed the tapes destruction investigation without filing charges.