The man accused of planning the attacks was waterboarded 183 times. The now outlawed “enhanced interrogation” technique is considered a form of torture.

In the years after the C.I.A. waterboarded the man accused of plotting the Sept. 11 attacks, the agency offered explanations of how he withstood the technique 183 times at a secret overseas prison.

The prisoner, Khalid Shaikh Mohammed, was strapped to a gurney with his head tilted down and a cloth covering his face. Somehow, the theory went, he realized that his captors would pour water on the cloth for at most 40 seconds at a time. So he used his fingers to count until he could breathe again as he experienced the sensation of drowning.

This week, at a hearing in the case, Mr. Mohammed’s lawyer, Gary D. Sowards, offered an alternative explanation while questioning a psychologist who administered the waterboarding.

Some Muslims, including Mr. Mohammed, repeatedly put a thumb to three fingers as they say a prayer praising Allah, Mr. Sowards said. Some also point upward, as if to the sky, when they believe they are taking their last gasps of life — a gesture some C.I.A. observers interpreted as Mr. Mohammed signaling that the time limit was approaching on that round of simulated drowning, and to let him breathe.

No prisoner in U.S. history is known to have been subjected to the technique as many times as Mr. Mohammed. And while waterboarding has been discussed and described periodically during hearings since his arraignment in 2012, this week’s testimony offered a clinical discussion of how C.I.A. representatives repeatedly used it and evaluated its efficacy in a secret prison in Poland in March 2003.

The military judge in the case is trying to decide whether the confessions of Mr. Mohammed and the other Sept. 11 defendants are tainted by torture. If so, they would not be admissible at their eventual capital trial.

The psychologist, John Bruce Jessen, said he agreed with C.I.A. cables to headquarters at the time that Mr. Mohammed “yelled and writhed” while guards “were trying to put him on the waterboard.” Dr. Jessen confirmed that, in his first month of custody, Mr. Mohammed “would sob when he was taken off the waterboard.”

But Dr. Jessen also recalled that Mr. Mohammed was “extremely, uncharacteristically resilient on the waterboard” and “defeated it quite early,” as the C.I.A. has often said.

Waterboarding involves restraining a prisoner and then pouring water onto a cloth on his face to suffocate him long enough to make him physically feel that he is drowning. The United States has condemned its use on U.S. prisoners of war as torture, and it is defined as such under international law.

But lawyers for the George W. Bush administration authorized the C.I.A. to waterboard prisoners in its secret overseas network. President Barack Obama subsequently declared it illegal.

Before Sept. 11, Dr. Jessen oversaw Defense Department programs that trained U.S. forces to resist and survive captivity. He said he had observed exercises where U.S. military personnel were waterboarded — each person just once. But, he testified, he had never done or experienced it before he proposed that the C.I.A. use it on terrorism suspects in 2002.

So he was voluntarily strapped down and waterboard three times, he said, knowing that his colleagues would not kill him. Still, he said, he got the feeling of “wow, if this doesn’t stop, I’m in trouble.”

The C.I.A. has officially admitted to using the technique on three prisoners in the years before they were transferred to Guantánamo in September 2006.

In the summer of 2002, Dr. Jessen poured water on the face of a prisoner known as Abu Zubaydah 63 times in Thailand in his “enhanced interrogation.” The team also tried to do it while interrogating Abd al-Rahim al-Nashiri, who is accused of plotting the bombing of the Navy destroyer Cole off Yemen in 2000. But Mr. Nashiri was too small and slid off the waterboard.

Dr. Jessen testified this week that a fourth man, Mustafa al-Hawsawi, described having it done to him at a C.I.A. prison in Afghanistan — and that he believed him and reported it. Mr. Hawsawi is also charged in the Sept. 11 case.

After Mr. Mohammed was captured in 2003, Dr. Jessen said, the waterboarding team, now in Poland, was under pressure from the president “on down” to get information out of him. During that time, Mr. Mohammed was kept nude and forced to stand in chains to deprive him of sleep, at one point for a week.

Bad intelligence suggested that terrorists would soon detonate a nuclear bomb, possibly in the United States, and the interrogators wanted that information. But Mr. Mohammed apparently had no information to share because, Dr. Jessen testified, a device was never found.

“You’re not there to hurt them,” Dr. Jessen said of the prisoners.

During the hearing, he frequently seemed confused when the defendant was referred to as Mr. Mohammed, his surname. In the C.I.A. prison network, the black sites, Mr. Mohammed was called K.S.M., his initials.

“I had no personal animosities towards Mr. K.S.M.,” Dr. Jessen said. “But he was a lethal enemy. And my job was to do the best I could, along with the rest of the people, to find out if these attacks were real.”

Based on his professional experience, “moral compass” and legal opinions, Dr. Jessen said, he was satisfied that the techniques he helped devise did not constitute torture.

Dr. Jessen was a contractor at the C.I.A. in a consulting partnership with another psychologist, James E. Mitchell, with whom he waterboarded and interrogated prisoners. In 2005, they set up a business that the U.S. government paid $81 million to provide all of the contract guards at the black sites and 80 percent of the agency’s interrogators.

The two men have been testifying in part as stand-ins for full-time C.I.A. employees, whose identities are secret.

Dr. Mitchell had testified earlier that during his “enhanced interrogation,” Mr. Mohammed tried to offer information about the Sept. 11 attacks. But the psychologists said their mission was to get him to reveal details of future plots. So the interrogators repeatedly rammed him backward into a wall when he tried to discuss the coordinated hijackings that killed 2,976 people in New York, at the Pentagon and in Pennsylvania.

In video testimony from Virginia on Wednesday, Dr. Jessen offered a slow-motion demonstration of the “walling technique” on one of Mr. Mohammed’s lawyers. He gently placed a rolled-up, duct-taped towel around the lawyer’s neck and lifted a dark hood off his head as he was standing against a wall inside a courtroom annex. Then the interrogator slowly pushed the lawyer’s back, shoulder blades and head against a wall.

Interrogators have described a dual purpose for the towel: It protects against whiplash and gives a captor a way to take hold of a prisoner who is naked, or wearing only a diaper, as he “bounces off the wall.”

Dr. Jessen started the testimony more than four years ago. His return to the court was repeatedly postponed, first by the its 500-day closure for the coronavirus pandemic and then by health problems.

For this week’s hearing, Dr. Jessen declined to return to Guantánamo. He appeared on a large screen over the court’s witness stand on the opposite side of the room from Mr. Mohammed.

It was hard to discern how much of the testimony the prisoner was following. He mostly huddled with defense team members at the far end of his lawyers’ table, his head down or turned away from the screen, flipping through documents or reading case-related material on a laptop.