The plaintiffs said that Drs. Jessen and Mitchell, former military psychologists, profited from their work as contractors for the C.I.A. The men received up to $1,800 a day and later formed a company that was paid about $81 million to help operate the interrogation program over several years.
The United States government also agreed to indemnify the men and their company, including paying legal fees, judgments and settlements up to $5 million. Some of those funds were used to cover legal bills during Justice Department investigations. As of November 2011, there was close to $4 million left, according to a document made public in the lawsuit.
James T. Smith, the psychologists’ lead counsel, said in a statement that his clients were “public servants whose actions in regard to the interrogation of suspected terrorists were authorized by the U.S. government, legal and done in an effort to protect innocent lives.”
Speaking by phone after the settlement was announced, Dr. Mitchell said he found it “regrettable that one guy died and those other guys were treated badly,” adding: “We had nothing to do with it. We’re not responsible for it. They say we are, but in my view they’re wrong.”
The psychologists produced a memo in 2002 proposing harsh techniques to be used on terrorism suspects thought to be resisting interrogations. The C.I.A. adopted nearly all of these methods, including waterboarding, stuffing prisoners into small boxes, forcing them to hold painful positions for hours and slamming them into flexible walls.
The so-called enhanced interrogation techniques were based on those used in military survival schools to simulate what service members might undergo if captured by regimes violating the laws of war. They were later condemned as illegal under United States and international law and were ultimately banned. The American Psychological Association consequently prohibited its members from participating in national security interrogations.
As a candidate, President Trump said he would bring back waterboarding “and a hell of a lot worse,” but later said he would defer to Defense Secretary Jim Mattis’s strong opposition — widespread in the military — to torture and prisoner mistreatment.
The case against the psychologists proceeded despite multiple attempts by their lawyers to have it dismissed. They argued that the men acted solely under the authority of the government and were entitled to the same immunity as government officials. The judge, Justin L. Quackenbush, also denied motions by both sides requesting that he rule summarily in their favor before a trial.
Although there will be no public trial, the case — over its nearly two-year course — expanded public knowledge about the C.I.A.’s torture program. Previously secret documents were declassified, including C.I.A. cables from the covert prisons known as black sites. And the two psychologists, along with the former C.I.A. officials Jose Rodriguez and John Rizzo, were subjected to lengthy questioning by opposing lawyers in video depositions. Their sometimes sterile description of the techniques contrasted with the emotional accounts, in separate depositions, of the men who underwent them.
The plaintiffs and some of their experiences are described in the executive summary of the 6,700-page Senate Intelligence Committee Report on Torture. The report, published in December 2014 and based on a five-year review of over six million pages of documents, lists 38 men known to have been subjected to the techniques in C.I.A. prisons. It denounced the methods as brutal and criticized the C.I.A. for providing false and misleading information to federal officials about the interrogation program’s effectiveness.
The psychologists came into direct contact with only one of the three detainees, Gul Rahman, who died in C.I.A. custody in Afghanistan in 2002, probably of hypothermia, according to an agency investigation into his death.
The judge ruled last week that a trial could also proceed on behalf of the two other former prisoners — Mr. Ben Soud and Suleiman Salim — whose lawyers argued that the psychologists had aided and abetted their torture.
Mr. Ben Soud, a Libyan detained by the C.I.A. in 2003 and held in Afghanistan, was locked in small boxes, slammed against a wall and doused with buckets of ice water while naked and shackled. Mr. Salim, a Tanzanian also captured in 2003 and held by the C.I.A. in Afghanistan, was beaten, isolated in a dark cell for months, doused with water and deprived of sleep.
The A.C.L.U. and the Gibbons law firm of Newark brought the lawsuit under the Alien Tort Statute, which allows foreign citizens to seek justice in United States courts for violations of their rights under international law or United States treaties.