Investigators concluded:

[Brig. General Janis]Karpinski and Pappas "knew, or should have known, abuses were taking place and taken measures to prevent them."

Chief abuser Charles Graner, who got a 10 year sentence, claimed Pappas and his deputy, Lt. Col. Steven L. Jordan, ordered the abuse.
Jordan's fate is still pending.

The ACLU sued Pappas in Connecticut for prisoner abuse. The complaint is here.(pdf) Read pages 46 - 49, detailing the torture of detainees. This information was obtained from Government reports and from reports of the Red Cross and other agencies.

Soldiers tore out detainees’ toenails, administered electric shocks, beat detainees with hard objects (including pistols and rifles), slapped and punched detainees, kicked them with knees or feet on various parts of the body (legs, sides, lower back, groin), forcefully pressed detainees’ faces into the ground by stepping on their heads, purposely exposed detainees to severe heat and sun for prolonged periods, and forced detainees to stay in “stress” positions (kneeling, squatting, standing with arms raised over their heads) for hours at a time.

It gets worse. Another example of torture found by the Red Cross (p. 50):

At least two detainees were forced to sit or lie down on blistering surfaces, causing severe burns that resulted in large crusted lesions and, in one case, three months’ hospitalization, the amputation of a finger and large skin grafts.

Is this what Alberto Gonzales believes to be conduct falling short of torture?

"Torture, as a matter of prosecution, is defined by Congress as the intentional infliction of severe physical and mental pain or suffering. Congress intended a very high bar here in order to be prosecuted for engaging in torture," he said. "There may be conduct that you may find offensive that falls far short of torture."