The Matthew Alexander that Paul mentions is a former USAF officer who served in Iraq until 2006 and who was involved in many high-level interrogations. He wrote this interesting Op-Ed back in November:
Torture and abuse are against my moral fabric. The cliche still bears repeating: Such outrages are inconsistent with American principles. And then there’s the pragmatic side: Torture and abuse cost American lives.
I learned in Iraq that the No. 1 reason foreign fighters flocked there to fight were the abuses carried out at Abu Ghraib and Guantanamo. Our policy of torture was directly and swiftly recruiting fighters for al-Qaeda in Iraq. The large majority of suicide bombings in Iraq are still carried out by these foreigners. They are also involved in most of the attacks on U.S. and coalition forces in Iraq. It’s no exaggeration to say that at least half of our losses and casualties in that country have come at the hands of foreigners who joined the fray because of our program of detainee abuse. The number of U.S. soldiers who have died because of our torture policy will never be definitively known, but it is fair to say that it is close to the number of lives lost on Sept. 11, 2001. How anyone can say that torture keeps Americans safe is beyond me — unless you don’t count American soldiers as Americans.
(…)
We’re told that our only options are to persist in carrying out torture or to face another terrorist attack. But there truly is a better way to carry out interrogations — and a way to get out of this false choice between torture and terror.
Indeed

The Emperor, er, um, I mean Dick Cheney still insists as of last Sunday that torture produced useful results and saved thousands of lives. Hmm… who to believe, the guys who were there, or a bureaucrat?