You've alluded to "other" methods of extracting information out of combatants without "willfully causing great suffering or serious injury". Care to go into some detail about that?
Sure. One method is to put them in a room with no windows. You give them enough food, but at random intervals. You give them enough sleep, but also at random times. Within a few days, the part of the brain that marks time basically stops functioning, as they have no frame of reference...It's a form of sensory deprivation that causes no discomfort or injury, and impairs their judgement, and they sing like canaries. The Germans and the Russians used this to great effect, starting in the early 40s. Thing is, as soon as they gain a point of reference (a clock, a window through which they can see the sun, etc), they revert to normal.
Also, the regular old Reid Technique used by police usually works, especially when conducted for 12 hours a day, 7 days a week.
Also, you try them as unlawful combatants, and you have a firing squad to use as leverage (The GC and American law allow for executing illegal combatants). It's amazing how many wannabe holy warriors have a change of heart when they actually have to look at the blindfold. This, also, is perfectly legal.
And if they don't sing? Find a suitable backstop, a blindfold, and a cigarette, and let the other illegal combatants watch the show. Someone will talk.
Strapping on the great moral compass and riding into the sunset doesn't necessarily win friends and endear ourselves to the bad guys.
I don't give a shit what the bad guys think. I am concerned with the ethics of America, and nobody else.