The parachutes in the KC-135 had two ripcords. One ceded control of deployment to an altimeter -- chute opened at ~14,000'. The other ripcord opened the chute immediately.
I believe two major factors affecting parachute deployment altitude are oxygen and hang time. IIRC, the descent rate on those canopies is somewhere south of 1000 fpm. Anyone who has hung in a military parachute harness -- especially one hastily fitted close to, ummm, sensitive areas -- knows more than about 15 seconds is too long. Ten minutes would be good preparation for the treatment one is sure to receive after landing in the gulag.
--Mark
Skip Slater said: 'My memory is a bit scratchy here, but I believe it was somewhere around 20,000'. You could always manually release yourself too. At low altitudes, you separated immediately.'