They gave him enough slack in the rope and used a large hangmans knot. In this picture you can tell that they almost ripped his head off (notice the blood on the back of his neck).
http://img.photobucket.com/albums/v47/dallas59/Post%20pics/saddam.jpg
That large hangmans knot slams hard against the head causing his head to slam backwards and to the right while at the same time the rope tightens around his neck due to the free fall and his weight.
He was dead before 3 minutes had passed.
I have to agree that the later pictures leave little doubt
that Saddam is dead. Thank you for the clarifying remarks.