In reply to Mr Lopez:
I don't think that video is correct - he pulls off loop after loop that has been coiled (with an inherrent twist) rather than laid (no twist).
Some ropes come coiled, some come laid. The rope he is demonstrating has been coiled. You can see the effect of this as he pulls it through the quickdraw - lots of little pigtails that put a spiral into the rope.
If you reverse coil it (turn the coil of rope round and round, feeding the rope off) then you take all the kinks out and you don't get the pigtails in the rope. One cursory pull through is all it takes to make it good to go.
From then on, NEVER coil it - always lay it alpine style or stack it in a heap on a rope sheet (with both ends tied off to prevent knots)
badly spiralled ropes are more a case of prevention than cure IMO.