Well there's a video on this page from the petzl site. They describe 2 methods. The classic method involves taking your break hand mostly off
the rope, if not completely off.
http://www.petzl.com/en/outdoor/belay-devices/grigri
The 'new' way does not. However, I have to say everything looks easy on brand new ropes in clean gri-gri's.
The issue I've been specifically referring to this whole time (I guess I should've tried to explain it from the start) is when you take either a novice belayer, or a veteran atc user and give them a gri-gri. If they are using the 'classic' way, which is what everybody used to do when they first came out, then if the climber fell while you were feeding slack via the pinch technique described in that video, your hand is on the device itself. The natural instinct at this point of a veteran atc user, or a new belayer is to squeeze hard with the brake hand. Unfortunately, the brake hand is on the gri-gri, and squeezing results in the leader falling rapidly towards the ground. The 'proper' thing to do is to rapidly slide your break hand back up to the rope. But I find that it is easier, at least at first, to just tell them to let go when in doubt. If they let go, on a normal lead fall, it is guaranteed to hold, unless the device itself fails, which I've never seen or heard of. Then the belayer can put his hand back on the brake line, and everybody is alive and well.
I use the 'classic way' although I find myself having to do the pinch to feed slack nearly all the time on anything other than a new rope, or a really thin rope. Sometimes I'll try to just hold the bottom of the device which seems to prevent it from cinching while feeding slack, but not in the event of a fall. This is, of course, when I'm not busy letting go with both hands and turning my back on the leader.