In reply to Neil Williams:
That works fine in theory, but as the leader climbs past a clip you transition from taking in to paying out in the blink of an eye. If I'm doing the old "walk hands up the dead rope" then my leader is gonna be p***ed off when they snag immediately above the clip because I'm switching my hands about trying to pay out rope with both hands below the belay plate.
In reality, if I'm in the split second between taking in rope and reaching my hand back up to the plate to take the more rope in, then if the leader falls in that 0.25 second interval, the difference in speed between the rope and my hand is almost negligible. I'm gonna have no issues at all tightening my grip around the rope and catching the fall. It's happened to me before and it's a complete non-issue. It's arguably more of an issue if the leader falls while I'm paying out rope and reaching down to feed more rope through as the speed of the rope relative to my hand is higher and I'm more likely to get rope burn. Again though, in reality, it's a complete non-issue.
In summary: keep your hand around the dead rope ready to tighten it, keep an eye on your climber, and never let go of the dead rope completely!