I seem to remember (me remember?) that is was a 5/16", but I am certain that you can trust your instincts as to how far to relieve the 'upset' portion of the rivet.
I'm overly cautious, so I drill and smack, drill and smack, etc.
Usually it pops back out leaving a perfect little ring around the punch.
I have been reminded off-forum how bad my memory is. Please measure your replacement rivets, as 5/16" must be for common Chiefs. (I keep them all in the same drawer.) I guess that leaves 1/4". Perhaps I might remember to look tomorrow at the shop.