Hi Larry,
I've been countersinking for NAS1097AD3 rivets. They have a VERY small head, but the rivets that hold the nutplates only need to hold them while you're threading the screw into the nutplate. Then the screw holds everything together. Since the rivet head is so small, you don't need to remove much metal. A few turns with a deburring tool is all it takes.
Hope this helps.