A rivet table connected to the nosepiece of a rivet setting apparatus. The rivet table includes an outer sleeve which controllably slides back and forth within the nosepiece and supports opposing jaws pivotally connected to the outer sleeve about spaced transverse pivot axes. The jaws pivot between a closed position and an open position, biased toward the closed position and define a flat transverse distal rivet head receiving surface, and a central mandrel-receiving aperture therebetween to slidably receive a rivet mandrel and to support the rivet head against said rivet head receiving surface during rivet setting. The jaws are momentarily forced into the open position by the mandrel moving laterally into the aperture and being carried on a flexible strip. The exposed surface of the rivet head is thereby substantially free of tool marks after being set.