A method and apparatus for forming rivet joints that allow pivotal motion of the parts interconnected by such joints with a desired amount of clearance. Parts to be riveted together are aligned with each other and held in place on a parts support anvil, and a rivet is placed into aligned holes. A rivet support anvil is positioned against the head of the rivet to establish an initial condition. The rivet support is adjusted a required amount with respect to the parts support anvil prior to formation of the second head on the opposite end of the rivet. The rivet is allowed to move a controlled amount prior to formation of the second head, to provide the desired amount of clearance.