An impact-compensating bucking bar and its use to reduce impacts during riveting, where the bucking bar includes a body; a strike surface on a distal portion of the body, a compensating inertial mass coupled to the body by a flexible and resilient mass support, and a handgrip coupled to the body and configured for the user to urge the strike surface of the bucking bar against a tail of a rivet to facilitate upsetting the rivet tail during riveting. A relative movement of the compensating inertial mass of the bucking bar in response to a strike on the rivet head at least partially dissipates energy imparted to the body during riveting, reducing impact stresses on the bucking bar user.