A method of making self-tensioning rings, including the steps of circumferentially machining an out-of-round ring blank on inner and outer surfaces thereof and subsequently cutting a ring segment out of the ring for obtaining a ring gap therein; measuring a circumferential contour of the ring subsequent to the machining step; and calculating the circumferential length of the ring segment and a cutting angle for removing the ring segment from the ring as a function of data obtained in the measuring step.