An eyeglass assembly including an endpiece which is adapted to engage a flexible strand for holding a lens, the endpiece having an inner surface which is disposed adjacent to the lens when the lens is present; the inner surface of the endpiece having a front edge and a back edge for being located adjacent to front and back sides of the lens; the front edge being chamfered to define a chamfer angle of substantially 8° to 65° with respect to the lens; and the back edge being chamfered to define a chamfer angle of substantially 8° to 50° with respect to the lens. The chamfering of the edges of the endpiece is effective to reduce the risk of chipping the lens when the endpiece is adjusted to fit the wearer's head. Also disclosed is an elastic cushioning ring disposed between the lens and the frame and/or the flexible lens supporting strand in a rimless or semi-rimless frame.