To reduce damage to surrounding tissue while fragmenting some tissue such as for example not damaging the capsular wall while removing the lens during cataract removal surgery or not damaging artery or vein walls during bypass surgery while freeing the artery or vein to be transplanted, an incision is made for the insertion of surface--a handpiece tip. The tip is rotated and reciprocated ultrasonically at the same time so that tissue is fragmented by the combined motion of a fragmenting surface perpendicular to the surface and at an angle to the surface many times during a single revolution or part of a revolution.