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-discriminating fragmenting handpiece. The surface-discriminating fragmenting handpiece fragments and permits aspiration of the tissue without damaging the surrounding wall by moving surfaces which permit the diseased tissue to fall within their cutting zone but which move at a rate of speed and have openings between them of such a size that the more integrated and smoother tissue does not fall within their cutting zone.