Laser radiation is coupled to an optical instrument having a relatively narrow working edge from which the radiation is emitted in a relatively narrow zone of intense radiation leakage. The working edge is placed in contact with vascularized tissues, and the laser radiation emanating from the working edge in combination with the contact between the working edge and the tissues forms an incision, and the laser radiation photocoagulates tissue adjacent the incision. The contact between the working edge and the tissues accurately positions the laser radiation with respect to the tissue, places pressure on vessels to aid hemostasis, mechanically stresses the incision line and provides the surgeon with tactile feedback. Radiation propagates from a laser to the optical instrument through a low-loss flexible fiberoptic waveguide by means of multimode optical waveguide propagation. As the radiation reaches the working edge of the optical instrument the radiation is emitted from the instrument because the incident angles of individual modes fall below the critical internal reflection angle of the instrument. Radiation leakage is further increased by the presence of blood on the working edge. The frequency of the laser radiation is selected to achieve a desired penetration depth. Deeper penetration may be necessary under some circumstances to produce a clot of sufficient size to allow adequate coagulation. A power control mounted on the handle of the optical instrument or elsewhere allows the surgeon to adjust the intensity of the radiation.