Apparatus and methods are provided for thermally and/or mechanically treating tissue, such as valvular structures, to reconfigure or shrink the tissue in a controlled manner. Mechanical clips are implanted over the leaflets of a valve, e.g., in the heart, either alone or after thermal treatment to cause the valve to close more tightly. The clips are delivered by a catheter and may be configured to traverse directly over the valve itself or to lie partially over the periphery of the valve to prevent obstruction of the valve channel. The clips can be coated with drugs or a radiopaque coating. Alternatively, individual anchors with a tensioning element, like a suture, may be used to approximate the valves towards each other. The catheter can also incorporate sensors or energy delivery devices, e.g., transducers, on its distal end.