A method and apparatus for providing safe and efficient transcatheter correction of the shape of heart chambers, valves, or other body members. The apparatus generally performs this correction by securing a tether to body surfaces. The attachment device includes an anchor comprising a wire braid and at least one clamp affixed to and constraining a portion of the wire braid, the clamp having threading for temporarily coupling the anchor to a delivery member and an internal lumen through which the tether can pass. The device also includes a locking member cooperating with the lumen to lock the tether to the clamp at a preselected position along the length of the tether.