One embodiment is directed to a method for tensioning a suture member that crosses a portion of a wall of a tissue structure, comprising: advancing a distal portion of the suture member across at least a portion of a wall of the tissue structure; advancing a tensioning assembly, through which the suture member is threaded, toward the wall of the tissue structure; manipulating a elongate compressive loading member to adjust the physical relationship between the tensioning assembly, suture member, and tissue structure wall by modulating the position of the tensioning member base relative to the suture member and tissue structure wall with the tensioning mode switching member in the first mode; and controllably switching the tensioning mode switching member to the second mode.