One embodiment is directed to a system for tensioning a suture member that crosses a portion of a tissue structure, comprising: a tensioning member base having a tissue interface surface configured to engage a portion of the tissue structure when coupled to a suture member that may be threaded through the tensioning member base and into the tissue structure; a suture clamping member configured to be switched from a first mode, wherein a suture may be tensioned back and forth through a space defined at least in part by the clamping member, to a second mode, wherein a suture may only be tensioned in one direction relative to the suture clamping member; and a mode switching member movably coupled to the suture clamping member and configured to be operable to switch the suture clamping member from the first mode to the second mode.