An apparatus for cinching an anatomic passage (e.g., the annulus of the mitral valve or another cardiac valve) includes a cinching cord (33), slotted anchors (40), and corresponding sliding members (50) disposed in the slots of the anchors. The sliding members are held captive within the slots by a protrusion on one side of the slot and by the presence of the cinching cord in apertures of the sliding members on the other side of the slot, because the cinching cord passes through the aperture in each of the sliding members. In some embodiments, at least one sleeve of material that accepts tissue ingrowth is disposed over the cinching cord. A closed loop of cord may also be used in place of the cinching cord in alternative embodiments, so that subsequent to implantation, the closed loop of cord prevents the anatomic annulus from expanding.
