A cardiac valve annulus may be constricted by using an apparatus to deliver a cord to the annulus, affixing the cord, and subsequently tightening that cord. In some embodiments, this apparatus includes a housing, a spool, and an elongated core with lumens that run through the core. The lumens are dimensioned to slidably accommodate portions of the cord. The cord, the lumens, and the spool are configured so that after a distal loop portion of the cord is anchored to the annulus, movement of the housing in a proximal direction will (a) cause the core to progressively move in a proximal direction with respect to portions of the cord and (b) cause extension sections of the cord to progressively unwind from the spool and be progressively drawn into the lumens.
