The diameter of an annulus in a patient (e.g., the mitral valve annulus) can be reduced using a tissue engaging member that is installed on the annulus and an actuator that is implanted into the patient's body. The tissue engaging member has anchors used to implant the tissue engaging member into the annulus, and a cinching loop runs through the tissue engaging member. The cinching loop terminates onto cinching wires. Preferably, tissue healing is used to enhance the bond between the tissue engaging member and the annulus. The actuator, which can be actuated from outside the patient's body, pulls the cinching wires in a proximal direction while holding the distal end of the cinching wires in close proximity to each other, so as to cause a reduction in the diameter of the cinching loop. This will cause a corresponding reduction in the diameter of the annulus.
