Adjustable annuloplasty rings for repair of a mitral or tricuspid valve which incorporate at least two separate parts that are adjustably interconnectable to create a ring the circumference of which can be changed in dimension. Rings having interconnections at spaced-apart lateral locations, which interconnections allow bidirectional movement to either shorten or lengthen the ring at either such location, afford a surgeon opportunity to make further adjustments to the dimensions of the annuloplasty ring after its initial partial securing to the heart valve tissue and thereby adjust the AP diameter of the valve being repaired. The mating interconnections at two lateral locations on the ring can be constructed so as to allow hinged movement about an axis defined by the interconnections to permit hinged movement between the two separate parts.