A novel system for performing a heart valve annuloplasty. The system involves the use of a plication band. In one embodiment, the annulus of the valve is reduced by constriction of the plication band itself. More particularly, each plication band enters the tissue at two or more points which are spaced from one other by a distance which is dictated by the geometry of the plication band. Subsequent constriction of the plication band causes these points to move toward each other, thereby constricting the tissue trapped between these points and thus reducing the overall circumference of the valve annulus. In a second embodiment, the annulus of the valve is reduced by linking multiple plication bands to one other, using a linkage construct, and then using a shortening of the length of the linkage construct between each plication band so as to gather the tissue between each plication band, whereby to reduce the overall circumference of the valve annulus.