A system for treating mitral valve regurgitation includes a tensioning device having a flexible annuloplasty ring, a plurality of anchoring members and a tensioning filament attached to the flexible ring. One embodiment of the invention includes a method for attaching a flexible annuloplasty ring to the annulus of a mitral valve, and adjusting the lengths of segments of the tension filament attached to the flexible ring in order to exert force vectors on the annulus, thereby reshaping the mitral valve annulus so that the anterior and posterior leaflets of the mitral valve close completely during ventricular contraction.