A mitral annuloplasty ring with an inner core and an outer band located therearound is disclosed. The ring has an anterior region, a posterior region opposite the anterior region, and two side regions therebetween. A cross-sectional width dimension of the outer band is greater in the posterior region of the ring than in the anterior region. A cross-sectional width dimension of a semi-flexible core is thinner in the anterior and posterior regions than in the side regions so that the mitral ring is more rigid in the anterior-posterior direction. A tricuspid annuloplasty ring of the invention has an inner core and an outer band located therearound. The inner core has an anterior region separated across a gap from a septal region, and a posterior region. A cross-sectional width dimension of the outer band is greater in the septal region than either the anterior or posterior regions.