A minimally-invasive annuloplasty ring for implant at a mitral annulus. The annuloplasty ring has an inner core member with a C-shaped plan view that generally defines an oval with a major axis and a minor axis, and is symmetric about the minor axis. A posterior portion of the core member bisected by the minor axis has a thicker radial dimension than a pair of free end regions terminating on an anterior side of the core member. The radial thickness smoothly transitions between the posterior portion and the end regions. The inner core member may be covered with a fabric, and is a superelastic metal so that it can be straightened out and delivered through an access tube. The curvatures and thicknesses around the core member are selected so that the strain experienced when straightened does not exceed 7-8%.