A prosthetic tricuspid remodeling annuloplasty ring having two free ends that are upturned in the inflow direction to help avoid unnecessary leaflet abrasion. The free ends are desirably separated across a gap that is large enough to reduce the risk of passing sutures through the conductive system of the heart, yet not too large that support of the septal leaflet of the tricuspid annulus is degraded. The ring may define an inflow bulge in the first segment and/or an inflow bulge in the fourth segment that help the ring conform to the natural bulges created by the adjacent aorta, thereby reducing stress and the potential for ring dehiscence.