A prosthetic tricuspid remodeling annuloplasty ring having two free ends (56a,56b) that are upturned in the inflowdirection to help avoid unnecessary leaflet abrasion. The free ends aredesirably separated across a gap (G) that is large enough toreduce the risk of passing sutures through the conductive system of the heartyyet not too large that support of the septal leaflet ofthe tricuspid annulus is degraded. The tricuspid ring may have four sequentialsegments (60a, b, c,d) looking from the inflow sideand extending in a clockwise direction from a free end located adjacent theantero septal commissure after implant. The ring maydefine an inflow bulge (64) in the first segment and/or an inflow bulge (65)in the fourth segment that help the ring conform to thenatural bulges created by the adjacent aorta, thereby reducing stress and thepotential for ring dehiscence. Desirably, the ring hasvariable flexibility, either gradual and/or between or within differentsegments, so as to adapt or harmonize its 3-dimensionalshape to each individual patient and, therefore, to significantly reduce theconstraints on the annulus and adjacent structures,particularly the leaflets and the conduction tissue.