A prosthetic heart valve of the type that includes a hollow annular stent and a plurality of flexible leaflets that are attached to the stent. One or more fixture structures are used to attach the leaflets to the stent so that sutures do not have to be used for that purpose. The fixture structures preferably extend annularly at least substantially all the way around the valve. Surfaces of the fixture structures that can come into contact with portions of the leaflets that move during use of the valve can be shaped to help beneficially shape those leaflet portions during their movements.
