A prosthetic heart valve includes an annular stent structure having a plurality of annularly spaced stent post regions, a plurality of leaflets that extend radially inward from the stent structure and that include radially outer portions that lie against a radially outer surface of the stent structure, and a clamping structure that is radially outside the other components and that clamps the radially outer portions of the leaflets against the radially outer surface of the stent structures to secure the leaflets to the stent structure. The above-described structural arrangement applies to the stent post regions as well as to other portions of the stent structure.