A prosthetic heart valve comprising a stent having an annular base and a plurality of legs extending upwardly from said base; a valve element circumscribing said stent and attached thereto, said valving element comprising a number of cooperating valve leaflets equal to the number of said legs; and a layer of biologically-compatible material secured to said stent and positioned between said stent and said leaflets, said layer having a smooth, non-abrasive outer surface and covering all of the surfaces of said stent that, in the absence of said layer, would contact the mobile portions of said leaflets during the normal function of the valve.