Packaging for prosthetic heart valves including an assembly for securely retaining a heart valve within a jar and facilitating retrieval therefrom. The assembly includes a packaging sleeve that fits closely within the jar and has a clip structure for securing a valve holder. Contrary to previous designs, in one embodiment the valve holder is directed downward into the jar, and the valve is retained with an inflow end upward. The valve may have flexible leaflets, and a leaflet parting member on the end of the shaft extends through the leaflets and couples with the valve holder. The assembly of the packaging sleeve, valve, and holder can then be removed from the jar and a valve delivery tube connected with the holder, or to the leaflet parting member. The packaging sleeve may be bifurcated into two halves connected at a living hinge to facilitate removal from around the valve/holder subassembly.