Packaging for dry prosthetic tissue heart valves and their delivery systems includes a primary sterile barrier that permits gas sterilization of the tissue implant, and a secondary sterile barrier that also prevents oxidation of the implant during long-term storage. Dry tissue heart valves and their delivery systems are placed within a primary container such as a rigid tray that limits movement of the components therein. The primary container is placed within a secondary container, and the assembly is then sterilized. The outer sterile barrier may include a double seal so that a first gas-permeable seal can be closed for sterilization, after which a second gas-impermeable seal can be closed to seal out any further oxygen contact with the tissue implant. A collapsible delivery handle for a surgical heart valve may be provided which reduces the size of the packaging.