Systems and methods for supporting a replacement heart valve are presented herein. A bioprosthesis may be stored in a storage container by suspending the bioprosthesis from a support structure. The volume of storage solution may be reduced by using a lid with a boss extending therefrom to displace some of the volume of the storage container. The support structure may rest on the base of the storage container. Additionally, there may be a holder attached to the bioprosthesis above the support structure. The holder-bioprosthesis-support structure may be constrained between the lid and base of the storage container.