A prosthetic heart valve having a cuff attached to a stent provides a seal for preventing paravalvular leakage. The cuff may be constructed from known sealing materials to fill in and around paravalvular leakage gaps, while continuously collapsing down into a low profile volume within the stent. The cuff is coupled circumferentially about the stent by members which may be in the nature of dimension and/or shape memory material having a tensioned and relaxed state. The members may be in the form of elongated elastic members or coiled members. When in the tensioned state, the cuff is located within the stent volume to provide a low profile prosthetic heart valve. Upon relaxing of the members, the cuff is pulled over the abluminal surface of the stent to form a cuff seal circumscribing the stent for preventing paravalvular leakage.
