A prosthesis including a frame configured for positioning at or near a native heart valve annulus, shaped and sized to prevent the frame element from shifting downstream of the native heart annulus, and at least two frame extensions attached to the frame at a first end proximal to the frame, the frame extensions configured and circumferentially arranged to extend between native heart valve leaflets, wherein the frame is configured for positioning at or near the native heart valve annulus with minimal interfering with opening and closing of the native heart valve leaflets, and the frame extensions are at least as long as the native heart leaflets, and are configured to extend between the native heart valve leaflets without interfering with opening and closing of the native heart valve leaflets. Related apparatus and methods are also described.
