A prosthetic heart valve comprising: an outer frame assembly having an atrium portion, a ventricle portion, and an annulus portion between the atrium portion and the ventricle portion; and an inner valve assembly including an inner frame having an atrium end and a ventricle end and valve leaflets supported on the inner frame, the inner valve assembly coupled to the outer frame assembly by a connection between the ventricle end of the inner frame and the ventricle portion of the outer frame assembly, the inner frame extending from the connection towards the atrium portion of the outer frame assembly, the inner frame and the outer frame assembly diverging from the connection towards the atrium portion of the outer frame assembly, the annulus portion and the atrium portion of the outer frame assembly being spaced radially from the inner valve assembly and being radially inwardly deflectable towards the inner valve assembly, the outer frame assembly having a stiffness in resistance to hoop compression that varies in an axial direction of the outer frame assembly, characterized in that the annulus portion has an hourglass shape with a minimum perimeter disposed between a larger perimeter near the atrium portion and a larger perimeter near the ventricle portion, the ventricle portion of the outer frame assembly having a maximum perimeter larger than a maximum perimeter of the annulus portion of the outer frame assembly, and the ventricle portion having a minimum perimeter smaller than a minimum perimeter of the annulus portion, at least a portion of the inner valve assembly and inner frame being positioned within the annulus portion. an outer frame assembly having an atrium portion, a ventricle portion, and an annulus portion between the atrium portion and the ventricle portion; and an inner valve assembly including an inner frame having an atrium end and a ventricle end and valve leaflets supported on the inner frame, the inner valve assembly coupled to the outer frame assembly by a connection between the ventricle end of the inner frame and the ventricle portion of the outer frame assembly, the inner frame extending from the connection towards the atrium portion of the outer frame assembly, the inner frame and the outer frame assembly diverging from the connection towards the atrium portion of the outer frame assembly, the annulus portion and the atrium portion of the outer frame assembly being spaced radially from the inner valve assembly and being radially inwardly deflectable towards the inner valve assembly, the outer frame assembly having a stiffness in resistance to hoop compression that varies in an axial direction of the outer frame assembly, characterized in that the annulus portion has an hourglass shape with a minimum perimeter disposed between a larger perimeter near the atrium portion and a larger perimeter near the ventricle portion, the ventricle portion of the outer frame assembly having a maximum perimeter larger than a maximum perimeter of the annulus portion of the outer frame assembly, and the ventricle portion having a minimum perimeter smaller than a minimum perimeter of the annulus portion, at least a portion of the inner valve assembly and inner frame being positioned within the annulus portion.