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 . <EOS>