A prosthetic heart valve, comprising: an annular frame comprising an inflow end and an outflow end and being radially compressible and expandable between a radially compressed configuration and a radially expanded configuration having a cylindrical shape, wherein the frame comprises a plurality of rows of angled struts arranged end-to-end and extending circumferentially, wherein a first, uppermost row of angled struts and a second row of angled struts immediately adjacent to the first row of angled struts along with frame portions and struts define an upper row of cells defining openings; a leaflet structure positioned within the frame and secured thereto; and an outer skirt mounted outside of the frame and adapted to seal against surrounding tissue when the prosthetic heart valve is implanted within a native heart valve annulus of a patient, wherein the outer skirt comprises an inflow edge portion and an outflow edge portion defining a plurality of alternating projections and notches that follow the shape of a row of angled struts (24, 26, 28, 32) of the frame, wherein the outer skirt is sized and shaped relative to the frame such that when the prosthetic valve is in its radially expanded state, the outer skirt fits snugly against the outer surface of the frame, and an inner skirt mounted on an inner surface of the frame, the inner skirt having an inflow edge portion that is secured to an inflow edge portion of the outer skirt, wherein an outflow edge portion of the inner skirt is secured to the second row of angled struts such that the openings of the upper row of cells are not covered by the inner skirt. an annular frame comprising an inflow end and an outflow end and being radially compressible and expandable between a radially compressed configuration and a radially expanded configuration having a cylindrical shape, wherein the frame comprises a plurality of rows of angled struts arranged end-to-end and extending circumferentially, wherein a first, uppermost row of angled struts and a second row of angled struts immediately adjacent to the first row of angled struts along with frame portions and struts define an upper row of cells defining openings; a leaflet structure positioned within the frame and secured thereto; and an outer skirt mounted outside of the frame and adapted to seal against surrounding tissue when the prosthetic heart valve is implanted within a native heart valve annulus of a patient, wherein the outer skirt comprises an inflow edge portion and an outflow edge portion defining a plurality of alternating projections and notches that follow the shape of a row of angled struts (24, 26, 28, 32) of the frame, wherein the outer skirt is sized and shaped relative to the frame such that when the prosthetic valve is in its radially expanded state, the outer skirt fits snugly against the outer surface of the frame, and an inner skirt mounted on an inner surface of the frame, the inner skirt having an inflow edge portion that is secured to an inflow edge portion of the outer skirt, wherein an outflow edge portion of the inner skirt is secured to the second row of angled struts such that the openings of the upper row of cells are not covered by the inner skirt.