An assembly for implanting a balloon-expandable prosthetic aortic valve in a patient's body, the assembly comprising: a delivery apparatus comprising an elongated shaft having an inflatable balloon, and a radially expandable prosthetic aortic valve adapted to be mounted on the shaft in a radially collapsed configuration for delivery into the body, the prosthetic aortic valve comprising: a balloon-expandable annular frame having an inflow end portion and an outflow end portion, and a plurality of angularly spaced commissure windows at the outflow end portion, each commissure window comprising an enclosed opening between first and second axially oriented side struts; a leaflet structure positioned within the frame, the leaflet structure comprising a plurality of commissure portions that extend outwardly through respective commissure windows; an annular inner skirt positioned along and secured to an inner surface of the frame; and an annular outer skirt positioned around an outer surface of the frame, the outer skirt comprising an inflow edge, an outflow edge, and an intermediate portion between the inflow edge and the outflow edge, wherein the inflow edge of the outer skirt is sutured to the inflow edge of the inner skirt at the inflow end portion of the frame or is secured to the frame at a first location, and the outflow edge of the outer skirt is secured to the frame at a second location; wherein when the prosthetic aortic valve is in the expanded configuration, the intermediate portion of the outer skirt comprises slack in the axial direction between the inflow edge of the outer skirt and the outflow edge of the outer skirt, and when the prosthetic aortic valve is collapsed to the collapsed configuration, the axial distance between the inflow edge of the outer skirt and the outflow edge of the outer skirt increases, reducing the slack in the outer skirt in the axial direction, wherein an outer diameter of the inflow end portion of the frame is smaller than an outer diameter of the outflow end portion of the frame when the prosthetic aortic valve is radially collapsed on the shaft. a delivery apparatus comprising an elongated shaft having an inflatable balloon, and a radially expandable prosthetic aortic valve adapted to be mounted on the shaft in a radially collapsed configuration for delivery into the body, the prosthetic aortic valve comprising: a balloon-expandable annular frame having an inflow end portion and an outflow end portion, and a plurality of angularly spaced commissure windows at the outflow end portion, each commissure window comprising an enclosed opening between first and second axially oriented side struts; a leaflet structure positioned within the frame, the leaflet structure comprising a plurality of commissure portions that extend outwardly through respective commissure windows; an annular inner skirt positioned along and secured to an inner surface of the frame; and an annular outer skirt positioned around an outer surface of the frame, the outer skirt comprising an inflow edge, an outflow edge, and an intermediate portion between the inflow edge and the outflow edge, wherein the inflow edge of the outer skirt is sutured to the inflow edge of the inner skirt at the inflow end portion of the frame or is secured to the frame at a first location, and the outflow edge of the outer skirt is secured to the frame at a second location; a balloon-expandable annular frame having an inflow end portion and an outflow end portion, and a plurality of angularly spaced commissure windows at the outflow end portion, each commissure window comprising an enclosed opening between first and second axially oriented side struts; a leaflet structure positioned within the frame, the leaflet structure comprising a plurality of commissure portions that extend outwardly through respective commissure windows; an annular inner skirt positioned along and secured to an inner surface of the frame; and an annular outer skirt positioned around an outer surface of the frame, the outer skirt comprising an inflow edge, an outflow edge, and an intermediate portion between the inflow edge and the outflow edge, wherein the inflow edge of the outer skirt is sutured to the inflow edge of the inner skirt at the inflow end portion of the frame or is secured to the frame at a first location, and the outflow edge of the outer skirt is secured to the frame at a second location; wherein when the prosthetic aortic valve is in the expanded configuration, the intermediate portion of the outer skirt comprises slack in the axial direction between the inflow edge of the outer skirt and the outflow edge of the outer skirt, and when the prosthetic aortic valve is collapsed to the collapsed configuration, the axial distance between the inflow edge of the outer skirt and the outflow edge of the outer skirt increases, reducing the slack in the outer skirt in the axial direction, wherein an outer diameter of the inflow end portion of the frame is smaller than an outer diameter of the outflow end portion of the frame when the prosthetic aortic valve is radially collapsed on the shaft.