This disclosure is directed to prosthetic heart valves having elongated sealing members. As one example, a prosthetic heart valve comprises an annular frame, a leaflet assembly comprising a plurality of leaflets, and a skirt assembly comprising an inner skirt, an outer skirt, and/or a third skirt. The frame is radially compressible and expandable between a radially compressed state and a radially expanded state and comprises a plurality of apices at an inflow end. The skirt assembly forms a pocket at the inflow end of the frame that creates extra space between the inflow end of the frame and the skirt assembly when the frame is in the radially expanded state. This pocket allows the apices at the inflow end of the frame to move towards an inflow end of the pocket when the frame is radially compressed to the radially compressed state without protruding through the skirt assembly.