An implantable prosthetic valve, according to one embodiment, comprises a radially collapsible and expandable frame and a leaflet structure supported within the frame. The leaflet structure can comprise a plurality of leaflets paired together at commissures. In one embodiment, the commissures can comprise leaflet tabs rolled into spirals around non-rigid reinforcing inserts. In another embodiment, the commissures can comprise a reinforcing sheet folded around leaflet tabs.