A transcatheter valve prosthesis including a tubular stent includes an interior skirt or skirt portion is coupled to and covers an inner circumferential surface of the stent, and an exterior skirt or skirt portion is coupled to and covers an outer circumferential surface of the stent. A prosthetic valve component is disposed within and secured to the interior skirt or skirt portion. The interior and exterior skirts or skirt portions may overlap to form a double layer of skirt material on the stent, or may be portions of a skirt that do not overlap such that only a single layer of skirt material covers the stent. When the stent is in at least the compressed configuration, at least one endmost crown may be positioned radially inwards with respect to the remaining endmost crowns formed at the inflow end of the stent in order to accommodate the exterior skirt.