A prosthetic heart valve includes a frame having an inflow end and an outflow end, and defining a longitudinal axis. The prosthetic heart valve further includes a leaflet structure situated at least partially within the frame, and a covering disposed around the frame. The covering includes a first woven portion extending circumferentially around the frame and including a plurality of texturized strands or yarns extending along the longitudinal axis of the frame. The covering further includes a second woven portion extending circumferentially around the frame and spaced apart from the first woven portion along the longitudinal axis of the frame. The texturized strands extend along the longitudinal axis of the frame from the first woven portion to the second woven portion and form a floating portion between the first woven portion and the second woven portion.