A prosthetic heart valve, comprising: a frame comprising a plurality of strut members, the frame being radially collapsible and expandable between a collapsed configuration and an expanded configuration, the frame having an inflow end and an outflow end, and defining a longitudinal axis; a leaflet structure situated at least partially within the frame; and a covering disposed around the frame, the covering comprising: a first woven portion (1002A-C) extending circumferentially around the frame, the first woven portion (1002A-C) comprising a plurality of texturized strands extending along the longitudinal axis of the frame; a second woven portion (1004A-G) extending circumferentially around the frame and spaced apart from the first woven portion (1002A-C) along the longitudinal axis of the frame; an inflow protection portion and/or an outflow protection portion, the first and second woven portions (1002A, 1002C, 1004A, 1004G) being disposed at least partially beneath the inflow protection portion and/or the outflow protection portion; wherein the texturized strands extend along the longitudinal axis of the frame from the first woven portion (1002A-C) to the second woven portion (1004A-G) and form a floating portion (1006A-E) between the first woven portion (1002A-C) and the second woven portion (1004A-G); wherein the texturized strands are woven into a leno weave pattern in the second woven portion (1004A-G). a frame comprising a plurality of strut members, the frame being radially collapsible and expandable between a collapsed configuration and an expanded configuration, the frame having an inflow end and an outflow end, and defining a longitudinal axis; a leaflet structure situated at least partially within the frame; and a covering disposed around the frame, the covering comprising: a first woven portion (1002A-C) extending circumferentially around the frame, the first woven portion (1002A-C) comprising a plurality of texturized strands extending along the longitudinal axis of the frame; a second woven portion (1004A-G) extending circumferentially around the frame and spaced apart from the first woven portion (1002A-C) along the longitudinal axis of the frame; an inflow protection portion and/or an outflow protection portion, the first and second woven portions (1002A, 1002C, 1004A, 1004G) being disposed at least partially beneath the inflow protection portion and/or the outflow protection portion; a first woven portion (1002A-C) extending circumferentially around the frame, the first woven portion (1002A-C) comprising a plurality of texturized strands extending along the longitudinal axis of the frame; a second woven portion (1004A-G) extending circumferentially around the frame and spaced apart from the first woven portion (1002A-C) along the longitudinal axis of the frame; an inflow protection portion and/or an outflow protection portion, the first and second woven portions (1002A, 1002C, 1004A, 1004G) being disposed at least partially beneath the inflow protection portion and/or the outflow protection portion; wherein the texturized strands extend along the longitudinal axis of the frame from the first woven portion (1002A-C) to the second woven portion (1004A-G) and form a floating portion (1006A-E) between the first woven portion (1002A-C) and the second woven portion (1004A-G); wherein the texturized strands are woven into a leno weave pattern in the second woven portion (1004A-G).