A prosthetic heart valve is provided with a cuff having features which promote sealing with the native tissues even where the native tissues are irregular. The cuff may include a portion adapted to bear on the LVOT when the valve is implanted in a native aortic valve. The valve may include elements for biasing the cuff outwardly with respect to the stent body when the stent body is in an expanded condition. The cuff may have portions of different thickness distributed around the circumference of the valve in a pattern matching the shape of the opening defined by the native tissue. All or part of the cuff may be movable relative to the stent during implantation.