A valved stent including a stent structure having a generally tubular body portion with an interior area, a first end, a second end, and a longitudinal axis; a valve structure including a plurality of leaflets and positioned within the interior area of the stent structure; and an invertible structure extending from one of the first and second ends of the stent structure. The invertible structure can be rotatable relative to the end of the stent structure from which it extends.