1. A method for fabricating a bioprosthetic heart valve, the method comprising:providing: a sheet of biological tissue, a sheet of a biocompatible material, and a stent, the stent having an upstream edge and a downstream edge as well as an inner surface and an outer surface;
attaching the biological tissue to the biocompatible material along a suture line;
folding the biocompatible material to form a tubular structure with the attached biological tissue located on an inner surface of the tubular structure, the biological tissue forming leaflets of the heart valve;
securing the stent around an outer surface of the tubular structure such that the tubular structure extends in an upstream direction beyond the upstream edge of the stent and in a downstream direction beyond the downstream edge of the stent;
cutting at least one region of the biocompatible material at a downstream end of the tubular structure;
folding the biocompatible material at the at least one cut region away from the biological tissue and around the downstream edge of the stent and securing it to the outer surface of the stent; and
folding and attaching the biocompatible material at an upstream end of the tubular structure around the upstream edge of the stent so that the inner and outer surfaces of the stent are covered with no more than a single layer of the biocompatible material.