A prosthetic valve for percutaneous implantation in a body channel, comprising: a substantially cylindrical stent structure made of a deformable material and configured for radial expansion using a balloon catheter, the stent comprising at least an outflow ring of angled struts and an adjacent ring of angled struts interconnected with the outflow ring of angled struts by a plurality of axially extending struts; a valvular structure providing a flexible conduit having an inlet and an outlet, the valvular structure being formed of a pliant material attached to the stent structure and forming three valve leaflets; a layer of compressible cloth material disposed along an outer surface of the stent structure, the compressible cloth material being adapted for expansion after deployment to fill gaps between the prosthetic valve and the body channel, wherein the compressible cloth material: is formed of polyethylene terephthalate; extends entirely around the stent structure in the form of a sleeve having an outflow edge defining a plane that is substantially perpendicular to a longitudinal axis of the stent structure; and entirely covers an inflow end portion of the outer surface of the stent structure; and wherein the outflow edge of the compressible sleeve material is axially spaced from the outflow ring of angled struts such that the outflow ring of angled struts remains entirely uncovered by the compressible cloth material and the adjacent ring of angled struts remains partially uncovered by the compressible cloth material. a substantially cylindrical stent structure made of a deformable material and configured for radial expansion using a balloon catheter, the stent comprising at least an outflow ring of angled struts and an adjacent ring of angled struts interconnected with the outflow ring of angled struts by a plurality of axially extending struts; a valvular structure providing a flexible conduit having an inlet and an outlet, the valvular structure being formed of a pliant material attached to the stent structure and forming three valve leaflets; a layer of compressible cloth material disposed along an outer surface of the stent structure, the compressible cloth material being adapted for expansion after deployment to fill gaps between the prosthetic valve and the body channel, wherein the compressible cloth material: is formed of polyethylene terephthalate; extends entirely around the stent structure in the form of a sleeve having an outflow edge defining a plane that is substantially perpendicular to a longitudinal axis of the stent structure; and entirely covers an inflow end portion of the outer surface of the stent structure; and is formed of polyethylene terephthalate; extends entirely around the stent structure in the form of a sleeve having an outflow edge defining a plane that is substantially perpendicular to a longitudinal axis of the stent structure; and entirely covers an inflow end portion of the outer surface of the stent structure; and wherein the outflow edge of the compressible sleeve material is axially spaced from the outflow ring of angled struts such that the outflow ring of angled struts remains entirely uncovered by the compressible cloth material and the adjacent ring of angled struts remains partially uncovered by the compressible cloth material.