A prosthetic heart valve (10) (e.g., a prosthetic aortic valve) is designed tobe somewhat circumf erentially collapsible and then re-expandable. The collapsedcondition may be used for less invasive delivery of the valve into a patient. Whenthe valve reaches the implant site in the patient, it re-expands to normal operatingsize, and also to engage surrounding tissue of the patient. The valve includesa stent portion (200) and a ring portion (100) that is substantially concentricwith the stent portion but downstream from the stent portion in the directionof blood flow through the implanted valve. When the valve is implanted, the stentportion engages the patient's tissue at or near the native valve annulus,while the ring portion engages tissue downstream from the native valve site (e.g.,the aorta).