A prosthetic heart valve (10) (e.g., a prosthetic aortic valve) is designed to be somewhat circumferencially collapsible and then re-expandable. The collapsed condition may be used for less invasive delivery of the valve into a patient. When the valve reaches the implant site in the patient, it re-expands to normal operating size, and also to engage surrounding tissue of the patient. The valve includes a stent portion (200) and a ring portion (100) that is substantially concentric with the stent portion but downstream from the stent portion in the direction of blood flow through the implanted valve. When the valve is implanted, the stent portion 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).
