Abstract: A valve frame includes a tubular portion defining a plurality of valve-frame coupling elements disposed circumferentially around a longitudinal axis of the valve frame, and a plurality of arms, extending radially outward from an upstream portion of the tubular portion to define an arm span, and configured to engage tissue in the atrium. An outer frame is coupled to the valve frame, and includes a ring circumscribing the tubular portion, and a plurality of flanges that extend radially outward from the ring to define a flange span, and are configured to engage ventricular tissue. Each arm defines a rigid portion and a flexible portion that is disposed radially outward from the rigid portion, and is more flexible than the rigid portion. The majority of the flexible portion is disposed further radially outward than the flange span. Other embodiments are also described.