A tubular portion (32) of a valve frame (30) circumscribes a longitudinal axis, and defines a lumen along the axis and a plurality of valve-frame coupling elements (31) disposed circumferentially around the axis. An outer frame (60): (a) comprises a ring (66) defined by a pattern of alternating peaks and troughs, the pattern having an amplitude, (b) comprises a plurality of legs (50), coupled to the ring at respective troughs, and (c) is shaped to define a plurality of outer-frame coupling elements (61), each coupled to the ring at a respective peak, and fixed with respect to a respective valve-frame coupling element. Compression of the tubular portion from an expanded state toward a compressed state reduces a circumferential distance between each of the outer-frame coupling elements and its adjacent outer-frame coupling elements, and increases the amplitude of the pattern of the ring.
