A tubular portion of a valve frame circumscribes a longitudinal axis, and defines a lumen along the axis and a plurality of valve-frame coupling elements disposed circumferentially around the axis. An outer frame: (a) comprises a ring defined by a pattern of alternating peaks and troughs, the pattern having an amplitude, (b) comprises a plurality of legs, coupled to the ring at respective troughs, and (c) is shaped to define a plurality of outer-frame coupling elements, each coupled to the ring, 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.