Embodiments of the present disclosure include a method for use at a native valve of a heart of a subject. At a distal portion of a delivery tool, a balloon is coupled to a shaft. The distal portion is advanced to the heart with an implant and the balloon disposed within a capsule. The implant includes a tubular frame and one or more shape-memory flanges. The tubular frame is compressed around the balloon, and the flanges are constrained within a downstream capsule-portion of the capsule. The flanges are exposed from the downstream capsule-portion such that the flanges automatically deflect radially outward. Subsequently, the flanges are pressed against a downstream surface of the native valve by moving the implant in an upstream direction. While the flanges are in contact with the downstream surface, the tubular frame is plastically expanded radially by inflating the balloon. Other embodiments are also described.