Apparatus is provided for use with a heart of a subject, the apparatus including an inner stent frame defining a tubular portion, and an outer stent frame. The apparatus has a relaxed expanded state in which an outer-stent-frame relaxed expanded diameter defined by the outer slept frame is smaller than an inner-stent-frame expanded diameter defined by the tubular portion. Together, the inner stent frame and the outer stent frame define a frame assembly in which outer-frame coupling elements are fixed to inner-frame coupling elements. The frame assembly is expandable into an expanded state in which the tubular portion defines an inner-stent-frame constrained expanded diameter that is smaller than the inner-stent-frame relaxed expanded diameter. The frame assembly includes prosthetic leaflets secured to, and disposed within, the tubular portion, and has a compressed state in which the frame assembly is transluminally advanceable to the heart. Other embodiments are also described.