An implant includes first and second clasps, each having first and second tissue-engaging portions which are movable with respect to each other to clamp one of the native heart valve leaflets between respective tissue-engaging surfaces. Each of the tissue-engaging portions has a surface opposite the respective tissue-engaging surface. For each clasp, the implant includes a respective leg portion and a respective intermediate portion. Each intermediate portion is (i) coupled to the opposite surface of the second tissue-engaging portion of the clasp such that an orientation of the intermediate portion is fixed with respect to an orientation of the opposite surface of the second tissue-engaging portion of the clasp, and (ii) coupled to the leg portion at a respective portion of the implant that allows movement of the leg portion with respect to the intermediate portion. Other embodiments are also described.