For some applications, apparatus is provided for facilitating implantation of a prosthetic valve (150) at a native heart valve (120) of a subject, the apparatus comprising a prosthetic valve support (22), the prosthetic valve support (a) being configured to be transluminally-deliverable to the native valve and to be deployable at the native valve, and (b) comprising one or more tissue-engaging elements (24), configured to couple the prosthetic valve support to leaflets (128) of the native valve without eliminating check valve functionality of the native valve. Other embodiments are also described.