Apparatus is provided for use with a native valve of a heart of a subject, the apparatus including (1) an annular upstream support portion, configured to be transluminally placed against an atrial surface of the native valve (2) a tissue-engaging element that includes a coupling portion configured to be transluminally coupled to tissue in a ventricle of the heart (3) an elastically-stretchable holding element, configured to secure the upstream support portion against the atrial surface by elastically coupling the coupling portion to the upstream support portion and (4) a prosthetic valve, configured to be transluminally delivered to the native valve and intracorporeally coupled to the upstream support portion subsequently to the securing of the upstream support portion against the atrial surface. Other embodiments are also described.
