Apparatus is provided, including: (1) a delivery tube, transluminally advanceable to the heart of the subject; (2) a prosthetic valve support, configured to support a prosthetic valve at a native valve of the heart, and including an upstream support portion, the upstream support portion: (A) having a working configuration in which it is generally annular and (B) having a delivery configuration in which it defines a channel, and is configured to be disposed within the delivery tube; (3) a tissue anchor, slidable through the channel; and (4) an anchor driver. The anchor driver is slidable within the delivery tube and the channel, and configured to anchor the upstream support portion to tissue of the heart by driving the tissue anchor through the upstream support portion and into the tissue, while at least part of the upstream support portion is disposed within the delivery tube.