Apparatus for delivery through a cardiac tissue wall in a constrained state within a deployment tool, the apparatus comprising a tissue anchor, which comprises: an anchor shaft having a central longitudinal axis; a tissue-coupling element, configured to have a predetermined shape when unconstrained by the deployment tool and automatically transition to the predetermined shape when released from being constrained by the deployment tool, and which (a) extends from a distal end of the anchor shaft, and (b) comprises a wire, wherein when the tissue anchor is unconstrained by the deployment tool: (a) the wire is shaped as an open shape, and (b) if the tissue-coupling element were to be projected onto a plane that is perpendicular to the central longitudinal axis, the projection of the open shape would surround between 170 and 355 degrees of a point in the plane; and a flexible elongate tension member, which includes (a) a distal portion that is fixed to a site on the wire, (b) a proximal portion, which has a longitudinal segment that runs alongside at least a portion of the anchor shaft, and (c) a crossing portion, which (i) is disposed between the distal and the proximal portions (204, 208) along the flexible elongate tension member, and (ii) crosses at least a portion of the open shape when the tissue anchor is unconstrained by the deployment tool, wherein the tissue anchor is configured to allow relative axial motion between the at least a portion of the anchor shaft and the longitudinal segment of the proximal portion of the flexible elongate tension member when the tissue anchor is unconstrained by the deployment tool, wherein the point falls on a projection onto the plane of a line segment that terminates at (a) the site on the wire and (b) a proximal end of the wire when the tissue anchor is unconstrained by the deployment tool. an anchor shaft having a central longitudinal axis; a tissue-coupling element, configured to have a predetermined shape when unconstrained by the deployment tool and automatically transition to the predetermined shape when released from being constrained by the deployment tool, and which (a) extends from a distal end of the anchor shaft, and (b) comprises a wire, wherein when the tissue anchor is unconstrained by the deployment tool: (a) the wire is shaped as an open shape, and (b) if the tissue-coupling element were to be projected onto a plane that is perpendicular to the central longitudinal axis, the projection of the open shape would surround between 170 and 355 degrees of a point in the plane; and a flexible elongate tension member, which includes (a) a distal portion that is fixed to a site on the wire, (b) a proximal portion, which has a longitudinal segment that runs alongside at least a portion of the anchor shaft, and (c) a crossing portion, which (i) is disposed between the distal and the proximal portions (204, 208) along the flexible elongate tension member, and (ii) crosses at least a portion of the open shape when the tissue anchor is unconstrained by the deployment tool, wherein the tissue anchor is configured to allow relative axial motion between the at least a portion of the anchor shaft and the longitudinal segment of the proximal portion of the flexible elongate tension member when the tissue anchor is unconstrained by the deployment tool, wherein the point falls on a projection onto the plane of a line segment that terminates at (a) the site on the wire and (b) a proximal end of the wire when the tissue anchor is unconstrained by the deployment tool.