Apparatus for delivery in a constrained state within a deployment tool, the apparatus comprising a tissue anchor (200, 258, 300), which comprises: a shaft; a tissue-coupling element, which extends from a distal end of the shaft, the tissue-coupling element comprising an elastically deformable wire, which is shaped as an open loop having more than one turn when the tissue anchor (200, 258, 300) is unconstrained by the deployment tool; and a flexible elongate tension member, which includes (a) a distal portion that is fixed to a site on the open loop, (b) a proximal portion, which has a longitudinal segment that runs alongside at least a portion of the 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) distally crosses at least a portion of the open loop when the tissue anchor (200, 258, 300) is unconstrained by the deployment tool, wherein the tissue anchor (200, 258, 300) is configured to allow relative axial motion between the at least a portion of the shaft and the longitudinal segment of the proximal portion of the flexible elongate tension member when the tissue anchor (200, 258, 300) is unconstrained by the deployment tool, characterized in that the longitudinal segment of the proximal portion of the flexible elongate tension member is coupled in axially sliding communication along the at least a portion of the shaft when the tissue anchor (200, 258, 300) is unconstrained by the deployment tool, so that the open loop is compressed and stiffened when tension is applied to the proximal portion of the flexible elongate tension member against the outward force of the open loop. a shaft; a tissue-coupling element, which extends from a distal end of the shaft, the tissue-coupling element comprising an elastically deformable wire, which is shaped as an open loop having more than one turn when the tissue anchor (200, 258, 300) is unconstrained by the deployment tool; and a flexible elongate tension member, which includes (a) a distal portion that is fixed to a site on the open loop, (b) a proximal portion, which has a longitudinal segment that runs alongside at least a portion of the 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) distally crosses at least a portion of the open loop when the tissue anchor (200, 258, 300) is unconstrained by the deployment tool, wherein the tissue anchor (200, 258, 300) is configured to allow relative axial motion between the at least a portion of the shaft and the longitudinal segment of the proximal portion of the flexible elongate tension member when the tissue anchor (200, 258, 300) is unconstrained by the deployment tool, characterized in that the longitudinal segment of the proximal portion of the flexible elongate tension member is coupled in axially sliding communication along the at least a portion of the shaft when the tissue anchor (200, 258, 300) is unconstrained by the deployment tool, so that the open loop is compressed and stiffened when tension is applied to the proximal portion of the flexible elongate tension member against the outward force of the open loop.