An expandable tissue anchor (20, 120, 190, 220, 320, 420) configured to be delivered to a cardiac chamber in an unexpanded generally elongate configuration within a deployment tool, the expandable tissue anchor (20, 120, 190, 220, 320, 420) configured to be anchored to a cardiac tissue wall at a target site such that a tensile force can be applied to the expandable tissue anchor (20, 120, 190, 220, 320, 420) and thus to the cardiac tissue wall, once the expandable tissue anchor (20, 120, 190, 220, 320, 420) is deployed, so as to move the cardiac tissue wall at the target site relative to adjacent cardiac tissue, the expandable tissue anchor (20, 120, 190, 220, 320, 420) comprising: an elongate tissue-coupling portion (30, 130, 192, 230, 330, 430) supported by an anchor shaft (32, 194) at a first end of the tissue-coupling portion (30, 130, 192, 230, 330, 430), the tissue-coupling portion (30, 130, 192, 230, 330, 430) configured to be delivered in an unexpanded generally elongate configuration through the cardiac tissue wall from a first side of the wall to a second side of the wall, the tissue-coupling portion (30, 130, 192, 230, 330, 430) further configured to expand, on the second side of the cardiac tissue wall, to an expanded coil open shape configuration generally orthogonal to the anchor shaft (32, 194), such that the expanded tissue-coupling portion (30, 130, 192, 230, 330, 430) can be drawn tightly against the second side of the cardiac tissue wall at the target site when the tensile force is applied to the tissue-coupling portion (30, 130, 192, 230, 330, 430), the tissue-coupling portion (30, 130, 192, 230, 330, 430) having a first stiffness; characterized by an elongate tip portion (38, 138, 238, 338, 438) supported at a second end (40, 240, 340, 440) of the tissue-coupling portion (30, 130, 192, 230, 330, 430) and configured to be delivered through the cardiac tissue wall ahead of the tissue-coupling portion (30, 130, 192, 230, 330, 430), the tip portion (38, 138, 238, 338, 438) having a second stiffness less than the first stiffness. an elongate tissue-coupling portion (30, 130, 192, 230, 330, 430) supported by an anchor shaft (32, 194) at a first end of the tissue-coupling portion (30, 130, 192, 230, 330, 430), the tissue-coupling portion (30, 130, 192, 230, 330, 430) configured to be delivered in an unexpanded generally elongate configuration through the cardiac tissue wall from a first side of the wall to a second side of the wall, the tissue-coupling portion (30, 130, 192, 230, 330, 430) further configured to expand, on the second side of the cardiac tissue wall, to an expanded coil open shape configuration generally orthogonal to the anchor shaft (32, 194), such that the expanded tissue-coupling portion (30, 130, 192, 230, 330, 430) can be drawn tightly against the second side of the cardiac tissue wall at the target site when the tensile force is applied to the tissue-coupling portion (30, 130, 192, 230, 330, 430), the tissue-coupling portion (30, 130, 192, 230, 330, 430) having a first stiffness; characterized by an elongate tip portion (38, 138, 238, 338, 438) supported at a second end (40, 240, 340, 440) of the tissue-coupling portion (30, 130, 192, 230, 330, 430) and configured to be delivered through the cardiac tissue wall ahead of the tissue-coupling portion (30, 130, 192, 230, 330, 430), the tip portion (38, 138, 238, 338, 438) having a second stiffness less than the first stiffness.