Apparatus for repairing a cardiac valve comprising, a flexible annuloplasty structure (222) having a sleeve (26) with an elongated tubular side wall (253) and at least one distal end wall (251) having a surface substantially transverse to a lateral surface of the tubular side wall (253), a first tissue anchor (32a) passing through the distal end wall (251) of the sleeve (26) and a second tissue anchor (32b) passing through the tubular side wall (253) in a manner in which a portion of the tubular side wall (253) that is between the first and second tissue anchors (32a, 32b) assumes a shape in which: the portion has a first part of the lateral surface of the tubular side wall (253) and a second part of the lateral surface of the tubular side wall (253) opposite the first part, and the second part of the lateral surface of the tubular side wall (253) has a degree of tension that is larger than a degree of tension of the first part of the lateral surface of the tubular side wall (253).
