Apparatus comprising an implantable annuloplasty structure , which comprises: a flexible sleeve , having first and second sleeve ends; and a contracting assembly , which comprises: a contracting mechanism , which is disposed at a first site along the sleeve ; and a longitudinal contracting member , having (a) a first member end, (b) a second member end , which is coupled to the sleeve longitudinally at a second site , which is longitudinally between the first site and the second sleeve end, exclusive, and (c) a first member end portion, which (i) extends from the first member end toward the second member end along a longitudinal portion of the contracting member , and (ii) is coupled to the contracting mechanism , wherein the contracting mechanism is configured to apply a longitudinal contracting force between the first and the second sites ; and a plurality of tissue anchors , at least three of which are coupled to the sleeve alongside the contracting member , longitudinally between the first and second sites , exclusive, characterized in that two or more of the tissue anchors are coupled to the sleeve at respective third sites longitudinally between the second site and the second sleeve end, exclusive. a flexible sleeve , having first and second sleeve ends; and a contracting assembly , which comprises: a contracting mechanism , which is disposed at a first site along the sleeve ; and a longitudinal contracting member , having (a) a first member end, (b) a second member end , which is coupled to the sleeve longitudinally at a second site , which is longitudinally between the first site and the second sleeve end, exclusive, and (c) a first member end portion, which (i) extends from the first member end toward the second member end along a longitudinal portion of the contracting member , and (ii) is coupled to the contracting mechanism , wherein the contracting mechanism is configured to apply a longitudinal contracting force between the first and the second sites ; and a plurality of tissue anchors , at least three of which are coupled to the sleeve alongside the contracting member , longitudinally between the first and second sites , exclusive, characterized in that two or more of the tissue anchors are coupled to the sleeve at respective third sites longitudinally between the second site and the second sleeve end, exclusive. a contracting mechanism , which is disposed at a first site along the sleeve ; and a longitudinal contracting member , having (a) a first member end, (b) a second member end , which is coupled to the sleeve longitudinally at a second site , which is longitudinally between the first site and the second sleeve end, exclusive, and (c) a first member end portion, which (i) extends from the first member end toward the second member end along a longitudinal portion of the contracting member , and (ii) is coupled to the contracting mechanism , wherein the contracting mechanism is configured to apply a longitudinal contracting force between the first and the second sites ; and a plurality of tissue anchors , at least three of which are coupled to the sleeve alongside the contracting member , longitudinally between the first and second sites , exclusive, characterized in that two or more of the tissue anchors are coupled to the sleeve at respective third sites longitudinally between the second site and the second sleeve end, exclusive. <EOS>