Apparatus comprising an implantable annuloplasty structure, which comprises: flexible sleeve, having first and second sleeve ends; and a contracting assembly, which comprises: a contracting mechanism, which is disposed at a first site of 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 only 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 only between the first and the second sites (34, 36); 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 (34, 36), exclusive, characterized in that one or more of the tissue anchors are coupled to the sleeve at respective third sites longitudinally between the first site and the first sleeve end, exclusive. flexible sleeve, having first and second sleeve ends; and a contracting assembly, which comprises: a contracting mechanism, which is disposed at a first site of 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 only 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 only between the first and the second sites (34, 36); 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 (34, 36), exclusive, characterized in that one or more of the tissue anchors are coupled to the sleeve at respective third sites longitudinally between the first site and the first sleeve end, exclusive. a contracting mechanism, which is disposed at a first site of 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 only 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 only between the first and the second sites (34, 36); 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 (34, 36), exclusive, characterized in that one or more of the tissue anchors are coupled to the sleeve at respective third sites longitudinally between the first site and the first sleeve end, exclusive.