An annuloplasty device comprising first and second support rings having a coiled configuration in which the first and second support rings are arranged as a coil around a central axis, wherein the first and second support rings are configured to be arranged on opposite sides of native heart valve leaflets of a heart valve, wherein the first and/or second support ring comprises a plurality of sides (104, 104') forming a non-circular cross-section of the first and/or second support ring, wherein the cross-section varies along a longitudinal direction of the first and/or second support ring, wherein the first support ring comprises a first posterior bow and a first anterior portion, the second support ring comprises a second posterior bow and a second anterior portion, the first and second posterior bows are adapted to conform to a posterior aspect of said heart valve, and the first and second anterior portions are adapted to conform to an anterior aspect of said heart valve, the first posterior bow transitions to the first anterior portion over a first commissure section, the first anterior portion transitions to the second posterior bow over a second commissure section, the second posterior bow transitions to the second anterior portion over a third commissure section (115"), wherein any of the first, second and third commissure sections (115, 115', 115") have a first cross-section which has an area and/or shape which is different than an area and/or shape of a second cross-section of any of the first posterior bow, the second posterior bow, the first anterior portion, and the second anterior portion, wherein the first cross-section transitions gradually to the second cross-section along the longitudinal direction. first and second support rings having a coiled configuration in which the first and second support rings are arranged as a coil around a central axis, wherein the first and second support rings are configured to be arranged on opposite sides of native heart valve leaflets of a heart valve, wherein the first and/or second support ring comprises a plurality of sides (104, 104') forming a non-circular cross-section of the first and/or second support ring, wherein the cross-section varies along a longitudinal direction of the first and/or second support ring, wherein the first support ring comprises a first posterior bow and a first anterior portion, the second support ring comprises a second posterior bow and a second anterior portion, the first and second posterior bows are adapted to conform to a posterior aspect of said heart valve, and the first and second anterior portions are adapted to conform to an anterior aspect of said heart valve, the first posterior bow transitions to the first anterior portion over a first commissure section, the first anterior portion transitions to the second posterior bow over a second commissure section, the second posterior bow transitions to the second anterior portion over a third commissure section (115"), wherein any of the first, second and third commissure sections (115, 115', 115") have a first cross-section which has an area and/or shape which is different than an area and/or shape of a second cross-section of any of the first posterior bow, the second posterior bow, the first anterior portion, and the second anterior portion, wherein the first cross-section transitions gradually to the second cross-section along the longitudinal direction.