Tissue ingrowth on the distal loop portion of a constricting cord can dramatically improve the bond between the constricting cord and a cardiac valve annulus. But tissue ingrowth on the proximal portions of the constricting cord can interfere with the constricting action of the cord. This problem can be addressed by covering the proximal portions of the constricting cord with a material that resists tissue ingrowth, and waiting for tissue ingrowth to strengthen the bond between the distal loop portion of the constricting cord and the annulus. The reduced ingrowth on the proximal portions of the constricting cord make it easier to constrict the annulus when the constricting operation is eventually performed.