A holder for an annuloplasty ring having a template defining a proximal face opposite the distal face, and a peripheral edge about which the annuloplasty ring conforms. The annuloplasty ring anchors to the template using one or more flexible filaments. The template includes a single cutting well on its proximal face over which the flexible filament is suspended. Desirably, the single cutting well is located adjacent the peripheral edge so as to be away from any handle connections for ease of access. The flexible filament emerges above the proximal face of the template at only one location at the cutting well, thus presenting a one cut quick-release structure that is highly visible to the surgeon. The annuloplasty ring may have a relatively rigid inner core surrounded by a suture-permeable cover, and the peripheral edge may be formed by a lower axial wall and an upper radial ledge that projects outward from the rigid inner core but not quite as far as a sewing margin of the ring. The ring and holder may be for mitral annuloplasty rings and generally have a D shape in plan view, and may be three-dimensional with upward anterior and posterior bows.
