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.