An overcheck rein, also known as a bearing rein or a false martingale, is a piece of horse equipment designed to limit a horse's head carriage and prevent them from lowering their head too much. There are a few synonyms for an overcheck rein, including a running martingale or a check rein. The word "martingale" is often used more broadly to refer to any piece of horse equipment that limits a horse's head carriage. Other synonyms for an overcheck rein in colloquial language might include headgear, head restraint, or head control equipment. Ultimately, the purpose of any of these pieces of equipment is to help ensure horse riding safety and control.