One of the more common varieties of double jointed snaffles is the French link snaffle. The two joints help to reduce the nutcracker effect of the jointed snaffle, while still allowing the rider independent control over the two sides of the mouth. It also transfers rein pressure more evenly over the bars.
The French link refers to a flat spatula between the two joints, which is designed to lay flat over the tongue. This is easy for the untrained eye to confuse with the Dr. Bristol, which has the spatula angled such that the thin edge can push harshly into the horse’s tongue. Some horses prefer the rounder version of the French link, often called an oval mouth or lozenge, although the French link can be preferable for horses with less palate clearance.