A double-jointed snaffle? Those are very mild bits, about the most mild you can get, although they tend to put more pressure on the tongue. They eliminate the "nutcracker effect" you can get with a regular jointed snaffle, when pressure is exerted downwards onto the reins and the jointed end bends and bangs into the top of the mouth. There are a few kinds of double-jointed snaffles, like a french-link, which has a middle piece shaped like a bone, and a Dr. Bristol, which is NOT a mild bit...the center piece is long, flat and slanted so it bites into the tongue. Are you considering using one on your horse?