Double jointed bradoons come with flat spatula links, like a French link snaffle, and with oval lozenges. In both cases, the two joints help to reduce the nutcracker effect of the single 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.
Some horses prefer the rounded lozenge as it perhaps encourages them to mouth the bit and obviates any thin edges that could be uncomfortable.