"Gag bits (called elevator bits in the English world) seem to have a negative connotation, perhaps because their name conjures up images of a horse spitting and choking on a too-tight mouthpiece. In fact, when used correctly, gag bits can be quite mild. I personally like them (and Wonder/Half-Wonder bits in particular) for teaching the breaking at the poll elements of collection, flexion, and lateral movement to a green horse moving out of a snaffle. Gag bits are popular in the training pen, barrel racing and in gaited horse communities.
Physically, they are composed of the mouthpiece (often a chain or snaffle mouth), shanks of varying lengths, and a curb. What sets them apart from ordinary curb bits is that the mouthpiece is not fixed in place—it is free to move and slide about. This is the “gag action.” When pressure is applied via the reins, the bit rotates and the mouthpiece slides around the ring. When the curb has tightened as much as it can and/or the mouthpiece reaches the end of its track, increasing pressure is applied from the mouthpiece. Poll pressure is also applied as the curb mouthpiece slides and the bridle effectively shortens. This gag action gives the horse plenty of warning from the time the rider picks up the reins to the time harsh pressure is applied. It also allows for independent movement of the shanks, meaning you can “pick up” one side of the horses head without affecting the other—great for lateral movement."
Read more: My Own Informative Bits and Bitting Thread