Combing the design of a Full Cheek Bit and a Running Gag is called a Nelson Gag.
Full cheek: This cheekpiece style offers cheek sides that guide the horse to turn easier and educate the horse of lateral movements. Full Cheek mouth is also good to ensure the bit is never pulled through the horses mouth. This makes the Full cheek snaffle bit useful for schooling young horses.
The Full cheek snaffle bit lies stable and calm in the mouth.
A Running Gag bit has extra eyelets, in the bottom and on top of the bit rings to allow for Gag straps to run through. The gag can be attached on to the bridle with a special piece of rope, called a Gag rope or Gag Strap. This Gag Strap must be placed through the eyelets in the bit rings top to bottom. At the end of the gag rope is a buckle, with that buckle the rope can be attached to the bridle. A Gag rope is specially made for a Gag bit. A ring is placed at the bottom of the Gag rope, the rein has to be attached to that ring.
A Gag bit can be used with two reins. One attached to the bit rings and the other attached to the ring of the Gag strap. By using the second rein a leverage effect is created. A Gag is often used for horses who put a lot of weight in the riders hands and this bit is also used for teaching a horse to bring the head up.
This bit is not suitable for inexperienced riders and horses, as it can be pretty sharp because of the leverage. The rider must know what he's doing before he decides to use this bit.