Back in stock are the Scorriers / Cornish snaffles. This style of bit has been around for many years. Unlike normal rounded mouthpieces the Scorrier has a squared off mouthpiece like a Magenis and one side is slightly serratted and the other side smooth. The cheeks attach to the inner ring and the rein to the outer ring thus giving a slight squeezing action.
The bit can be used either with the serratted side facing or the smooth side.