The Eggbutt cheekpiece to be the most simple and common. Therings do not move up and down, resulting in a more stable position in themouth and more direct rein aids. The lips dont get pinched by this cheekpiece,so bit rings are not necessary.

The Inno Sense Mullen is a straight bar that slightly bends forward. This mouthpiece is
fabricated of synthetic material.The bit has a rigid core thatmakes the mullen bar not flexiblebut the material around it stillgives the bit a soft touch.