The Eggbutt cheek piece prevents pinching of the lips and gives a solid feel against the side of the face. It also prevents the bit being pulled through the mouth. The release is slower than the loose ring and also introduces light poll pressure.
The Colin Miles is a great schooling bit with a wide centre piece creating greater tongue pressure and reducing bar pressure. The rings give the horse something to play with and help keep the horses attention on the bit.
Cheekpiece
For the horse that shakes its head up when in a snaffle. Recommended over the elliptical as the control plate offers a larger surface area for the pressure to be distributed over.
Mouthpiece
This particular joint exerts more pressure than the Control Plate or Elliptical.