The Williams cheek piece allows for multiple rein positions. If connected to the main ring the bit acts as a loose ring, but when connected to the bottom ring it promotes pole flexion by creating more positive poll pressure. The Williams cheek piece helps to prevent drifting.
The Elliptical is a 45 mm lozenge, it is stronger than the Control Plate due to it having a smaller surface area. Consequently, a horse using his tongue as a means of pushing against the bit and therefore taking control, will draw back and tuck his chin in, coming back to a better point of control.