When a loose ring bit is not comfortable for a horse because of pinching around the lips or hyper-mobility, an eggbutt is the primary alternative. By flaring out the ends of the mouthpiece and joining the rings with flush swivel joints above and below where the lips contact the edge of the bit, the eggbutt can be more comfortable for many horses, as the edges of the mouthpiece are less likely to pinch the horse’s lips.

The eggbutt does give up some mobility, in that the position of the mouthpiece is more influenced by the movement and position of the cheek pieces than by the movement of the horse’s mouth, unlike the case with a loose ring snaffle. While this in generally somewhat of a disadvantage, the fixed position could be advantageous with horses that tend to play with the bit too much.

A dee ring snaffle bit is a compromise between an eggbutt and a full cheek snaffle.  It has vertical shanks that extend above and below the mouthpiece, and these are joined on the top and bottom by a D-shaped ring on swivel joints.  Like the eggbutt, it helps prevent pinching at the corners of the mouth, though generally without as much bulk as an eggbutt, and it provides fairly substantial lateral control through the vertical shanks, though without the dangers posed by the arms on a full cheek snaffle.  

Because of this combination of control and safety, the dee ring snaffle has been popular in horse racing and jumping disciplines for a long time.

As with the eggbutt snaffle, the fixed position of the cheeks and mouthpiece mean that this bit is less mobile in the horse’s mouth, for better or worse.  In disciplines where high sensitivity is required, such as dressage, the fixed position is generally disadvantageous.  However, with horses who need extra control in high energy situations, the tradeoff is undoubtably worthwhile.  Because the shanks are longer and straighter than the sides of an eggbutt, the dee ring exerts more lateral force on the sides of the mouth, and is less able to be pulled through the mouth, thus affording more control in turning, though slightly less than with a full cheek snaffle. 

With the dee rings attached at the top and bottom of these shanks, the point of rotation is somewhat further away from the mouthpiece than on an eggbutt horse bit, thus making it arguably less mobile and somewhat harsher through a slight leverage action, depending on the angle of the force applied.