The eggbutt is a fixed cheek bit, this may be useful for horses that are a bit unsure of the bit as it doesnt move around to much in the mouth, it should encourage the horse to stretch into the contact. An eggbutt bit would be less suitable if your horse is prone to leaning or taking hold of the bit
Single Jointed Bits
The single joint puts pressure on the sides of the tongue, on the lips and on the bars due to the nutcracker. The single jointed bits also may have a head raising action so would be less suitable for your horse if they ride with a high head carriage or above the bit. Also breeds such as Irish Draughts, may have particularly large tongues, therefore having less room in the mouth for a single jointed bit as this pushes the bit nearer the roof of the mouth, also Arabs and alike may have a low palate, both of these examples may not benefit from the single jointed bits as the nutcracker action may cause brushing of the roof of the mouth.