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curb bit 
Bit composed of a mouth and two side bars; it lowers the horse’s nose and is used in conjunction with a snaffle bit.
sliding cheek bit 
Bit whose mouth slides up and down the cheeks; this action is gentler to the horse but provides slightly less control.
Liverpool bit 
Bit that can be used alone; it combines the characteristics of the snaffle and curb bits.
jointed mouth bit 
Curb bit whose mouth is composed of two articulated parts; it is gentler to the horse than a straight mouth bit.