for the driving people

Overcheck is a rein that goes from an additional bit (overcheck bit) up thru the crown, and then attaches to a hook on the harness saddle. In fine harnesses you'll often see these. I'm not sure the exact purpose except for maybe to keep a horse from dumping his head down and having a buck.
 
its the moderen name for the bearing rein & thankfully used for totally different reasons now.

as someone said it can stop bucking (like a daisy rein but we used on the youngster when he was learning to stop him dropping his nose down too far & then promptly putting his leg through the rein (no matter how much you kept contact with his mush)
 
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