Pulley Martingale Attachment.
Many are not aware of the Pulley Martingale. Its advantage is that for lateral movement of the head and the quick changes of direction required in jumping, it allows the horse to bend his head and neck in the required direction without the restriction against the opposite side of the mouth.
The unrestricted up and down movement of the rings through the pulley accomodate themselves according to the position of either rein without putting unwanted pressure on either side when turning sharply.