My teacher will often use a full disengagement of the hind, and a step over of the fore to soften the horse. But, it's a bit more complicated than I am making it sound. The desired result is the the horse rockst backward, lifts the base of the neck, flexes at the poll and jaw, steps the inside hind well under itself, and while staying rocked back over its' hind, step the now lightened forehand over to the inside. LIke inside hind steps to the right, inside fore steps to the left, and horse makes a 180 degree turn, more or less..
If the horse locks up her jaw, then her hind end is often locked up , too.
When I ask Z to back up , as I put some rein pressure on, I look for him to soften his mouth, flex at the poll and prepare to rock backward. If I ask him to flex a bit more to one side than the other, I will usually get him a bit softer in the mouth. Watch that inner eye. If the horse is backing, or turning to the right, for example, but you still see the white of the eye, then the eyeball is rolled in the opposite direction, which means the horse is still THINKING in the direction he is looking, NOT in the direction you are asking him to bend/flex toward. Even if you can pull his/her head all the way to the right , and you can, if the hrose is still looking left (evidenced by eye and ear), his thinking is not WITH you, and the brace is still in his body.
Watch the ears and eyes to see if the mind (and thus, the body) goes with you or opposes you