The key was doing as much as possible to prevent the rear in the first place. My horse was highly responsive to leg cues and was soft to lateral bending. I used that to my full advantage. He wanted to rear, we would walk sideways down the trail. No amount of stopping him or circling ever worked. Soon as we would straighten out he would be back on his hind legs. I would ask for a bend in the body and just move sideways. Soon as I noticed the tension leave his body I would let him straighten out until he acted up again then again we would be walking sideways.
Now understand this did not solve his barn sour problem in the least. I just swapped what he did when he got agitated or excited. I prefer sidestepping and prancing everyday over rearing. It took about a year and a half for the rear to disappear. Its was a long process to rewire him that way. This wasn't the only method I used but the only one I am willing to share that helped with my horse.
Remember, never encourage backwards motion with a rearer. Its only going to promote up and back, trust me you never want that. Forward is always better than back.
Get control of lateral movement at home and use them. A horse can't rear if they are crossing their back legs and kept off of their hindquarters.
Always give a horse their head, lean forward and wrap your arms around the neck while they are rearing. Don't try to pull the sideways (or back) if their front feet are off the ground, wait until they land then pull the head over. If you feel before it starts turn the head, but if they're going up let them have their balance.
And always, get help from a trainer.