I was auditing a clinic today. The clinician was Jina Smith, an Olympic rider and a very knowledgeable instructor. She was working with a girl who had trouble sitting vertical because her horse was tipping her to the left. The horse's ribcage was dropped on the left side and pushed out to the right. To correct this Jina Smith offered following exercises:

Riding on the right rein renvers. Renvers helped the horse to push his ribcage to the left and step under with his right hind leg.
Next was shoulder-in to the renvers to the shoulder-in again on the right rein. All that worked horse's right hind leg and made him straighten his ribcage. However, the girl had to watch out for the left shoulder in shoulder-in which was outside shoulder. It must stay up and no overbend in the neck.
When previous exercises straightened his ribcage to some extend they changed direction and tried them on the left rein. The shoulder-in to the renvers was hardest to achieve. At first, the horse didn't want to change the bend at all. This is because renvers on the left rein require more effort then right shoulder-in but the bend is the same. Renvers demand from the ribcage not just vertical position but bend and slight drop of the right pelvis to step forward with the right hind.. This is complete opposite to the horse's natural way of going. Read the blog posted on October 28, "Questions of straightness".
They finished this part of the lesson with riding counter shoulder-in to travers to shoulder-in.

All these exercises are really great tools to stretch and bend a horse through the whole body. This is truly gymnastic work, all muscles get dynamic stretch and thorough work out. The only caution is do not work on them for too long. Otherwise, your horse will start to resist because fatigue sets in very quickly.