Several of you have asked me if there's any value in counter flexing your horse while in true canter so I'd like to discuss that here.
1. Generally, you want to flex your horse in the direction of the canter lead he's on. That goes for true canter as well as counter canter. So if you're cantering on left lead, position his head so you just barely see his left eye and/or nostril.
2. I do often ask students to counter-flex their horses while cantering. For example, they'd just barely see the right eye or nostril when they're in left canter. I do this to help riders feel if their horses are straight. The exercise helps because:
A. When in true canter (left lead while riding to the left), riders tend to bend the neck too much to the inside and the shoulders pop out. This happens even more so when the horse's hollow (soft) side is on the inside.
B. In counter canter, riders overbend the neck to the inside in BOTH directions mostly because they're trying to keep the horse from switching leads.
If you bend your horse's neck too much, his shoulders will pop out in the other direction. As a result, he won't be straight, and he can't be in a good, uphill balance.
Counter-flexing slides the shoulders over so they lie softly between the two reins. This teaches you the FEELING of riding your horse straight. Once this feeling of riding your horse straight feels "normal" to you, go back to riding in true flexion. (Your horse is straight when his shoulders are between the two reins, they're in front of your hips, and they're in front of your horse's hips.)
When you go back to true flexion, check that his shoulders stay in exactly the same spot that they were in when you were in counter-flexion. (i.e. they don't pop to the outside again.) If they do pop out again, just quietly go back to counter flexion.
Repeat the true flexion/counter-flexion exercise until the horse's shoulders feel like they're in the same place regardless of which way he's flexed.