I tried a cool canter exercise out with Huey the other night -- one that I learned from Wolfgang a long time ago. It can be used as a baby step towards schooling canter pirouette. I seem to remember that when I learned this exercise I trotted it at first, to get the feel for the pattern.
In this exercise you ride the whole figure on the same lead. So, you pick up the right lead where the arrow is (you're in counter canter to the wall). In the corner you circle right as small as you can for three-quarters of a circle, sending you onto your next straight line, lather, rinse, repeat, all the way around the square. As the horse's collection increases, you can decrease the size of each 3/4 circle, and theoretically eventually achieve 3/4 pirouettes at the corners.
Huey's first response to this was "go fast!" Which is his first response to anything new and/or difficult. This exercise makes use of the corners as half halts, so you don't have to rely on your hands. It didn't take long for Huey to realize that blasting down the straightaways wasn't getting him out of anything, and he slowed down and seemed to enjoy the exercise. Left got very easy; right needs some more work.