As much as I love two-point position, I'll be the first to tell you that if you're up in two-point on a tight turn in slick footing, you're making your horse's job harder--because you're putting him on his forehand, where he's more likely to slip.
Here I'll give you two additional positions--full seat and half-seat. Once you've completely and confidently mastered one new position I describe, move on to the next. But don't abandon the earlier ones. Keep practicing them all, because there will always be situations where you'll need them.
When making a very wide turn, covering a lot of ground where I want my horse to gallop freely, or approaching a nice friendly fence, I get up of his back in two-point position, with a closed hip angle and weight dropping own into my heel. In this position, I have minimum control, and he has maximum freedom to do his job.
2. Full Seat
For maximum control, to collect or balance my horse on a very tight turn in slippery footing, or to drive him when he's clearly about to stop at a fence, I assume a full seat, sitting deep in the saddle with my upper body close to the vertical. Full seat is a very important riding tool, but be careful not to practice it too much until you're absolutely certain that you can first stay with your horse's motion in any situation.
For medium control, a somewhat tighter turn,or the approach to a fence that I think may be spooky, I'm in a rather deep open half-seat position--with three points of contact, my seat in the saddle and my hip angle slightly closed. There are many gradations of half-seat; if I wanted to lighten this one, I'd simply close my hip angle a bit.
Jeff Cook, who lives with his wife and children in Oregon, gives clinics all over the country--and systematically teaches two-point, full seat and half-seat as a matter of course.
This article is excerpted from "Beyond Two-Point," which appeared in the May 2006 issue of Practical Horseman.