Dr Cook's Bitless Bridle
Sicily and I had a seamless transition to this bridle. It works the same way in my hands as a traditional bridle. Unlike a bridle with bit, this bridle applies only pressure to the sides of the head. It works differently from a bosal or hackamore in that it does not rely on pinching or pressure points, and different from a side-pull or halter with reins in that you get specific pressure along the cheeks, which allows for finesse.
My mare was notably more relaxed in this bridle, even though she never showed any 'typical' symptoms of problems with bit... Although I'm sure if I went back to the bit I would be able to find these symptoms very quickly.
This is the product website for the cross-under bitless bridle: http://www.bitlessbridle.com/
Although the web design may be lacking, the bridle itself is well-made. I ride in the padded english leather bridle, but use my own reins.