The Myler bit you are showing is actually a Billy Allen mouth piece. Myler calls it a "barrel" mouth or sometimes a Level One.
Great bit. I use a snaffle similar to the Myler except mine is sweet iron. I also have one with shanks and the same mouth piece. The horse I use it on is dead broke and on his way to becoming a Bridle Horse. (See the picture of Bobo on my horse page).
This is the shanked bit I use: