I use a biothane Nurtral brand Bitless bridle
. I tried the Dr Cooks and just didn't care for how "loose" the cross-under straps were. They would pull off center easily and turn the noseband.
I like the Nurtural bridle. It's good quality, my mare goes well in it for trails and lessons, and I don't have to worry about beginners yanking her mouth. I have used my bitless on a few other horses. Only one didn't go well in it, and at the time, he needed a uxter kimberwick with reins on the bottom slot... He was an ex-western horse that was always ridden in a curb bit. He just completely ignored the bitless, lol. Now that he goes in a full cheek snaffle, he can be ridden in a bitless, though he goes better in his bit.
If a horse goes well in a simple snaffle (o-ring/loose ring, d-ring, egg butt, etc.) or other bitsless bridle (side-pull or halter), then a cross-under style bitless will work great. If your horse goes in a curb or shanked bit, or a mechanical hackamore, then you'll need to work on some ground and saddle training to get him to respond to a cross-under bitless.
I have attached two pictures of my mare giving a lesson in her bitless bridle. The first is an adult who had never ridden English before. The second is a young girl in her 5th lesson. Bridgette, the horse, also goes western.