When it comes to riding our horse, we can choose between using a bridle with a mouthpiece (fillet or bit) or without it. The English term for this form of riding is Bitless riding, which literally means "ride without a mouthpiece." This is a very good alternative for those very sensitive mouth horses that do not support any embouchure, nor the softest fillet, as well as simply a different way of seeing horsemanship. More and more people have become interested in this class of training methods, being hailed as much gentler and fairer on the horse, by not using pressure on its mouth, but on other parts of the head.
Even so, there are very few equestrian disciplines in which its use has become official and, therefore, it is allowed in official competitions; the jump and the complete one are those that have their most extended use. Unfortunately, in the Dressage "They have drawn a thick veil" with this. Even though there are riders and riders who have successfully tamed their horses up to the Grand Prix level, performing the exercises as well or better than a horse with a double reins, its use in competition is almost nil.
Just In England (and I think that in no other, or at least I did not find) a category is made official, within the different categories that exist in a dressage contest, in which riders who use headless headbands can participate. It is only contemplated at low levels and, of course, separately from those of the same level who use steak, and with special judges. Come on, what we here call being outcasts.
Nothing could be further from the truth. It is absolutely possible to tame your horse using methods such as hackamore, or rotational (which we will talk about), and achieve bend, placement (of the horse's head in the vertical), drive ... Even many riders, once they try these methods, they see their horse's attention increase significantly, and they notice it less tense and more active and flexible.
Just as a curious example, the international Grand Prix rider, Alizee froment, he trained his horse Mistral du Coussoul 3 months before the Global Dressage Forum in 2011 with an elastic headband without a mouthpiece to be able to make a demonstration, with simply spectacular results. Here I leave you, to finish, some snapshots of that marvel (I feel its low resolution):