"A horse must self-balance and have release when he's moving correctly so that he may do so. First I want them to achieve balance and learn to freely move in response to my cues "asking" for particular movement.
Like the toddler that must learn to walk before he can run, jump and skip; the horse must first learn to self carry his gaits with a rider on board, in balance and *without rider support* or framing. If you "have" to hold a horse up in the front to achieve a correct walk then he is dependent on you and not self-carrying."
An Icelandic Horse should be trained bitless, and then move into a small curb with an unjointed mouthpiece or a mullen-mouth snaffle.
I believe that the jointed snaffles are torturous to Icelandics if they are ridden icelandic-style, and of course the shanked jointed-mouth bit (i.e. icelandic bit) compound the problems for them.