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Although nosebands designed to force a horse to drop his head may serve a needed purpose for certain riding schools or cases, I prefer cosmetic nosebands that do not apply any pressure to a horse's nose. Collection is entirely possible without the use of harsh nosebands. For example, I work with Mountain horses, a gaited breed that requires good collection, yet I use a simple snaffle bridle for most training purposes.
Only you can decide what specific noseband best suits you, but keep in mind if you use a harsher noseband and it's worn too low, a sharp yank can easily injure the fragile nasal bones or tissue. A noseband should allow at least two fingers worth of slack – anything less is too tight.
The CheekpieceThe cheekpiece plays a vital role for the bridle since it determines the level of "communication" that will exist between your reins and the bit. If a cheekpiece is fit too loosely the bit will rest low in the horse's mouth, causing the bit to hit the horse's front teeth and the tongue to be subjected to uncomfortable pressure. Naturally both results are quite jarring, if not outright painful, so if that isn't enough of a deterrent to ensure a proper fit also keep in mind it will negatively affect your horse's performance.
A cheekpiece that is too tight is little better since it will cause the bit to rest too high in the mouth and dig into the cheeks, causing a painful pinch. When this happens your horse will usually try and bite down on the bit and/or push it forward to alleviate the pain.
A properly fit cheekpiece will allow one wrinkle in the corners of the horse's mouth.
ThroatlashAlso called a throat latch, this piece rests underneath the upper jaw near the neck. Its purpose is to hold the bridle in place and prevent the horse from rubbing the bridle off his head. Make sure the throatlash is not fit so tightly that it constricts your horse's breathing – the rule of thumb for proper clearance is three fingers width. Although you don't want to fit the throatlash too loosely as a loose fit will reduce its effectiveness, it's far better for you to err on the side of too loose than too tight.
As you can see from the above, ensuring a proper bridle fit is extremely important and almost equally simple – so take a few moments to test each piece's position to verify you're not inadvertently causing your equine partner any discomfort.