In the Double Bridle, two bits are used on one bridle -- a bridoon (a type of snaffle) and a curb bit. These two bits, when properly fitted and when used by an experienced rider can refine the communication between horse and rider. Poorly fitted, or in the hands of an inexperienced rider, the bits can cause considerable discomfort or even pain to the horse and the resulting picture won't be one of harmony and elegance. (Please note that the bridoon is usually a small ringed bit, however there wasn't a suitable one available when taking the above photograph)
To fit the double bridle, the bits should lie in a natural position on the bars of the mouth, with the bridoon slightly above the curb. They should be far enough apart to allow them to function correctly, while not being so far apart that the horse is at risk of getting his tongue stuck between them. Care should also be taken with the fitting of the curb chain.
The simplest form of double bridle is one with a medium bridoon, preferably single-jointed, and a curb with a medium port, allowing room for the tongue. The bridoon is used for turning the horse and the curb bit encourages the horse to relax his jaw, poll and neck.