Close contact saddles are made for the jumper rider in mind. The goal of the close contact saddle is to keep the rider as close to the horse's movement as possible, therefore they do not have a lot of extras to 'hold' the rider in position like deeper-seated saddles do. In order for the rider to get up out of the saddle and out of the horse's way over fences, the stirrups need to be shorter than what is used during flatwork. The saddle flaps/skirts are shorter and more forward in these saddles to allow for this, most have a minimal knee block but not the large thigh blocks seen in dressage saddles.
Some brands such as Bates, Collegiate and Wintec have the EASY-CHANGE Gullet system, which allows adjustment of the saddle to the horse, or CAIR panel system which uses air to distribute the rider's weight over the horse's back. Find close contact saddles from top brands at Equestrian Collections.