A Tennessee Walking Horse walks with a lot of rolling shoulder motion, and a deep nodding action of the neck.  Consequently, it requires a saddle that is cut back at the withers to accommodate the increased neck action, and also one that is pared away on the skirts to allow for the shoulder action.  These cutback saddles are not padded with knee rolls because the gait does not require any grip to ride it, so the leg is extended straighter down in a more relaxed manner.  There is very little bend at the knee and the stirrup leather is only short enough to cause the toe to tip up slightly to maintain contact with the stirrup.  This leg position is not as straight and rigid as in a Western Saddle, nor is the foot thrust forward like in Western equitation.  Rather, the leg is held back and slightly behind the girth line to stay out of the way of the horse's shoulder. 

Any other type of saddle runs the risk of interfering with the action of the neck and shoulder, and impeding the gaits.  The saddle is placed in the middle of the horse's back, and not up close to the withers as on a trotting horse.  There should be a comfortable hand span between the girth and the horse's elbow.

Cutback saddles are designed for maximum comfort of both the horse and the rider.

Below is a link to all the suitable cutback saddles that are currently being offered on eBay.