A cleave gag is a more effective variant of the OTM gag. Instead of being tied over the bottom's mouth, the scarf or cloth is pulled between his or her teeth. While a thin material isn't very effective, a thick scarf can be used to hold his or her mouth open, and the tighter that gag is tied the better it works.
A knotted gag is a cleave gag where the scarf has a knot (often a double or triple knot to make it larger) tied in the middle and placed in the gagged person's mouth. This helps to fill the mouth and makes the gag much more effective than a simple cleave gag. Alternatively, the scarf may be tied round the head with the ends in front, knotted together with the knot in the mouth.
It has much the same effect as a ball gag, but the scarf can absorb saliva hence there is less drooling than a ball gag.