A saddle for a sheeting head includes a pair of semi-circular concave edges configured to seal a pair of rollers. The oppositely facing concave edges each include a tongue that fits in a corresponding groove in the roller and a retracted concave edge adapted to wrap around half the roller surface. The saddle includes a top portion wherein the concave edges downwardly converge, and a bottom portion wherein the concave edges downwardly diverge. A narrow waist is provided at the proximal-most position of the concave edges and adapted to fit in a pinch point between the rollers. A sheeting head assembly incorporating the saddle may include a sidewall to which the saddle need not be fastened. The self-locking characteristics of the saddle enable an assembly to omit sidewalls altogether.