PL Simple procedure is used to construct the damping functions for extending the Axilrod-Teller-Muto triple dipole dispersion energy for arbitrary three-atom systems to smaller distances. The new damping functions incorporate the Tang-Toennies two-body damping functions at the appropriate united atom limits. The accuracy of the damping function is illustrated by comparing with ab initio and third-order perturbation calculations of the H-3 three-body polarization energy.