We investigate the freezing behavior of particles interacting with an inverse nth power potential under the modified weighted density approximation (MWDA) formalism of Denton and Ashcroft [A. R. Denton and N. W. Ashcroft, Phys. Rev. A 39, 470 (1989)]. We model the liquid state with the perturbative hypernetted chain (PHNC) integral equation [H. S. Kang and F. H. Ree, J. Chem. Phys. 103, 3629 (1995)], chosen for its small computational time and high degree of accuracy. The deterioration of MWDA predictions of equilibrium properties with decreasing n is traced to its inability to accurately estimate the free energy in the static solid limit. An improvement in the MWDA theory is suggested by incorporating information on the static lattice into the model. This is done by moderating the direct correlation function via the Ornstein-Zernicke equation. It is found that this new model can drastically improve results for the coexisting densities for inverse nth power fluids. Other properties, such as the Lindemann parameter, are also improved in this new scheme.