A previous generalization of the Percus-Yevick (PY) and hypernetted chain (HNC) equations for simple fluids, involving a density- and temperature-dependent coefficientm, is extended by including a spatial dependence inm.The new approximation yields an exact fourth virial coefficient and, by further requirement, a consistent equation of state from both the virial and compressibility forms. Comparison of calculated results for the hard sphere potential shows an improvement over the PY, HNC, and previous pressure-consistent equations