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A thermodynamically self-consistent integral equation theory in which the hypernetted-chain (HNC) and Percus-Yevick (PY) approximations are mixed as a function of intermolecular separation for pair correlation functions of molecular fluids is described. This integral equation has been solved for a fluid of hard ellipsoids of revolutions (HER) of fixed geometry. Thermodynamic consistency between the virial and compressibility equation of state is achieved by varying a single parameter in a suitably chosen mixing function. When compared to available computer simulation data, the equation is found to yield excellent results for both the thermodynamic properties and the pair-correlation functions.