A simple algorithm for obtaining accurate pair distribution functions gij of hard-sphere mixtures is proposed. This generalizes the pure-fluid procedure of Verlet and Weis for improving the Percus–Yevick distribution functions. Two theorems are proved concerning the distribution functions yij = exp (uij/kT)gij, and an approximation for these functions is proposed. Finally, a method for computing direct correlation functions, given the pair distribution functions, is described. © 1972 Taylor & Francis Group, LLC.