A number of consistency conditions for the contact values g(ij)(sigma (ij)) of the pair correlation function of species i and j in an additive hard-sphere fluid mixture are discussed. It is shown that most of the theoretically-based expressions, as well as other more empirical in character, existing for these functions, fail to satisfy at least one of the conditions. It is suggested that one could improve the performance of the expressions for g(ij)(sigma (ij)) and the equation of state by using the consistency conditions. This is illustrated by modifying the Boublik-Mansoori-Carnahan-Starling-Leland expressions for g(ij)(sigma (ij)), which results in better predictions for these functions as well as for the compressibility factor and the fourth and fifth virial coefficients.