The authors extend the method of energy-dependent potentials introduced by one of the authors in an earlier paper (Clark and Dawber, ibid., vol.2, p.930 (1972)) to study the properties of random binary alloys. Some of the approximations made in that paper are removed and the improved model is used to calculate not only the specific heat and resistivity, but also to study the distribution of charge density around the two types of atom in the alloy. Calculations are made on silver-gold and silver-palladium alloys.