We compare the general Beran bounds on the effective electrical conductivity of a two‐phase composite to the bounds derived by Torquato for the specific model of spheres distributed throughout a matrix phase. For the case of impenetrable spheres, these bounds are shown to be identical and to depend on the microstructure through the sphere volume fraction &fgr;2and a three‐point parameter &zgr;2, which is an integral over a three‐point correlation function. We evaluate &zgr;2exactly through third order in &fgr;2for distributions of impenetrable spheres. This expansion is compared to the analogous results of Felderhof and of Torquato and Lado, all of whom employed the superposition approximation for the three‐particle distribution function involved in &zgr;2. The results indicate that the exact &zgr;2will be greater than the value calculated under the superposition approximation. For reasons of mathematical analogy, the results obtained here apply as well to the determination of the thermal conductivity, dielectric constant, and magnetic permeability of composite media and the diffusion coefficient of porous media.