Abstract. The problem of predicting the effective absorption coefficient of random media is discussed. The variational estimates on this coefficient, recently derived by the authors, are explicitly evaluated for random dispersion of spheres to the order `square of concentration''. A comparison with the bounds of Talbot and Willis is performed as well. It appears that the proposed bounds are more restrictive but, unlike those of Talbot and Willis, are only applicable for sphere concentrations that do not exceed 0.10.