In order to confirm the validity of our previous results for the albedos and the asymmetry factors of the phase functions of alumina, stainless steel and glass beads, data of the emerging intensities at the boundaries of these packed beds are reanalyzed using the extended emerging-intensity fitting (EIF) method. In the analysis, a value of the optical thickness is varied stepwise and, for each value of the optical thickness, the albedo and the asymmetry factor of the phase function are estimated using the previously described EIF method. The optical-thickness dependencies of the minima of the sums of the squares of the differences between the observed and calculated emerging intensities at each value of the optical thickness are examined. Furthermore, a theoretical model to account for experimental results for the asymmetry factor of the phase function of a packed bed of diffuse spheres is proposed.