Integrated phase curves of Callisto and Ganymede have been intepreted using the Lumme-Bowell theory. The brightness of these satellites up to about 80¿ solar phase angle can be explained by the theory, but at larger phase angles (~120¿), the observed brightness drops off more rapidly than predicted. We suggest a physical explanation for the discrepancy: single regolith particles must have phase functions which are much more elongated in the forward or backward scattering directions than allowed for by the Lumme-Bowell theory. The model parameters derived for Callisto and Ganymede therefore can aonly approximately represent the surface-scattering properties. For the dark hemisphere of Ganymede, we derive: &rgr; (roughness)=1.0, g (asymmetry factor of the single particle scattering function)=-0.2, ω˜0 (single-scattering albedo of a particle)=0.9. For the eastern hemisphere of Callisto, we obtain &rgr;=1.0 and for the western hemisphere &rgr;=0.4, with g=-0.2 and ω˜0=0.5 for both hemispheres. The hemispheric asymmetry in Callisto's surface texture can be explained by invoking the formation of an ice film on the trailing side. Such an explanation is consistent with Voyager detailed photometry and thermometry of Callisto. Earth-based polarimetric measurements of Callisto are reinterpreted so as not to conflict with the Voyager results.