This outline of plausible geologic explanations for the icy Galilean satellites' radar properties takes into consideration electromagnetic scattering models for the echoes, available empirical and theoretical information about regolith formation, and ice physics. The strange radar signatures arise because (1) ice is electrically different from silicates and/or (2) icy regoliths contain bulk-density (and hence refractive-index) structures absent within silicate regoliths. Ice's relatively high radar-frequency transparency compared with that of silicates permits longer photon path lengths, deeper radar sounding, and a greater number of scattering events. Consequently, scattering mechanisms that cannot contribute significantly to lunar echoes can dominate icy-satellite echoes. Possible phenomena unique to icy regoliths include (1) smoothing out of discontinuities between solid ejecta fragments and more porous surroundings under the action of thermal annealing to form refraction-scattering (RS) “lenses” and (2) formation of density enhancements in the shape of crater floors that result in RS and/or total internal reflection (TIR). In either case, high-order multiple scattering is more likely to be responsible for the echoes than low-order scattering. Radar/radio observations can constrain the order of the scattering and the scale of the structures responsible for the echoes but might not determine whether TIR or RS dominates the scattering. Multiwavelength investigations of the degree of correlation between radar properties and geologic terrain type should prove most useful, because inter- and intrasatellite variations in radar properties probably correspond to variations in ice purity, regolith thickness, and regolith thermal history and age.