Cassini 2.2-cm radar and radiometric observations of seven of Saturn's icy satellites yield properties that apparently are dominated by subsurface volume scattering and are similar to those of the icy Galilean satellites. Average radar albedos decrease in the order Enceladus/Tethys, Hyperion, Rhea, Dione, Iapetus, and Phoebe. This sequence most likely corresponds to increasing contamination of near-surface water ice, which is intrinsically very transparent at radio wavelengths. Plausible candidates for contaminants include ammonia, silicates, metallic oxides, and polar organics (ranging from nitriles like HCN to complex tholins). There is correlation of our targets' radar and optical albedos, probably due to variations in the concentration of optically dark contaminants in near-surface water ice and the resulting variable attenuation of the high-order multiple scattering responsible for high radar albedos. Our highest radar albedos, for Enceladus and Tethys, probably require that at least the uppermost one to several decimeters of the surface be extremely clean water ice regolith that is structurally complex (i.e., mature) enough for there to be high-order multiple scattering within it. At the other extreme, Phoebe has an asteroidal radar reflectivity that may be due to a combination of single and volume scattering. Iapetus' 2.2-cm radar albedo is dramatically higher on the optically bright trailing side than the optically dark leading side, whereas 13-cm results reported by Black et al. [Black, G.J., Campbell, D.B., Carter, L.M., Ostro, S.J., 2004. Science 304, 553] show hardly any hemispheric asymmetry and give a mean radar reflectivity several times lower than the reflectivity measured at 2.2 cm. These Iapetus results are understandable if ammonia is much less abundant on both sides within the upper one to several decimeters than at greater depths, and if the leading side's optically dark contaminant is present to depths of at least one to several decimeters. As argued by Lanzerotti et al. [Lanzerotti, L.J., Brown, W.L., Marcantonio, K.J., Johnson, R.E., 1984. Nature 312, 139-140], a combination of ion erosion and micrometeoroid gardening may have depleted ammonia from the surfaces of Saturn's icy satellites. Given the hypersensitivity of water ice's absorption length to ammonia concentration, an increase in ammonia with depth could allow efficient 2.2-cm scattering from within the top one to several decimeters while attenuating 13-cm echoes, which would require a six-fold thicker scattering layer. If so, we would expect each of the icy satellites' average radar albedos to be higher at 2.2 cm than at 13 cm, as is the case so far with Rhea [Black, G., Campbell, D., 2004. Bull. Am. Astron. Soc. 36, 1123] as well as Iapetus.