The model of Mekler and Podolak (1994) for the growth of small ice grains in the nebula is extended to allow for the presence of additional absorbers. The properties of these "dirty" grains are explored. The presence of an additional absorber allows for several interesting effects. One is the possibility of having grains with a layer of amorphous ice surrounded by a layer of crystalline ice. Another effect is a limit to the size of grains in certain regions of the nebula. The rate of growth of these grains is also discussed.