Cook and Franklin (1970, Icarus 13, 282) consider Iapetus originally to have been coated with about a meter of ice. They suggest that Iapetus' orbital velocity about Saturn has caused an asymmetric erosion of this ice layer which has now nearly laid bare its "leading" hemisphere, but not as yet the entire "trailing" hemisphere. Rather than an erosion process which operates more actively on the leading side, this paper considers an ice deposition mechanism operating more actively on the trailing side. The two main assumptions used are (1) that there are more icy than rocky meteoroids in Saturn's environment, and (2) that some portion of each icy meteoroid will stick to a surface at collision velocities less than 2.4kmsec -1, but will completely vaporize itself at greater velocities. A meteoroid can have the minimum collision velocity of about 1.7kmsec -1 with Iapetus only if their velocity vectors are nearly parallel, and under these conditions such collisions would tend to be with the trailing hemisphere. Collisions with the leading hemisphere will tend to be at a much higher velocity.