Communications channels which have unknown, time-varying parameters frequently arise in practice. In certain instances, such as in jammed channels, the duration of memory is not known, and memory is not known, and may also be time-varying. Most models of jammed channels which appear in the literature, however, assume that the jammer is restricted to memoryless jamming techniques; this restriction is usually rationalized by arguing that the use of interleaving by the transmitter is sufficient to destroy channel memory. In this paper, the ability of interleaving to eliminate channel memory is investigated by comparing the capacity of jammed channels with memory and random interleaving with that of similar memoryless, jammed channels.