 Within the environmental decoherence literature, models tend to be formulated in terms of master equations for the evolution of the density operator describing the system. As a consequence of decoherence this very quickly becomes (at least approximately) diagonal in the basis of preferred states (whether discrete or continuous). Thus, the master equation for the density operator for the system is essentially equivalent to an evolution equation for the probability distribution over the preferred states. In models where coherent states are preferred, one can then compare this to the Liouville evolution of probability distributions over classical phase space, and in fact one obtains extremely good quantitative agreement. 