In this paper, we consider the forward problem in depolarization by optical systems. That is, we seek a compact parameterization that allows us to take an arbitrary "pure" optical system (namely one defined by a single Mueller-Jones matrix) and model all possible ways in which that system can depolarize light. We model this structure using compound unitary transformations and illustrate physical interpretation of the parameters involved by considering four examples, the family of depolarizers generated by scattering by random nonspherical particle clouds. We then turn attention to circular polarizers before considering all ways in which mirror reflection can cause depolarization. Finally, we consider a numerical example applied to a published Mueller matrix for backscatter from chiral turbid media.