  We address the deformation quantization of generally parametrized systems
displaying a natural time variable. The purpose of this exercise is twofold:
first, to illustrate through a pedagogical example the potential of quantum
phase space methods in the context of constrained systems and particularly of
generally covariant systems. Second, to show that a causal representation for
quantum phase space quasidistributions can be easily achieved through general
parametrization. This result is succinctly discussed.
