In this paper, we extend the work of Neumann et al. [NNSK99] and Stark et al. [SAS05] to a pair of 4D BRDF parameterizations with explicit changes of variables. We detail their mathematical properties and relationships to the commonly-used halfway/difference parametrization, and discuss their benefits and drawbacks using a few an- alytical test functions and measured BRDFs. Our preliminary study suggests that the alternative parametrization inspired by Stark et al. [SAS05] is superior, and should thus be considered in future work involving BRDFs.