The goals of this work were: (1) to improve the University of Washington shallow cumulus parameterization, first developed by the PI's group for better simulation of shallow oceanic cumulus convection in the MM5 mesoscale model (Bretherton et al., 2004, Mon. Wea. Rev.); (2) to explore its applicability to deep (precipitating) cumulus convection; and (3) to explore fundamental physical issues related to this cumulus parameterization.