A fundamental yet outstanding question about deep cumulus convection regards how convective updrafts, downdrafts, and surface-based cold pools are inter-related within organized storms, and how these three convective components are modulated by external and internal factors. The research begins to address this question through a series of idealized simulations using environments described by analytic thermodynamic and wind profiles. We find that environmental vertical wind shear exerts a significant control on updraft width, especially when the shear is characterized by a curved hodograph; our analyses of linear and nonlinear dynamic pressure forcing readily explain this control. In agreement with physical arguments, increases in updraft width are accompanied by corresponding increases in downdraft width, cold-pool depth, and cold-pool areal extent. These characteristics also are controlled by the environmental convective available potential energy (CAPE), but to a lesser degree. Such environmental sensitivities are compelling in light of climate-model projections of increased CAPE and decreased vertical wind shear under anthropogenic climate change. Indeed, this has motivated quantifications of convective components within midlatitude thunderstorms simulated via the pseudo-global warming (PGW) methodology. Our PGW results will be described, as will the implications of the more general results on the parameterized representation of deep cumulus convective in weather and climate models.