Deep convective storms assume many intensities, sizes and morphologies in Earth’s atmosphere, reflecting varying balances of the competing forces that arise in the diverse atmospheric conditions that promote and support such storms. The understanding of how these forces compete with each other lends itself only with great difficulty to observational study, but much more easily to idealized parameter space studies using numerical models. A parameter space study was recently designed and executed using an eight-dimensional framework, with 2-h experiments run using all possible combinations of reasonably chosen high and low values of the eight independent parameters. The basic parameters are those needed to build an idealized vertical profile of temperature, moisture and wind: bulk convective available potential energy (CAPE), radius of an assumed semicircular hodograph, shape of the buoyancy profile, shape of the shear profile, lifting condensation level, level of free convection, cloud-base temperature (roughly equivalent to total precipitable water), and free tropospheric relative humidity. Each of the parameters is found to exert noteworthy independent impacts on the intensity and morphology of the convection, with drastic differences in updraft overturning efficiency (the ratio of simulated peak updraft speed to that predicted from pseudoadiabatic parcel theory), updraft rotation, updraft steadiness and precipitation efficiency. Storm rotational efficiency relative to ambient vertical shear, and its steadiness, may also be examined. Results will be shown that demonstrate the strongly patterned convective response within this large parameter space, for both updraft overturning and rotational efficiency and their temporal steadiness. For example, in experiments having CAPE = 2000 J/kg, peak updraft efficiency reaches 94% in some cases, while in others with unfavorable combinations of parameters, that peak is less than 20%. While the eight basic parameters used in this study cover most of the variability of the vertical meteorological structure of the convective atmosphere, the framework can easily be expanded by adding new dimensions to deal with other physical effects, such as varying types and distributions of aerosols and other tracers that influence atmospheric chemistry.