This paper investigates the temporal properties of tropical precipitation in the Canadian Centre for Climate Modelling and Analysis (CCCma) third-generation atmospheric general circulation model (AGCM3). AGCM3 employs the penetrative mass-flux (PMF) scheme of Zhang and McFarlane (ZM) for the parameterization of deep cumulus convection. It is found that the temporal variability of the ZM scheme is sensitive to a number of its internal parameters as well to the use of a prognostic, rather than diagnostic, closure condition for the cloud-base mass flux. Sensitivity experiments suggest that the ZM scheme can produce realistic amounts of variability when compared to direct radar observations of deep cumulus convection in the Tropics. A central finding of this study is that the resolved large-scale stratiform precipitation (LSP) in the model can participate in the modeling of deep latent heating and so compete with the ZM scheme in the Tropics. In modeling deep latent heating the LSP is found to mimic the behavior of a moist-convective adjustment scheme. In AGCM3 it is found that typical parameter settings of the ZM scheme place it in a regime in which the temporal variability of tropical precipitation is dominated by this behavior of the LSP, while the temporal mean is dominated by the ZM scheme. In such circumstances it is the LSP, and not the ZM scheme, that provides the primary source of resolved tropical Kelvin and mixed Rossby‐gravity waves in the GCM. Such competition between LSP and the parameterization of deep convection appears to be active in other modeling studies. Consequently, it has the potential to complicate efforts to understand the nature of resolved tropical waves in GCMs and their role in the forcing of the quasi-biennial and semiannual oscillations.