Tropical multi-scale convective organization of the super-cluster kind and convectively coupled gravity waves are investigated by both two and three-dimensional cloud-system-resolving simulations. The experimental setup includes a constant-temperature ocean surface, constant and horizontally-uniform radiative cooling in the troposphere, and a uniform easterly background wind. The objective of this study is to quantify the impacts of dimensionality on the simulated large-scale convective patterns and associated gravity waves. Eastward propagating large-scale coherent precipitating convection occurs regardless of the spatial dimension. The convective organization has a horizontal wavenumber-one structure in the computational domain and travels at about 13-17 m s(-1) relative to the ground, equivalent to 19-23 m s(-1) relative to the environmental flow. However, the convectively-induced wave signature is much weaker in three dimensions than in two dimensions, as well as a faster translation and a smaller tilt of the vertical. Moreover, a two-dimensional framework generates additional organizational modes compared to the three-dimensional results, including a fast westward-moving system with a mean-flow-relative speed comparable to the eastward-moving wavenumber-1 counterpart and the quasi-stationary (relative to the background flow) higher wavenumber precipitating system. This does not necessarily imply that these additional modes are artifacts of two dimensionality.