In this study we use large-eddy simulation to explore the factors controlling stratiform cloudiness in the downstream trades. We perform sensitivity experiments with different large-scale forcings, radiation specifications and domain sizes, which isolate the influence of convective deepening, moisture-radiation interactions and mesoscale organization, respectively. Across the simulations with different large-scale forcings, we find that the deepening of the cloud layer and the associated increase in precipitation strongly correlate with decreasing inversion strength and stratiform cloudiness. The relationship between cloud-layer depth and cloud amount is largely independent of the way a specific change in the large-scale forcing induces the deepening. The interaction of radiation with the domain-averaged humidity and cloud profile is necessary for stratiform cloudiness to form. Strong radiative cooling experienced by updraughts overshooting a strong inversion induces the formation of detrained stratiform layers, and strong long-wave cooling associated with the stratiform layers stabilizes the inversion. Interactive radiation is also important for exposing differences in shallow convection under different free-tropospheric humidities. A drier initial free troposphere leads to both increased cloud-layer and free-tropospheric radiative cooling and increased surface evaporation, which forces deeper convection and more precipitation compared to a moister initial free tro-posphere. The simulations with a drier initial free troposphere thus have weaker inversions and less stratiform cloud. The organization of convection into larger clusters in large-domain simulations increases precipitation and weakens the inversion compared to a simulation on a 16-fold smaller domain, which does not support con-vective organization. Organized updraught clusters carry more moisture and liquid to the inversion, so that the same amount of stratiform cloudiness forms, despite the inversion being weaker. The simulations presented here suggest that the deepening and organization of shallow convection plays an important role in regulating stratiform cloudiness and thus total cloud cover in the downstream trades. K E Y W O R D S large-eddy simulation, mesoscale organization, moisture-radiation interactions, shallow convection, stratiform cloudiness This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.