Numerical simulations of the tropical mesoscales often exhibit a self-reinforcing feedback between cumulus convection and shallow circulations, which leads to the self-aggregation of large cloud structures. We investigate whether this basic feedback can be adequately captured by large-eddy simulations (LESs). To do so, we simulate the non-precipitating, cumulus-topped boundary layer of the canonical ‘BOMEX’; case over a range of numerical settings in two models. Since the energetic convective scales underpinning the self-aggregation are only slightly larger than typical LES grid spacings, aggregation timescales do not converge even at rather high resolutions (less than 100m). Therefore, high resolutions or improved unresolved scales models may be required to faithfully represent certain forms of trade-wind mesoscale cloud patterns and self-aggregating deep convection in large-eddy and cloud-resolving models, and to understand their significance relative to other processes that organise the tropical mesoscales.