An idealized case-study has been designed to investigate the modelling of the diurnal cycle of deep precipitating convection over land. A simulation of this case was performed by seven single-column models (SCMs) and three cloud-resolving models (CRMs). Within this framework, a quick onset of convective rainfall is found in most SCMs, consistent with the results from general-circulation models. In contrast, CRMs do not predict rainfall before noon. A joint analysis of the results provided by both types of model indicates that convection occurs too early in most SCMs, due to crude triggering criteria and quick onsets of convective precipitation. In the CRMs, the first clouds appear before noon, but surface rainfall is delayed by a few hours to several hours. This intermediate stage, missing in all SCMs except for one, is characterized by a gradual moistening of the free troposphere and an increase of cloud-top height. Later on, convective downdraughts efficiently cool and dry the boundary layer (BL) in the CRMs. This feature is also absent in most SCMs, which tend to adjust towards more unstable states, with moister (and often more cloudy) low levels and a drier free atmosphere. This common behaviour of most SCMs with respect to deep moist convective processes occurs even though each SCM simulates a different diurnal cycle of the BL and atmospheric stability. The scatter among the SCMs results from the wide variety of representations of BL turbulence and moist convection in these models. Greater consistency is found among the CRMs, despite some differences in their representation of the daytime BL growth, which are linked to their parametrizations of BL turbulence and/or resolution.