An intercomparison study for single-column models (SCMs) of the diurnal cycle of shallow cumulus convection is reported. The case, based on measurements at the Atmospheric Radiation Measurement program Southern Great Plains site on 21 June 1997, has been used in a large-eddy simulation intercomparison study before. Results of the SCMs reveal the following general deficiencies: too large values of cloud cover and Cloud liquid water, unrealistic thermodynamic profiles, and high amounts of numerical noise. Results are also strongly dependent on vertical resolution. These results are analysed in terms of the behaviour of the different parametrization schemes involved: the convection scheme, the turbulence scheme, and the cloud scheme. In general the behaviour of the SCMs can be grouped in two different classes: one class with too strong mixing by the turbulence scheme, the other class with too strong activity by the convection scheme. The coupling between (subcloud) turbulence and the convection scheme plays a crucial role. Finally, (in part) motivated by these results several models have been successfully updated with new parametrization schemes and/or their present schemes have been successfully modified.