Six Single-Column Model (SCM) versions of climate models are evaluated on the basis of their representation of the dependence of the stratocumulus-topped boundary layer regime on the free tropospheric thermodynamic conditions. The study includes two idealized experiments corresponding to the present-day and future climate conditions in order to estimate the low-cloud feedback. Large-Eddy Simulation (LES) results are used as a benchmark and GCM outputs are included to assess whether the SCM results are representative of their 3D counterparts. The SCMs present a variety of dependencies of the cloud regime on the free tropospheric conditions but, at the same time, several common biases. For all the SCMs the stratocumulus-topped boundary layer is too shallow, too cool and too moist as compared to the LES results. Moreover, they present a lack of clouds and liquid water and an excess of precipitation. The disagreement among SCMs is even more distinct for the response to a climate perturbation. Even though the overall feedback is positive for all the models, in line with the LES results, the SCMs show a rather noisy behaviour, which depends irregularly on the free tropospheric conditions. Finally, the comparison with the host GCM outputs demonstrates that the considered approach is promising but needs to be further generalized for the SCMs to fully capture the behaviour of their 3D counterparts. This article is protected by copyright. All rights reserved.