Abstract. This paper contains a description of recent changes to the formulation and numerical implementation of the Quasi-Geostrophic Coupled Model (Q-GCM), which constitute a major update of the previous version of the model (Hogg et al., 2014). The Q-GCM model has been designed to provide an efficient numerical tool to study the dynamics of multi-scale mid-latitude air–sea interactions and their climatic impacts. The present additions/alterations were motivated by an inquiry into the dynamics of mesoscale ocean–atmosphere coupling and, in particular, by an apparent lack of Q-GCM atmosphere’s sensitivity to mesoscale sea-surface temperature (SST) anomalies, even at high (mesoscale) atmospheric resolutions, contrary to ample theoretical and observational evidence otherwise. Major modifications aimed at alleviating this problem include an improved radiative-convective scheme resulting in a more realistic model mean state and associated model parameters, a new formulation of entrainment in the atmosphere, which prompts more efficient communication between the atmospheric mixed layer and free troposphere, as well as an addition of temperature-dependent wind component in the atmospheric mixed layer and the resulting mesoscale feedbacks. The most drastic change is, however, the inclusion of moist dynamics in the model, which may be key to midlatitude ocean–atmosphere coupling. Accordingly, this version of the model is to be referred to as the MQ-GCM model. Overall, the MQ-GCM model is shown to exhibit a rich spectrum of behaviours reminiscent of many of the observed properties of the Earth’s climate system. It remains to be seen whether the added processes are able to affect in fundamental ways the simulated dynamics of the mid-latitude ocean–atmosphere system’s coupled decadal variability.