Second-order expansion of the aspect ratio gives rise to simple equations with a quasi-hydrostatic approximation that perform far better than the classical hydrostatic system in the simulation of moist convection in a mesoscale model. It also suggests that a simple modification to this system may extend the validity of schemes for aspect ratios larger than 1. Abstract Second-order expansion of the aspect ratio gives rise to simple equations with a quasi-hydrostatic approximation that perform far better than the classical hydrostatic system in the simulation of moist convection in a mesoscale model. It also suggests that a simple modification to this system may extend the validity of schemes for aspect ratios larger than 1.