Simulations of baroclinic cyclones often cannot resolve moist convection but resort to convective parametrization. An exception is the hypohydrostatic rescaling, which in principle can be used to better represent convection with no increase in computational cost. The rescaling is studied in the context of a quasi-steady, convectively active, baroclinic cyclone. This is a novel framework with advantages due to the unambiguous time-mean structure. The rescaling is evaluated against high-resolution solutions up to a 5-km grid spacing. A theoretical scaling combining convective-scale dynamics and synoptic-scale energy balance is derived and verified by the simulations. It predicts the insensitivity of the large-scale flow to resolution and moderate rescaling, and a weak bias in the cyclone intensity under very large rescaling. The theory yields a threshold for the rescaling factor that avoids large-scale biases. Below the threshold, the rescaling can be used to control resolution errors at the convective scale, such as the distribution of extreme precipitation rates.