Sensitivity of model results to spatial and temporal resolution is one of the key topics in numerical modeling. In this presentation, we will show that subtropical marine stratocumulus clouds simulated by version 1 of the E3SM atmosphere model (EAMv1) are sensitive to the model's time step size, primarily due to the numerical coupling between the stratiform cloud parameterizations and the rest of the model. We will provide an in-depth explanation for the observed sensitivity both from a numerical perspective and by analyzing the physical processes involved in the formation and maintenance of the stratocumulus clouds. We will also present a revised coupling that substantially reduces this time-step sensitivity and hence can help provide more consistent results from simulations conducted with different resolutions.