The effect of anthropogenic aerosol on the reflectivity of stratocumulus cloud decks through changes in cloud amount is a major uncertainty in climate projections. The focus of this study is the frequently occurring non-precipitating stratocumulus. In this regime, cloud amount can decrease through aerosol-enhanced cloud-top mixing. The climatological relevance of this effect is debated because ship exhaust does not appear to generate significant change in the amount of these clouds. Through a novel analysis of detailed numerical simulations in comparison to satellite data, we show that results from ship-track studies cannot be generalized to estimate the climatological forcing of anthropogenic aerosol. We specifically find that the ship-track-derived sensitivity of the radiative effect of non-precipitating stratocumulus to aerosol overestimates their cooling effect by up to 200%. This offsetting warming effect needs to be taken into account if we are to constrain the aerosol-cloud radiative forcing of stratocumulus.