Artificial light at night has affected most of the natural nocturnal landscapes worldwide and the subsequent light pollution has diverse effects on flora, fauna and human well-being. To evaluate the environmental impacts of light pollution, it is crucial to understand both the natural and artificial components of light at night under all weather conditions. The night sky brightness for clear skies is relatively well understood and a reference point for a lower limit is defined. However, no such reference point exists for cloudy skies. While some studies have examined the brightening of the night sky by clouds in urban areas, the published data on the (natural) darkening by clouds is very sparse. Knowledge of reference points for the illumination of natural nocturnal environments however, is essential for experimental design and ecological modeling to assess the impacts of light pollution. Here we use differential all-sky photometry with a commercial digital camera to investigate how clouds darken sky brightness at two rural sites. The spatially resolved data enables us to identify and study the nearly unpolluted parts of the sky and to set an upper limit on ground illumination for overcast nights at sites without light pollution.