Several phenomena are neglected in the original "Berg model" in order to provide a simple model of the reactive sputtering process. There exist situations, however, where this simplified treatment limits the usefulness of the model. To partly correct for this, we introduce an upgraded version of the basic model. We abandon the simplifying assumption that compound targets are sputter eroded as molecules. Instead, the molecule is split and individual atoms will be sputter ejected. Also, the effect of ionized reactive gas atoms implanted into the target will be considered. We outline how to modify the original model to include these effects. Still, the mathematical treatment is maintained simple so that the new model may serve as an easy-to-understand tutorial of the complex mechanisms of reactive sputtering. (C) 2014 Elsevier B.V. All rights reserved.