Digitalization as a technological phenomenon of the 21st century has the power to redeem most environmental sins of our 20th century technology. This seems to be a popular belief shining through many of the optimistic media reports on digitalization. We believe, however, that this mindset is far too simplistic and counterproductive. The many indirect economic and social effects of digitalization, which turn efficiency gains into increased resource consumption, are often ignored. We discuss these countereffects in general, as well as their digitalization-specific flavor (i.e., the digital rebound). We give examples of digital rebound, and also analyze several conditions that seem to lead to its eschewal. Altogether, we try to make the case for a faithful consideration of the rebound effects of digitalization.