Incidental imaging findings are a considerable health problem, because they generally result in low-value and potentially harmful care. Healthcare professionals struggle how to deal with them, because once detected they can usually not be ignored. In this opinion article, we first reflect on current practice, and then propose and discuss a new potential strategy to pre-emptively tackle incidental findings. The core principle of this concept is to keep the proverbial Pandora's box closed, i.e. to not visualize incidental findings, which can be achieved using deep learning algorithms. This concept may have profound implications for diagnostic imaging.