Taxonomies are vehicles for thinking about what’s possible, for identifying unconsidered options, as well as for establishing formal relations between entities. We identify several shortcomings in 10 existing taxonomies for interpretability methods for explainable artificial intelligence (XAI), focusing on methods for deep neural networks. The shortcomings include redundancies, incompleteness, and inconsistencies. We design a new taxonomy based on two orthogonal dimensions and show how it can be used to derive results about entire classes of interpretability methods for deep neural networks.