While a taxonomic approach to maximizing stimulus-response (S-R) compatibility is frequently applied to improve system design, it can fall short because no taxonomy is ever complete. A model-based approach may uncover additional system flaws and can help us to understand the sources of S-R compatibility. A satisfactory model is defined as one that is acceptable on two vital dimensions: It is both theoretically correct and easy for system designers to use. This article revisits a satisfactory hierarchical model of S-R compatibility proposed by Kantowitz, Triggs and Barnes [1]. The model presupposes a recursive combination of frames, rules, and response tendencies to explain how actions are derived from stimuli mapped to responses. Several recent studies of S-R compatibility were selected to exercise the model. By using frames, rules, and response tendencies the hierarchical model generated explanations that are consistent with these empirical results. Control-display compatibility is maximized when frames, rules, and response tendencies are aligned.