Diagnosing the root causes of cloud feedback in climate models and reasons for inter-model disagreement is a necessary first step in understanding their wide variation in climate sensitivities. Here we bring together two analysis techniques that illuminate complementary aspects of cloud feedback. The first quantifies feedbacks from changes in cloud amount, altitude, and optical depth, while the second separates feedbacks due to cloud property changes within specific cloud regimes from those due to regime occurrence frequency changes. We find that in the global mean, shortwave cloud feedback averaged across ten models comes solely from a positive within-regime cloud amount feedback countered slightly by a negative within-regime optical depth feedback. These within-regime feedbacks are highly uniform: In nearly all regimes, locations, and models, cloud amount decreases and cloud albedo increases with warming. In contrast, between-regime components vary widely across models but are very small on average. This component, however, is dominant in setting the geographic structure of the shortwave cloud feedback: Thicker, more extensive cloud types increase at the expense of thinner, less extensive cloud types in the extratropics, and vice versa at low latitudes. The prominent negative extratropical optical depth feedback has contributions from both within- and between-regime components, suggesting that thermodynamic processes affecting cloud properties as well as dynamical processes that favor thicker cloud regimes are important. The feedback breakdown presented herein may provide additional targets for observational constraints by isolating cloud property feedbacks within specific regimes without the obfuscating effects of changing dynamics that may differ across timescales.