A variety of proxies have been developed to reconstruct paleo-CO₂ from fossil leaves. These proxies rely on some combination of stomatal morphology, leaf δ¹³C, and leaf gas exchange. A common conceptual framework for evaluating these proxies is lacking, which has hampered efforts for inter-comparison. Here we develop such a framework, based on the underlying physics and biochemistry. From this conceptual framework, we find that the more extensively parameterised proxies, such as the optimisation model, are likely to be the most robust. The simpler proxies, such as the stomatal ratio model, tend to under-predict CO₂, especially in warm (>15^°C) and moist (>50% humidity) environments. This identification of a structural under-prediction may help to explain the common observation that the simpler proxies often produce estimates of paleo-CO₂ that are lower than those from the more complex proxies and other, non-leaf-based CO₂ proxies. The use of extensively parameterised models is not always possible, depending on the preservation state of the fossils and the state of knowledge about the fossil's nearest living relative. With this caveat in mind, our analysis highlights the value of using the most complex leaf-based model as possible.