<p><strong>Abstract.</strong> Leaf gas-exchange models show considerable promise as paleo-CO₂ proxies. They are largely mechanistic in nature, provide well-constrained estimates even when CO₂ is high, and can be applied to most subaerial, stomata-bearing leaves from C₃ taxa, regardless of age or taxonomy. Here we place additional observational and theoretical constraints on one of these models, the <q>Franks</q> model. In order to gauge the model's general

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... cy in a way that is appropriate for fossil studies, we estimated CO₂ from 40 species of extant angiosperms, conifers, and ferns based only on measurements that can be made directly from fossils (leaf δ¹³C and stomatal density and size) and a limited sample size (1&amp;ndash;3 leaves per species). The mean error rate is 28 %, which is similar to or better than the accuracy of other leading paleo-CO₂ proxies. We find that leaf temperature and photorespiration do not strongly affect estimated CO₂, although more work is warranted on the possible influence of O₂ concentration on photorespiration. Leaves from the lowermost 1&amp;ndash;2 m of closed-canopy forests should not be used because the local air δ¹³C value is lower than the global well-mixed value. Such leaves are not common in the fossil record, but can be identified by morphological and isotopic means.</p>