We have applied evolutionary comparative methods to control for phylogenetic relationships between species in order to determine if three recently proposed relationships between leaf structure and function are upheld, using a large database comprising a wide range of species from tropical and temperate ecosystems. The three hypotheses tested were: (i) leaf thickness is positively correlated with total stomatal density (adaxial and abaxial values summed); (ii) amphistomatous leaves (stomata present on the upper and lower surfaces) have a higher maximum stomatal conductance than hypostomatous (stomata on the lower surface only) leaves, and (iii) changes in the stomatal density on upper and lower leaf surfaces are regulated in a compensatory manner. The results showed that, contrary to several mathematical modelling studies, thicker leaves were not associated with more stomata either in species from lowland tropical rain forests or from central Europe. Amphistomatous leaves had a higher maximum stomatal conductance, indicating that one aspect of previous modelling work is correctly underpinned after accounting for relatedness. Finally, we found no evidence that the stomatal densities on upper and tower leaf surfaces are closely regulated. These three physiological traits are discussed with reference both to the modelling of leaf gas exchange and to plant function in relation to microclimate.