Summary Amazonian droughts are predicted to become increasingly frequent and intense, and the vulnerability of Amazonian trees has become increasingly documented. However, little is known about the physiological mechanisms and the diversity of drought tolerance of tropical trees due to the lack of quantitative measurements. Leaf water potential at wilting or turgor loss point (πtlp) is a determinant of the tolerance of leaves to drought stress and contributes to plant‐level physiological drought tolerance. Recently, it has been demonstrated that leaf osmotic water potential at full hydration (πo) is tightly correlated with πtlp. Estimating πtlp from osmometer measurements of πo is much faster than the standard pressure–volume curve approach of πtlp determination. We used this technique to estimate πtlp for 165 trees of 71 species, at three sites within forests in French Guiana. Our data set represents a significant increase in available data for this trait for tropical tree species. Tropical trees showed a wider range of drought tolerance than previously found in the literature, πtlp ranging from −1·4 to −3·2 MPa. This range likely corresponds in part to adaptation and acclimation to occasionally extreme droughts during the dry season. Leaf‐level drought tolerance varied across species, in agreement with the available published observations of species variation in drought‐induced mortality. On average, species with a more negative πtlp (i.e. with greater leaf‐level drought tolerance) occurred less frequently across the region than drought‐sensitive species. Across individuals, πtlp correlated positively but weakly with leaf toughness (R2 = 0·22, P = 0·04) and leaf thickness (R2 = 0·03, P = 0·03). No correlation was detected with other functional traits (leaf mass per area, leaf area, nitrogen or carbon concentrations, carbon isotope ratio, sapwood density or bark thickness). The variability in πtlp among species indicates a potential for highly diverse species responses to drought within given forest communities. Given the weak correlations between πtlp and traditionally measured plant functional traits, vegetation models seeking to predict forest response to drought should integrate improved quantification of comparative drought tolerance among tree species.