Key message : In tree communities, tree size inequality reduces productivity and interacts with tree shade tolerance to modulate stand productivity, with a higher productivity in stands where shade-intolerant species dominate shade-tolerant species in size.[br/] Context Positive diversity–productivity relationships have been reported in different plant communities, including tree communities. These effects may be strongly related to both structural diversity and functional diversity, but also to their interactions if there is a non-random distribution of species functional characteristics among canopy layers.[br/] Aims We explore the relative effects on forest productivity of tree species diversity, tree size inequality, and species shade tolerance diversity, as well as the effect of the distribution of tree shade tolerance in the canopy.[br/] Methods We used 11,054 mixed-species forest plots from the French Forest Inventory (IGN) distributed throughout France (2006–2011). We analyzed the effects of species richness, shade tolerance diversity, and height inequality on forest plot productivity, represented by basal area annual increment over a period of 5 years, while controlling for first-order structure characteristics (basal area and quadratic mean diameter) and environmental factors (soil water budget and sum of growing degree days). Using the covariance between tree height and shade tolerance in mixed species canopies, we also explored the effect of the distribution of species’ shade tolerance among canopy layers[br/] Results The results showed a positive effect of species richness (effect size, 0.02) and a negative effect of height inequality (− 0.05) on mixed-forest productivity. We also showed that a negative covariance between shade tolerance and height (e.g., higher proportion of shade-tolerant species in lower height classes) increased productivity (0.01). Shade tolerance diversity did not affect productivity.[br/] Conclusion In tree communities, as shown previously in monospecific forest stands, tree size inequality reduces productivity. This effect is modulated by the distribution of shade tolerance among canopy layers. Previous studies on species diversity effect have generally overlooked the importance of the size structure and the size hierarchy of functional characteristics. These effects are, however, crucial and deserve to be explored in greater detail.