It has been suggested that diverse forests utilize canopy space more efficiently than species‐poor ones, as mixing species with complementary architectural and physiological traits allows trees to pack more densely. However, whether positive canopy packing–diversity relationships are a general feature of forests remains unclear. Using crown allometric data collected for 12 939 trees from permanent forest plots across Europe, we test (i) whether diversity promotes canopy packing across forest types and (ii) whether increased canopy packing occurs primarily through vertical stratification of tree crowns or as a result of intraspecific plasticity in crown morphology. We found that canopy packing efficiency increased markedly in response to species richness across a range of forest types and species combinations. Positive canopy packing–diversity relationships were primarily driven by the fact that trees growing in mixture had sizably larger crowns (38% on average) than those in monoculture. The ability of trees to plastically adapt the shape and size of their crowns in response to changes in local competitive environment is critical in allowing mixed‐species forests to optimize the use of canopy space. By promoting the development of denser and more structurally complex canopies, species mixing can strongly impact nutrient cycling and storage in forest ecosystems.