Context Allometric equations describing the relationships between tree height (H) and breast height diameter (D) should be both statistically efficient and biologically relevant. Aims To determine whether selected allometric equations can meet established criteria for both efficiency and relevance. Methods Nine equations were compared to define the H–D relationships of 1122 individuals and 18 species from an Australian subtropical rainforest. Key results Three-parameter asymptotic equations described initial slope (a), curvature (b), and asymptotic height (Ha). Each equation was evaluated for precision (root mean square error, RMSE) and bias in H estimates, and ease of interpretation of function parameters. For both individual species and all stems, a non-rectangular hyperbola (NRH) provided almost equally high precision and low bias as did the statistically most parsimonious generalised Michaelis–Menten function, plus linear parameter values easily relatable to tree structural and functional attributes. The value of NRH a increased linearly with wood density for canopy species, but not for understorey and subdominant species, whereas the value of NRH b decreased as Ha increased from understorey to canopy species. Conclusions Species within understorey, subdominant, and canopy structural groups shared similar ranges of parameter values within groups that reflect both intrinsic architectural and developmental patterns, and environmental limitations to Ha. Implications The NRH can be used to visualise both early and later tree development stages and differences among the growth patterns of species occupying different positions within a forest.