What factors determine the extent of evolutionary diversification remains a major question in evolutionary biology. Behavioural changes have long been suggested to be a major driver of phenotypic diversification by exposing animals to new selective pressures. Nevertheless, the role of behaviour in evolution remains controversial because behavioural changes can also retard evolutionary change by hiding genetic variation from selection. In the present study, we apply recently implemented Ornstein-Uhlenbeck evolutionary models to show that behavioural changes led to associated evolutionary responses in functionally relevant morphological traits of pigeons and doves (Columbiformes). Specifically, changes from terrestrial to arboreal foraging behaviour reconstructed in a set of phylogenies brought associated shorter tarsi and longer tails, consistent with functional predictions. Interestingly, the transition to arboreality accelerated the rates of evolutionary divergence, leading to an increased morphological specialization that seems to have subsequently constrained reversals to terrestrial foraging. Altogether, our results support the view that behaviour may drive evolutionary diversification, but they also highlight that its evolutionary consequences largely depend on the limits imposed by the functional demands of the adaptive zone.