Acoustic signal complexity varies widely in animals from single notes to highly sophisticated vocal displays. In birds, vocal complexity can evolve as an honest signal of individual quality driven by sexual selection. However, this hypothesis is rarely explored in conjunction with alternative drivers, including competition for ecological resources (social selection) and intra-group communication, both of which may favour increased signal complexity. Using Bayesian phylogenetic models, we test whether these alternative mechanisms predict the complexity of innate songs in 1,288 species of suboscine passerine birds, while accounting for ecological constraints on sound production, transmission and detection. We found that overall song complexity was reduced by sexual selection (estimated from mating systems), and declined with body size and vegetation density. Conversely, note count and song length increased in territorial species, particularly those using song to defend year-round territories during the non-breeding season. These findings challenge the common assumption that sexual selection is the main driver of increased signal complexity, and highlight the role of social selection via territorial competition as a factor increasing the temporal complexity of songs. Our results suggest that signal complexity depends on social, cultural and ecological contexts, reflecting a combination of multiple inter-related drivers and constraints.