SummaryA critical component of language is the ability to recombine sounds into larger structures. Although animals also reuse sound elements across call combinations to generate meaning, examples are generally limited to pairs of distinct elements, even when repertoires contain sufficient sounds to generate hundreds of combinations. This combinatoriality might be constrained by the perceptual-cognitive demands of disambiguating between complex sound sequences that share elements. We test this hypothesis by probing the capacity of chestnut-crowned babblers to process combinations of two versus three distinct acoustic elements. We found babblers responded quicker and for longer toward playbacks of recombined versus familiar bi-element sequences, but no evidence of differential responses toward playbacks of recombined versus familiar tri-element sequences, suggesting a cognitively prohibitive jump in processing demands. We propose that overcoming constraints in the ability to process increasingly complex combinatorial signals was necessary for the productive combinatoriality that is characteristic of language to emerge.