Combinatoriality---the recombination of a small set of basic forms to create an infinite number of meaningful units---has long been seen as a core design feature of language, but its origins remain uncertain. Two hypotheses have been suggested. The first is that combinatoriality is a necessary solution to the problem of conveying a large number of meanings; the sec- ond is that it arises as a consequence of conventionalisation. We tested these hypotheses in an experimental-semiotics study. Our results supported the hypothesis based on conventionali- sation but offered little support for the hypothesis based on the number of meanings.