The paper argues that syntax is motivated by the need to avoid combinatorial search in parsing and semantic ambiguity in interpretation. It reports on a case study for the emergence and sharing of first-order phrase structures in a population of agents playing language games. First-order phrase structures combine words into phrases but do not yet generalise to hierarchical or recursive phrases. To study why human languages exhibit phrase structure, a series of strategies for creating and sharing linguistic conventions are examined, starting from a lexical strategy without syntax and then studying the use of groups, n-grams and patterns. Each time we show in which way a strategy improves on the computational complexity of the previous on.