Existing spoken dialogue systems are typically not designed to provide natural interaction since they impose a strict turn-taking regime in which a dialogue consists of interleaved system and user turns. To allow more responsive and natural interaction, this paper describes a system in which turn-taking decisions are taken at a more fine-grained micro-turn level. A decision-theoretic approach is then applied to optimise turn-taking control. Inverse reinforcement learning is used to capture the complex but natural behaviours from human-human dialogues and optimise interaction without specifying a reward function manually. Using a corpus of human-human interaction, experiments show that IRL is able to learn an effective reward function which outperforms a comparable handcrafted policy.