We present a first step towards a model of speech production for incremental dialogue systems. The model allows a dialogue system to incrementally interpret spoken input, while simultaneously planning, realising and self-monitoring the system response. The model has been implemented in a general dialogue system framework. Using this framework, we have implemented a specific application and tested it in a Wizard-of-oz setting, comparing it with a non-incremental version of the same system. The results show that the incremental version, while producing longer utterances, has a shorter response time and is perceived as more efficient by the users.