This paper describes a fully incremental dialogue system that can engage in dialogues in a simple domain, number dictation. Because it uses incremental speech recognition and prosodic analysis, the system can give rapid feedback as the user is speaking, with a very short latency of around 200ms. Because it uses incremental speech synthesis and self-monitoring, the system can react to feedback from the user as the system is speaking. A comparative evaluation shows that naïve users preferred this system over a non-incremental version, and that it was perceived as more human-like.