This paper presents a model of incremental speech generation in practical conversational systems. The model allows a conversational system to incrementally interpret spoken input, while simultaneously planning, realising and self-monitoring the system response. If these processes are time consuming and result in a response delay, the system can automatically produce hesitations to retain the floor. While speaking, the system utilises hidden and overt self-corrections to accommodate revisions in the system. The model has been implemented in a general dialogue system framework. Using this framework, we have implemented a conversational game application. A Wizard-of-Oz experiment is presented, where the automatic speech recognizer is replaced by a Wizard who transcribes the spoken input. In this setting, the incremental model allows the system to start speaking while the user's utterance is being transcribed. In comparison to a non-incremental version of the same system, the incremental version has a shorter response time and is perceived as more efficient by the users.