Unrehearsed spoken language often contains disfluencies. In order to correctly interpret a spoken utterance, any such disfluencies must be identified and removed or otherwise dealt with. Operating on transcripts of speech which contain disfluencies, our particular focus here is the identification and correction of speech repairs using a noisy channel model. Our aim is to develop a high-accuracy mechanism that can identify speech repairs in an incremental fashion, as the utterance is processed word-by-word. We also address the issue of the evaluation of such incremental systems. We propose a novel approach to evaluation, which evaluates performance in detecting and correcting disfluencies incrementally, rather than only assessing performance once the processing of an utterance is complete. This demonstrates some shortcomings in our basic incremental model, and so we then demonstrate a technique that improves performance on the detection of disfluencies as they happen.