We present an incremental dependency parsing model that jointly performs disfluency detection. The model handles speech repairs using a novel non-monotonic transition system, and includes several novel classes of features. For comparison, we evaluated two pipeline systems, using state-of-the-art disfluency detectors. The joint model performed better on both tasks, with a parse accuracy of 90.5% and 84.0% accuracy at disfluency detection. The model runs in expected linear time, and processes over 550 tokens a second.