Based on constraint optimization techniques, an architecture for robust parsing of natural language utterances has been developed. The resulting system is able to combine possibly contradicting evidence from a variety of information sources, using a plausibility-based arbitration procedure to derive fairly rich structural representations, comprising aspects of syntax, semantics and other description levels of language. The results of a series of experiments are reported which demonstrate the high potential for robust behaviour with respect to ungrammaticality, incomplete utterances, and temporal pressure.