This paper describes a system that leads us to believe in the feasibility of constructing natural spoken dialogue systems in task-oriented domains. It specifically addresses the issue of robust interpretation of speech in the presence of recognition errors. Robustness is achieved by a combination of statistical error post-correction, syntactically- and semantically-driven robust parsing, and extensive use of the dialogue context. We present an evaluation of the system using time-to-completion and the quality of the final solution that suggests that most native speakers of English can use the system successfully with virtually no training. .