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This paper addresses two problems that commonly arise in parsing with precision-oriented, rule-based models of grammar: lack of speed and lack of robustness. First, we show how we can reduce parsing times by restricting the number of tasks the parser will carry out, based on a generative model of rule applications. Second, we show that a combination of search space restriction and radically overgenerating robustness rules lead to a more robust parser, with only a small penalty in precision. Applying both the robustness rules and a fragment fallback strategy showed better recall than just giving fragment analyses, with equal precision. Results are reported on a medium-sized HPSG grammar for German.