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Broad-coverage grammars tend to be highly ambiguous. When such grammars are used in a restricted domain, it may be desirable to specialize them, in effect trading some coverage for a reduction in ambiguity. Grammar specialization is here given a novel formulation as an optimization problem, in which the search is guided by a global measure combining coverage, ambiguity and grammar size. The method, applicable to any unification grammar with a phrase-structure backbone, is shown to be effective in specializing a broad-coverage LFG for French.