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We present a general information-theoretic argument that all efficient communication systems will be ambiguous, assuming that context is informative about meaning. We also argue that ambiguity allows for greater ease of processing by permitting efficient linguistic units to be re-used. We test predictions of this theory in English, German, and Dutch. Our results and theoretical analysis suggest that ambiguity is a functional property of language that allows for greater communicative efficiency. This provides theoretical and empirical arguments against recent suggestions that core features of linguistic systems are not designed for communication.