Recent work suggests that variation in online language production reflects the fact that speech is information-theoretically efficient for communication. We apply this idea to studying the offline, structural properties of language, asking whether lexical properties may similarly reflect communicative pressures. We present evidence for the Communicative Lexicon Hypothesis (CLH): human lexical systems are efficient solutions to the problem of communication for the human language processor. While the relationship between sounds and meanings may be arbitrary, pressure for concise and error-correcting communication --- within the constraints imposed by human articulatory, perceptual and cognitive abilities --- has influenced which sets of phonological forms have emerged in the lexicons of human languages. We present two tests of the CLH: first, we show that word lengths are better predicted by a word's average predictability in context than its overall frequency. Second, we show that salient (lexically stressed) parts of words are more informative about a word's identity, in English, German, Dutch, Hawai'ian, and Spanish.