Language evolution can be viewed from two viewpoints: the development of a communicative system and the biological adaptations necessary for producing and perceiving said system. The communicative-system vantage point has enjoyed a wealth of mathematical models based on simple distributional properties of language, often formulated as empirical laws. However, be- yond vague psychological notions of “least effort”, no principled explanation has been proposed for the existence and success of such laws. Meanwhile, psychological and neurobiological mod- els have focused largely on the computational constraints presented by incremental, real-time processing. In the following, we show that information-theoretic entropy underpins successful models of both types and provides a more principled motivation for Zipf’s Law