  The mapping of lexical meanings to wordforms is a major feature of natural
languages. While usage pressures might assign short words to frequent meanings
(Zipf's law of abbreviation), the need for a productive and open-ended
vocabulary, local constraints on sequences of symbols, and various other
factors all shape the lexicons of the world's languages. Despite their
importance in shaping lexical structure, the relative contributions of these
factors have not been fully quantified. Taking a coding-theoretic view of the
lexicon and making use of a novel generative statistical model, we define upper
bounds for the compressibility of the lexicon under various constraints.
Examining corpora from 7 typologically diverse languages, we use those upper
bounds to quantify the lexicon's optimality and to explore the relative costs
of major constraints on natural codes. We find that (compositional) morphology
and graphotactics can sufficiently account for most of the complexity of
natural codes -- as measured by code length.
