Poetry is defined by structure, and structure is represented in grammar. But in the purely descriptive view, a grammar is essentially the reification of a particular analytic process: while interesting and useful in many scenarios, it has limited ability to directly add insight. We are considering the use of "Adaptor Grammars", a non-parametric extension of context-free grammars, to minimally specify the structure that (basically) all readers agree on, and allow the machine learning process to choose additional structure based on its information-theoretic objectives. If and how this structure aligns with human intuitions (about e.g. rhyme, scansion) is the underlying question.