We consider the automated generation of sonnets, a poetic form constrained according to meter, rhyme scheme, and length. Sonnets generally also use rhetorical figures, expressive language, and a consistent theme or narrative. Our constrained decoding approach allows for the generation of sonnets within preset poetic constraints, while using a relatively modest neural backbone. Human evaluation confirms that our approach produces Shakespearean sonnets that resemble human-authored sonnets, and which adhere to the genre’s defined constraints and contain lyrical language and literary devices.