Poems are treated by translators as hierarchical multilevel systems. Here we propose the notion of “multilevel poetry translation” to characterize such cases of poetry translation in terms of selection and rebuilding of a multilevel system of constraints across languages. Different levels of a poem correspond to different sets of components that asymmetrically constrain each other (e. g., grammar, lexicon, syntactic construction, prosody, rhythm, typography, etc.). This perspective allows a poem to be approached as a thinking-tool: an “experimental lab” which submits language to unusual conditions and provides a scenario to observe the emergence of new patterns of semiotic behaviour as a result. We describe this operation as a problem-solving task, and exemplify with Augusto de Campos’ Portuguese translation of John Donne’s poem “The Expiration.