This essay will argue for the relevance of the ‘neobaroque’ in relation to recent examples of Australian poetics. The baroque and neobaroque are central strains of Latin American poetry, and much has been made of the neobaroque turn in Latin American theory, with the alternatives it proposes to hegemonic, linear narratives of modernity and rationalism. However, despite the fact that some of Australia’s greatest writers have profoundly baroque qualities, the baroque as an aesthetic, ontological and/or political category receives scant attention in Australian criticism. In light of these concerns, this essay will provide an outline of both baroque and neobaroque poetics with relation to Australian, European and Latin American examples. I then address the work of leading Mexican poet Coral Bracho, and consider her influence on the last collection of the late Australian poet Martin Harrison (Happiness, 2015). In examining the relations between Bracho’s neobaroque contortions and Harrison’s ‘late style’, I propose that Happiness is illustrative of an alternative trajectory of Australian poetics, which turns from the discipline and reticence of Anglophone models in order to embrace ambiguity, disorder and incompletion – an imagination of complexity (as opposed to its reduction).