We do not need structuralist morphemes, but we do need constituent structure
In the prethematic high~mid alternation of Spanish third-conjugation verbs, allomorph selection by phonological subcategorization in the morphology interacts with allomorph selection by phonotactic optimization in the phonology, pace Paster (2015). The cyclic locality conditions on this alternation support frameworks with stem storage (Bermúdez-Otero 2013a) or spanning (Svenonius and Haugen & Siddiqi in this volume), and challenge single-terminal insertion. Embick’s (2012) alternative analysis weakens inward cyclic locality excessively. Myler’s (2015) counterproposal overgenerates and undermines the explanation of the parallel cyclic transmission of allomorphy and allosemy. Allomorphy-allosemy mismatches do occur: e.g. when English trànsp[ə]rtátion preserves the argument structure of trànspórt but not its bipedality. However, such mismatches are not generated computationally; they arise diachronically through the interplay of computation and storage (Bermúdez-Otero 2012). Theories asserting that words lack constituent structure cannot explain this fact, pace Blevins, Ackerman & Malouf (this volume).