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This paper investigates the role recursive structures play in prosody. In current understanding, phonological phrasing is computed by a general syntax–prosody mapping algorithm. Here, we are interested in recursive structure that arises in response to morphosyntactic structure that needs to be mapped. We investigate the types of recursive structures found in prosody, specifically: For a prosodic category κ, besides the adjunctive type of recursion κ[κ x], κ[x κ], is there also the coordinative type κ[κ κ]? Focusing on the prosodic forms of compounds in two typologically rather different languages, Danish and Japanese, we encounter three types of recursive word structures: coordinative ω[ω ω], left-adjunctive ω[f ω], right-adjunctive ω[ω f] and the strictly layered compound structure ω[f f]. In addition, two kinds of coordinative φ-compounds are found in Japanese, one with a non-recursive (strictly layered) structure φ[ω ω], a mono-phrasal compound consisting of two words, and one with coordinative recursion φ[φ φ], a bi-phrasal compound. A cross-linguistically rare type of post-syntactic compound has this biphrasal structure, a fact to be explained by its sentential origin. 

This paper proposes to subsume Syntax-Prosody Match Theory under General Correspondence Theory, which distinguishes purely existential MAX/DEP constraints (requiring nothing but the existence of a correspondent in the output/input, which can be rather different from the input element) from IDENT and other faithfulness constraints. Exact correspondence (preservation of edges, no deletion, no insertion, uniqueness of mapping, order preservation, etc.) is enforced by Syntax-Prosody and Prosody-Syntax Alignment and by standard Faithfulness. The empirical topic is the impossibility of phrase-final enclisis in English (*I don't know where Tom's vs. Tom's here) and its proper explanation.