Prosodic units, such as the phonological phrase 𝜙, typically correspond to morphosyntactic units, such as XPs. However, prosodic effects associated with individual morphemes may idiosyncratically disrupt these correspondences. In particular, some morphemes may condition 'prosodic smothering', a pattern in which outer morphemes trigger restructuring of inner prosodic domains. Most analyses of smothering assume that prosodically exceptional elements (i) have regular, unremarkable syntax; and (ii) are lexically specified for their unique prosodic effects. An alternative is to assume that (i) the syntax of smothering triggers is special; and (ii) their prosodic behavior follows directly from their special syntax. Here, I argue against the command-based theory of smothering proposed by Branan (2023), and in favor of the larger claim that smothering effects cannot be reduced to syntactic differences. Instead, I offer an analysis in the Cophonologies-by-Phase framework (Sande et al. 2020). Regardless of the specific implementation, prosodic smothering requires idiosyncratic lexical specification.