An important debate on the architecture of the language faculty has been the extent to which it relies on a compositional system that constructs larger units from morphemes to words to phrases to utterances on the fly and in real time using grammatical rules; or a system that chunks large preassembled, stored units of language from memory; or some combination of both approaches. Good empirical evidence exists for both ’computed’ and ’large stored’ forms in language, but little is known about what shapes multi-word storage / access or compositional processing. Here we explored whether predictive and retrodictive processes are a likely determinant of multi-word storage / processing. Our results suggest that forward and backward predictability are independently informative in determining the lexical cohesiveness of multi-word phrases. In addition, our results call for a reevaluation of the role of retrodiction in contemporary language processing accounts (cf. Ferreira and Chantavarin 2018).