This paper investigates how and why the lexical content of adjuncts contributes to specifying the aspectual information of verbs (and also other non-aspectual meanings), and what consequences this specification has for a general theory of the construction of the meaning of predication. The hypothesis argues that adjuncts are predicated of fragments of the content, not only aspectual, of the predicates to which they are attached. Sub-lexical feature-agreement mechanisms legitimize combinations in which the predicate satisfies the selection constraints of the adjunct, discard non-matching combinations or rescue a non-matching combination by means of a coercion operation, in which the adjunct displays the required meaning in the predicate, if the words that make it up potentially contain it in their definition. The adjunct focuses or visualizes sub-lexical contents of the verbal predicate, which explains why its presence disambiguates the aspectual polysemy of certain combinations of verb and complement. Likewise, its intervention is decisive for the legitimization of redundant and, therefore, informatively irrelevant predications. This conception of the adjunct as a predicate of sub-lexical contents of the predicate with which it co-occurs allows us to circumvent the problems traditionally associated with its nature as a non-selected constituent whose appearance, on the other hand, is not always optional or unrestricted, nor is it indifferent to aspectual effects: the proposal also has interesting consequences for the analysis of a set of phenomena for which syntax does not seem to have an explanation.