This paper focuses on conventionalized and non-conventionalized indirect speech acts, and more concretely, on (indirect) requests. We do so within a Natural Language Processing environment called FunGramKB, which adheres to a cognitively-oriented Construction Grammar view of language. Here, conventionalized formulations like Can you X? are treated as constructions in their own right; that is, as entrenched form-meaning pairings and, thus, they are not considered indirect. By contrast, non-conventionalized formulations such as those instantiated by negative state remarks (e.g. I’m hungry) require degrees of inferencing for interpretation. Both types are computationally handled in different modules of FunGramKB. Our aim is to show that a cognitive version of Construction Grammar can offer a solution to the computational treatment of illocution.