In everyday conversation, messages are often communicated indirectly or implicitly. Why do people sometimes communicate so inefficiently? How speakers choose to express a message (modulating confidence, using less explicit formulations) has been proposed to impact how committed they will appear to be to its content. We investigated two factors that may influence speaker accountability and the deniability of implicitly conveyed messages. In a preregistered online study, we tested the hypothesis that the degree of meaning strength (strongly or weakly communicated) and the level of meaning used by the speaker (an enrichment or a conversational implicature) modulate accountability and plausible deniability. Our results support these predictions both for level of meaning and for meaning strength. Participants’ responses indicated that enrichments were harder to deny than conversational implicatures, and that strongly implied contents were more difficult to deny that weakly implied contents. Furthermore, participants held speakers more accountable for strongly than for weakly implied contents. These results corroborate the differences found in the literature between levels of meaning (enrichment vs. implicature). Importantly, they also highlight the largely understudied role of meaning strength as a cue to speaker commitment in communication.