The paper presents a novel argument from Hausa (Chadic) for the analysis of counterfactual fake tense in terms of a lexically underspecified EXCL-operator (Iatridou 2000). Evidence comes from the facts (i.) that Hausa has no obligatory inflectional tense marking on the verb; and (ii.) that temporal anteriority and counterfactuality in Hausa are both expressed by a left-peripheral operator element with the segmental shape daa, which is then tonally disambiguated to temporal dâa and counterfactual dàa, respectively. The analysis is cast in von Prince's (2019) modified branching-world model of counterfactuals.