Recent descriptions have argued that what seem to be past tense markers in Capeverdean, a Portuguese-related language spoken in Cabo Verde, are instead allomorphs of a temporal agreement morpheme (Pratas 2018a). The rationale for this goes as follows. It is true that both -ba, from the variety of Santiago, and the related (and more complex) form tava, from São Vicente, are sometimes associated with a past tense in the terms of Klein (1994): the Topic Time is located before the Time of Utterance (Pratas 2014). This is the case in (i) past progressives and past habituals. But they also appear in (ii) subordinate clauses where no past interpretation is certain, such as some conditionals and other modal contexts. Since this subordinate lexical item is often licensed in the context of past situations denoted by their respective main clauses, it seems indeed better accounted for by this recent agreement proposal. That analysis, however, still leaves open the question of what this morpheme agrees with, and this is even more intriguing when it occurs fully separated from past situations. Alternatively, the approach taken in Pratas (2021) identifies a common point between (i) and (ii): all these structures denote situations with a low degree of accessibility from the speaker’s perspective. This (in)accessibility is perceived in terms of time: in the first case, we cannot go back to the past; in the second case, external factors may (have) provide(d) an (in)accessible time location. The main goal of this paper then is to further defend this novel insight on that apparent mismatch, which can bring clues to similar problems crosslinguistically.