Many researchers on bilingualism feel the need to state that a given bilingual stretch of talk is ”basically” in language A, although elements of language B may also be present in some way or other within it. The goal of this paper is to discuss both the limits of analysts abilities to attribute a given stretch of bilingual talk to language A or language B -i.e. to determine a ”base language” at all-, and the proper way of proceeding within these limits -i.e. in those cases in which it is indeed possible and useful to reconstruct what language participants are ”basically” speaking at a given point (or during a given activity). In this paper, it is also argued that in an interpretative approach to code-switching, based on conversation and using an analytically inspired methodology, great care is required not to confound linguists and participants´ identifications of languages. Several examples of how the ”language-of-interaction” is negotiated sequentially are shown in this contribution. Joined to these, others that point to the numerous strategies of ambiguity by which bilingual participants may choose to leave the question of one language-of-interaction locally unsettled, are discussed here.