One of the issues studies of language alternation among bilingual speaker still have to resolve is that of the base language (Auer, 1997; DeprÃ¨z de HÃ©rÃ©dia, 1991), of a scheme of interpretation (Garfinkel, 1967), with respect to which categories of language alternation are identified. Starting from the fact that the need for a scheme of interpretation is not felt by analysts only, but also by speakers themselves, this paper argues that, in order to â??discoverâ?� the relevant scheme, a speakers' own perspective must be adopted. Therefore, the paper illustrates this perspective by examining two activities bilingual speakers accomplish while talking, namely medium repair and other-language repair. Both activities are accomplished when, missing the mot juste in one language, speakers draw on their other languages to overcome that difficulty. As the discussion shows, through their own orientation to their language choice acts while accomplishing these activities, speakers themselves reveal, to one another and to analysts as well, the scheme they are attending to here and now. As that scheme speakers themselves orient to need not consist of the use of one language, in the paper, I refer to it, not as the base language, but as the medium of a bilingual conversation.