In a period given to emphasizing diversity among humans, we would do well to explore diversity among forms of discourse and among forms of talk-in-interaction in particular. Among the speech-exchange systems, ordinary conversation has been claimed to be distinctive and fundamental, but questions have been raised about both claims. The resources for discriminating among speech-exchange systems are located in such generic organizations of practice as turn-taking, sequence organization, the organization of repair and the overall structural organization of episodes of interaction. I try to show that 'conversation' as a distinctive speech-exchange system is real and is not only a residual category, and that it is to be understood as the 'basic' speech-exchange system, in part by reference to the distinctive turn-taking organization (among others) through which it is implemented. The 'motivation' for having developed a formal account of this turn-taking organization is recounted, and that formal account is defended for its usability in the analytic explication of singular, contexted episodes of talk. The remainder of the article is given over to such an exemplary account - an examination of an episode of interaction during a testing session between a man whose brain hemispheres had been surgically separated and a researcher.