Stochastic turn-taking models provide stationary estimates of the probability of a conversant's incipient speech activity, given their own and their interlocutors' recent speech activity. Existing research suggests that such models may be conversant specific, and even conversant-discriminative. The present work establishes this explicitly. It is shown that: (1) the conditioning context can be relaxed to exploit speech activity which need not be attributed to specific interlocutors; (2) the same duration of context can yield better results with a more statistically sound framework; and (3) results further improve asymptotically with the consideration of longer conditioning histories. The findings indicate that inter-conversant variability is a major contributor of variability across stochastic turn-taking models.