In this paper, we explore the mechanisms by which conversants control the direction of a dialogue. We find further evidence that control in task-oriented dialogues is subordinate to discourse structure. The initiator of a discourse segment has control; the non-initiator can contribute to the purpose of the segment, but this does not result in that person taking over control. The proposal has important implications for dialogue management, as it will pave the way for building dialogue systems that can engage in mixed initiative dialogues.