There are well-understood benefits of designing intelligent interactive systems to support mixed-initiative interaction, in which there is a back-and-forth dynamic between user and system. We explore the effects of introducing rhythmic elements into this interaction, building on the phenomenon of conversational entrainment in human-to-human conversation. We demonstrate that well-chosen rhythms reduce user stress, increase confidence, and improve the sense of agency through which a person feels in control of their own actions. We apply these findings in the context of a simple intelligent labeling system (based on a deployed product), showing that a more conversational dynamic in labeling retains all of the above benefits, while also improving accuracy of user contributions by comparison to the currently universal design approach in which the user is solely responsible for maintaining any rhythm in interaction events.