To deal with a broad spectrum of domains, intelligent agents have to generate their own task-oriented dialogue that stems from the need to interact with another agent when solving their own individual task. Most work created to date has either been focused on the task or on the dialogue, but not on both. A taxonomy that describes how the characteristics of a domain determine the types of dialogue needed would be useful, both for understanding how to create agents that are more adaptable to different domains, and also to facilitate reusing previous work. In this paper, we present a number of dimensions that could be included in such a taxonomy, and illustrate how they could be used to determine the nature of dialogue needed in a particular type of domain.