Conversations with computer agents can be used to measure skills that may be difficult to accomplish using traditional multiple-choice assessments. In order to achieve natural conversations in this form of assessment, we are exploring issues related to how test-takers interact with computer agents, such as what dialogue moves lead to interpretable responses, the influence of “cognitive characteristics” of computer agents, how should the system adapt to test-taker responses, and how these interactions impact test-taker emotions and affect. In this presentation we will discuss our current research addressing these questions, illustrating important dimensions that are involved with designing a conversation space and how each design decision can impact multiple factors within assessment contexts.