Sequential methods of experimentation involve conducting a study in different stages using the information available in previous stages in planning and executing the further experimentation. Sequential methods are particularly timely because, with the advent of Web-based surveying, choice experiments will increasingly be computer assisted. An advantage of computer-assisted discrete choice experimentation (DCE) is that it may be done in real time; that is, prior choices may be used to compose subsequent choice sets. Consequently, it will be possible to modify subsequent choice set composition based on earlier choices. In this chapter, we provide design strategies for sequentially augmenting choice experiments to diagnose whether two-way or three-way interactions are needed and for determining which components should be included in the choice model.