Discrete choice experiments have their genesis in conjoint analysis, which was based on first-order models. For this and other reasons, discrete choice experiments in practice are usually designed for estimation of main effects. In this paper, we explore the construction of maximin model robust designs when the experimenter is concerned about the presence of interactions. We consider three classes of models—main effects models, main effects models plus first-order interactions, and secondorder models, and we construct designs that maximize the minimum efficiency of the design for the three competing models. We do so first with standard linear models and then extend our analysis to nonlinear models and, in particular, to models for discrete choice experiments. We compare our results with existing approaches in the literature, such as Li et al., 2013.