This paper tests whether the dimensions involved in preferential choice tasks are evaluated independently from one another. Common decision heuristics satisfy dimensional independence, and multi‐strategy models that assume that decision makers use a repertoire of these heuristics predict that they are unable to represent and respond to dimensional dependencies in the decision environment. In contrast, some single‐strategy models are able to violate dimensional independence, and subsequently adapt to environments that feature interacting dimensions. Across five experiments, this paper documents systematic violations of the assumption of dimensional independence. This suggests that decision makers are able to modify their behavior to respond to dimensional dependencies in their environment, and in turn those models that are unable to do this do not provide a full account of human strategy selection and behavior change. This paper ends with a discussion of ways in which some existing models can be modified to incorporate violations of dimensional independence. Copyright © 2016 John Wiley & Sons, Ltd.