Human reasoning is often affected by order, such that later judgments depend on earlier ones. For example, such order effects have been observed when people answer counterfactual questions. The order in which questions are asked affects whether or not participants backtrack – imagining how variables that are upstream of a counterfactual change might have been different. Some counterfactual theories predict backtracking, while others don’t. We build on this prior work and develop a computational model of counterfactual reasoning that captures order effects. We evaluate different versions of this model on existing empirical results, finding that a model which backtracks and produces systematic order effects best explains human judgments. We discuss the implications for incorporating contextual evidence to a theory of counterfactual reasoning that is both in line with resource-rational and discourse-coherent explanations of reasoning.