This paper explores the role of causal explanations in evaluating counterfactual conditionals. In reasoning about what would have been the case if A had been true, the localist injunction to hold constant all the variables that causally influence whether A is true or not, is sometimes unreasonably constraining. We hypothesize that speakers may resolve this tension by including in their deliberations the question of what would explain the hypothesized truth of A. To account for our recent psychological findings about counterfactuals, an alternative approach based on Causal Bayesian networks is proposed in which the intervention operator utilizes the agents beliefs about the explanatory power of the antecedent of the counterfactual. The results of three psychological experiments are reported in which the new method succeeds in predicting subjects responses while the traditional method for evaluating counterfactuals in Bayesian networks fails.