We report the results of two experiments that compare if and if only counterfactual conditionals. We propose that if only counterfactual conditionals, e.g., if only Mary had gone to Dublin, then Paul would have gone to Cork emphasise their counterfactual nature - their conjecture is contrary to the presupposed facts (Mary did not go to Dublin and Paul did not go to Cork), even more so than a counterfactual conditional based on if alone. In Experiment 1 (n = 36), participants made more of the inferences that relied on the presupposed facts (e.g., Paul did not go to Cork, therefore Mary did not go to Dublin) from subjunctive if only compared to subjunctive if and indicative if. In Experiment 2 (n = 156) participants judged that conjunctions based on the presupposed facts (e.g., Mary did not go to Dublin and Paul did not go to Cork) were consistent with subjunctive if only more often than they did so for subjunctive if and indicative if. The implications of the results for theories of the mental representations of counterfactual conditionals are discussed.