Reasoners resist even the valid inferences, such asIf Lisa met her friend then she went to a play, Lisa met her friend, therefore she went to a play, when they are given an additional condition, e.g.,If Lisa had enough money then she went to a play.Four experiments test alternative accounts of this suppression effect. The first experiment shows that inferences are suppressed even when reasoners produce their own conclusions, based on the first or second conditional. The second experiment shows that suppression occurs even when the premises are expanded to rule out the converse. The third experiment shows that inferences are suppressed more when the background conditions are expressed in a biconditional. The fourth experiment shows that both valid and fallacious inferences can be suppressed when the premises refer to alternatives as well as to additional conditions. We suggest that suppression rests on the availability of counterexamples.