Do people punish others for defecting or for failing to conform to the majority? In two experiments, we manipulated the base rates with which the participants’ partners cooperated or defected in a Prisoner’s Dilemma game. The effects of this base-rate manipulation on cooperation and punishment were assessed using a multinomial processing-tree model. High compared to low cooperation rates of the partners increased participants’ cooperation. When participants’ cooperation was not enforced through partner punishment, the participants’ cooperation closely aligned with the partners’ cooperation rates which points to a conformist motive behind cooperation. Moral punishment of defection increased when cooperation rates were high compared to when defection rates were high. Likewise, antisocial punishment also increased when cooperation rates were high compared to when defection rates were high. This directly contradicts the assumption that people punish conformity-violating behavior irrespective of whether the behavior supports or disrupts cooperation. Also, moral punishment of defection remained the most frequent type of punishment even when defection was the more common behavior. Punishment is thus sensitive to the rates of cooperation and defection but, overall, it is primarily used to discourage defection and not to enforce blind conformity with the majority.