Many social scientists believe humans possess an evolved motivation to punish violations of norms—including norm violations that do not harm them directly. However, most empirical evidence for so-called altruistic punishment comes from experimental economics games that create experimental demand for third-party punishment, raising the possibility that the third-party punishment uncovered in these experiments has been motivated by a desire to appear concerned about social norms rather than by actual concern about upholding them. Here we present the results of five experiments in which we used an aggression paradigm to contrast second-party and third-party punishment with minimal experimental demand. We also summarize the results of these experiments meta-analytically. We found robust evidence that participants who were insulted by a stranger experienced anger and punished the insulter. To a lesser degree, participants who witnessed a friend receive an insult also became angry and punished the insulter. In contrast, we found robust evidence that participants who witnessed a stranger receive an insult did not punish the insulter, although they did experience modest amounts of anger. In only one experiment did we find any punishment on behalf of a stranger, and this result could plausibly be explained by the desire to escape the moral censure of other bystanders. Our results suggest that experimental designs that rely on demand-laden methods to test hypotheses about third-party punishment may have overstated the case for the existence of this trait.