Over-punishment often occurs in anonymous peer-to-peer punishment in public goods game experiments where punishment is free for all. We report a public goods game experiment in which a condition where punishment rights were restricted to one other player per player yielded higher total welfare than a condition with unrestricted punishment. In the restricted punishment condition, there was much less punishment but high levels of cooperation were achieved nonetheless. This indicates that it may be beneficial to groups to restrict punishment rights. In a second study we presented respondents from many different countries with three scenarios constituting everyday social dilemmas of various kinds. Across countries, respondents tended to judge it as inappropriate for most involved parties to punish selfish individuals in the scenarios. Typically, only one party was judged to have the right to punish. Whereas much prior work has considered punishment as a public good that needs to be encouraged, these findings suggest that informal norms about sanctions tend to constrain punishment to certain individuals. Such norms may serve the function to harness the positive effects of punishment while containing the negative effects, and we suggest that they are likely to arise from learning.