We analyze the interplay between cooperation norms and people's punishment behavior in a social-dilemma game with multiple punishment stages. By combining multiple punishment stages with self-contained episodes of interaction, we are able to disentangle the effects of retaliation and norm-related punishment. An additional treatment provides information on the norms bystanders use in judging punishment actions. Partly confirming previous findings, punishment behavior and bystanders' opinions are guided by an absolute norm. This norm is consistent over decisions and punishment stages and requires full contributions. In the first punishment stage, our results suggest a higher personal involvement of punishers, leading to a nonlinearity defined by the punishers' contribution. In later punishment stages, the personal-involvement effect vanishes and retaliation kicks in. Bystanders generally apply the same criteria as punishers in all stages.