Human groups can often maintain high levels of cooperation despite the threat of exploitation by individuals who reap the benefits of cooperation without contributing to its costs1-4. Prominent theoretical models suggest that cooperation is particularly likely to thrive if people join forces to curb free riding and punish their non-contributing peers in a coordinated fashion5. However, it is unclear whether and, if so, how people actually condition their punishment of peers on punishment behaviour by others. Here we provide direct evidence that many people prefer coordinated punishment. With two large-scale decision-making experiments (total n = 4,320), we create minimal and controlled conditions to examine preferences for conditional punishment and cleanly identify how the punishment decisions of individuals are impacted by the punishment behaviour by others. We find that the most frequent preference is to punish a peer only if another (third) individual does so as well. Coordinated punishment is particularly common among participants who shy away from initiating punishment. With an additional experiment we further show that preferences for conditional punishment are unrelated to well-studied preferences for conditional cooperation. Our results highlight the importance of conditional preferences in both positive and negative reciprocity, and they provide strong empirical support for theories that explain cooperation based on coordinated punishment.