Group identification can be both beneficial (a “social cure”) and detrimental (a “social curse”) for performance and well-being, which makes it crucial to explore its boundary conditions. Building on the norm enactment hypothesis and the influence hypothesis, we propose the group’s achievement norms as one such boundary condition. We argue that group identification predicts higher well-being and task performance if achievement norms are average, but lower well-being and task performance if achievement norms are very high. The results of a laboratory experiment ( N  = 163) partially supported our propositions for task-related stress, but not for task performance and other well-being indicators. Additionally, exploratory analyses showed a moderated indirect effect on task performance such that group identification predicted more task-related stress when achievement norms were very high (but not when they were average), which, in turn, predicted lower task performance. We discuss the theoretical and practical relevance of these findings.