All too commonly, we see groups of leaders fail to accomplish their stated goals when working together—legislators who cannot agree on a bill, heads of state who cannot draft meaningful environmental policy, or boards of trustees who make disastrous decisions for their school. The current research examines whether groups of leaders fail as often as they do in part because of the power each leader is accustomed to possessing among his or her constituents. In multiple studies we found that high power individuals, when working together in groups, performed worse than did other groups: individuals randomly assigned power in an initial task were less creative when they then worked together in groups on a subsequent task (Studies 1A and 4). Individuals with higher power who worked together in groups were also less likely to reach agreement on a difficult negotiation task, whether these groups comprised actual executives from an extant organization (Study 2) or participants randomly assigned power in the laboratory (Study 3). Mediation analyses suggest that groups of high power individuals performed worse because they fought over their relative status in the group, were less focused on the task, and shared information with each other less effectively. However, high power individuals were more effective when working on tasks that required less coordination: they were more creative (Studies 1B and 4) and persisted longer on a difficult task than other groups. Therefore, group processes are the key problem for groups of high power individuals when they work together.