The problem of cooperation is intensified when individuals derive different benefits from it. Heterogeneity has been shown to trigger normative conflict undermining group cohesion and making it difficult for groups to agree on what each member should do. The outcome that maximizes group welfare would prescribe the all individuals cooperate fully, but this would result to lower earnings for low-return members. Rewarding opportunities have the potential to alleviate normative conflict if high-benefit members agree to compensate low-benefit members. We present evidence from a public-good experiment in which group members that differ in the returns from the public good can reward each other. Our main result is that, in contrast to homogeneous groups that cooperate fully, heterogeneous groups fail to reach the socially optimal outcome even if communication between group members is permitted. The reason for this appears to be that group members are concerned about the equality of rewards which prevents them from using them to eliminate earning inequalities across the different types.