Between-group comparisons have been shown to foster within-group cooperation. Yet, here we demonstrate an important limitation to this result: the awareness of the own group’s structural disadvantages relative to a comparison group renders within-group cooperation more fragile. More specifically, we confirm the general pattern that the desire to avoid ‘lagging behind’ a comparison group motivates within-group cooperation. However, having information about the own group’s structural disadvantage, i.e., the own group’s lower return from cooperation, leads group members to become more sensitive to how well their group ‘stands together’. That is, they reduce their contributions more strongly in response to within-group free-riding. Further analyses suggest that particularly those group members who perceive that contributions are not comparable between groups reduce their contributions more strongly in response to within-group free-riding.