Abstract We study cooperation and group pressure on social networks by introducing a new concept termed norm-enforcing ties. By combining network characteristics and agents’ actions, direct and indirect norm-enforcing ties extend and refine the concept of social ties as well as the role of the tightness of a group as drivers of group pressure and cooperation. The results show that a strong commitment by agents with collective interests, or a high degree of confrontation between agents minimizes the effect of indirect norm-enforcing ties on cooperation. The analysis in terms of the agent’s utility reveals that an increase in indirect norm-enforcing ties does not necessarily lead to a decrease in the critical mass of compliers supporting cooperation. We demonstrate that network-oriented policies are more efficient in promoting cooperation than are standard economic policy instruments when the expected value of direct norm-enforcing ties is sufficiently large compared to the tightness of the group. Otherwise, standard economic policy instruments are more efficient.