Some traffic management measures route drivers towards socially-desired paths in order to achieve the system optimum: the traffic state with minimum total travel time. In previous attempts, the behavioral response to route advice is often not accounted for since some drivers are advised to take significantly longer paths for the system’s benefit. Hence, these drivers may not comply with such advice and the optimal state will not be achieved. In this paper, we propose a social routing strategy to approach the optimal state while accounting for fairness in the resulting state. This routing strategy asks travelers to take a limited detour in order to improve efficiency. We show that the best possible paths (in terms of efficiency) to be proposed by a service adopting this strategy can be found by solving a bilevel optimization problem with a non-unique lower-level solution. We use techniques from parametric analysis to show that the directional derivative of the lower-level link flows however exists. This derivative is the optimal solution of a quadratic optimization problem with a suitable route flow solution as parameter. We use the derivative in a descent algorithm to solve the bilevel problem. Numerical experiments in a realistic environment show that the routing strategy only asks a small fraction of the drivers to take a limited detour and thereby substantially improves the performance of the traffic system.