This paper provides general theorems about the control that maximizes the mixed Bentham-Rawls (MBR) criterion for intergenerational justice, which was introduced in Alvarez-Cuadrado and Long (2009). We establish sufficient concavity conditions for a candidate trajectory to be optimal and unique. We also show that the state variable is monotonic under rather weak conditions. And finally we prove that inequality among generations, captured by the gap between the poorest and the richest generations, is lower when optimization is performed under the MBR cri- terion rather than under the discounted utilitarian criterion. The two last properties are in line with some aspects of the rawlsian just savings principle.