The behaviour of future policy-makers substantially influences future greenhouse gas emissions. Uncertainty about the motives of future policy-makers may thus strongly influence the climate policy strategies of current policy-makers. Analytical and numerical analyses in this paper confirm this hypothesis. If current policy-makers want to constrain emissions accumulated over a prolonged period of time, and if future policy-makers tend, with a certain chance, to a less ambitious climate policy, then current policy-makers should intensify their efforts to reduce emissions and the costs of emission reduction. In this setting, if current policy-makers want to meet a cumulative emission constraint in expectation, then the preferred policy trajectory does not qualitatively deviate from one suggested by a standard cost-effective trajectory. If, however, the constraint is to be met with a certain probability, then the importance of early action is enhanced relative to that of postponed action. Costs substantially increase if current policy-makers want to set long-term goals without the full co-operation of future policy-makers.