Two important policy goals in intergenerational problems are Pareto-efficiency and sustainability, i.e. intergenerational equity. We demonstrate that the pursuit of these goals is subject to an intergenerational equity-efficiency trade-off. Our analysis highlights two salient characteristics of intergenerational problems and policy: (i) temporal irreversibility, i.e. the inability to revise one's past actions; and (ii) uncertainty of future consequences of present actions in human-environment systems. We employ a two-non-overlapping-generations model that combines an intragenerational production decision on the use of circulating capital and a non-renewable resource, with a negative intergenerational externality as an unforeseen contingency. If initially unknown problems become apparent and policy is enacted after irreversible actions were taken, policy-making faces a fundamental trade-off between ex-post Pareto-efficiency and sustainability. That is, one can achieve either one of these two goals, but not both.