In recent years, a family of approaches has emerged for supporting decision-making on complex environmental problems characterized by deep uncertainties and competing priorities. Many-Objective Robust Decision Making (MORDM), Multi-scenario MORDM and. Many-Objective Robust Optimization (MORO) differ with respect to the degree to which robustness is considered during the search for promising candidate solutions. To assess the efficacy of these three methods, we compare them using three different policy formulations of the lake problem: inter-temporal, planned adaptive, and direct policy search. The more robustness is considered in the search phase, the more robust solutions are also after re-evaluation but also the lower the performance in individual reference scenarios. Adaptive policy formulations positively affect robustness, but do not reduce the price for robustness. Multi-scenario MORDM strikes a pragmatic balance between robustness considerations and optimality in individual scenarios, at reasonable computational costs.