Self-adaptive systems often employ dynamic programming or similar techniques to select optimal adaptations at run-time. These techniques suffer from the ‘‘curse of dimensionality’’, increasing the cost of run-time adaptation decisions. We propose a novel approach that improves upon the state-of-the-art proactive self-adaptation techniques to reduce the number of possible adaptations that need be considered for each run-time adaptation decision. The approach, realized in a tool called Thallium, employs a combination of automated formal modeling techniques to (i) analyze a structural model of the system showing which configurations are reachable from other configurations and (ii) compute the utility that can be generated by the optimal adaptation over a bounded horizon in both the best- and worst-case scenarios. It then constructs triangular possibility values using those optimized bounds to automatically compare adjacent adaptations for each configuration, keeping only the alternatives with the best range of potential results. The experimental results corroborate Thallium’s ability to significantly reduce the number of states that need be considered with each adaptation decision, freeing up vital resources at run-time.