The classic repertory of tools for decision making in management is inspired by a fundamental and widespread assumption: as uncertainty increases and decisions become more difficult, the rationality of decision strategies decreases. Actors use heuristics that are said to avoid uncertainty, to save cognitive effort and to reduce the costs of search. Those heuristics are characterized as simple and frugal, as they shortcut complex analysis of problems by looking for and stopping at approximate and satisfying solutions. It is on this basis that they are characterized as efficient and effective. This paper and study is motivated by the observation that in decisions that are both uncertain and important, a different approach to uncertainty is possible and arguably better: to master rather than reduce it and to strengthen thought rather than to minimize cognitive effort. The study presented considers complex problems, which are unique and have to be defined, and shows that effective heuristics in those setting are themselves more complex. In addition, when problems are important, decision strategies should be evaluated not by being fast or having worked in the past but by more ambitious criteria as the validity of knowledge and the quality of judgments (epistemic rationality). Using a simulation of early-stage project evaluations by expert angel investors and a novel process tracing technique, we show that such complex heuristics are indeed applied and improve judgment. Furthermore, relying on set-theoretical methods, we provide initial evidence on the joint use of those heuristics, proposing a configurational analysis of decision strategies.