We investigated the relationship between two kinds of problem solving using Kitchener's model of hierarchical cognitive processing. We predicted that performance on well-defined problems (i. e. those with a single, guaranteed solution) would be independent of ill-defined problems (i. e. those with multiple, non-guaranteed solutions). We also predicted that self-reported epistemic beliefs (i. e. assumptions about the nature and acquisition of knowledge) would be related to ill-defined, but not well-defined, solutions. Results confirmed these predictions. We concluded that well-defined and ill-defined problems require separate cognitive processes and that epistemic beliefs play an important role in ill-defined problem solving. These findings supported Kitchener's three-level model of problem solving.