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We give an enumeration of possible problem frames, based on domain characteristics, and comment on the usefulness of the obtained frames. In particular, we investigate problem domains and their characteristics in detail. This leads to fine-grained criteria for describing problem domains. As a result, we identify a new type of problem domain and come up with integrity conditions for developing useful problem frames. Taking a complete enumeration of possible problem frames (with at most three problem domains, of which only one is constrained) as a basis, we find 8 new problem frames, 7 of which we consider as useful in practical software development.