Many single-domain proteins with <100 residues fold cooperatively; but the recently designed 92-residue Top7 protein exhibits clearly non-two-state behaviors. In apparent agreement with experiment, we found that coarse-grained, native-centric chain models, including potentials with and without elementary desolvation barriers, predicted that Top7 has a stable intermediate state in which the C-terminal fragment is folded while the rest of the chain remains disordered. We observed noncooperative folding in Top7 models that incorporated nonnative hydrophobic interactions as well. In contrast, free energy profiles deduced from models with desolvation barriers for a set of thirteen natural proteins with similar chain lengths and secondary structure elements suggested that they fold much more cooperatively than Top7. Buttressed by related studies on smaller natural proteins with chain lengths of approximately 40 residues, our findings argue that the de novo native topology of Top7 likely imposed a significant restriction on the cooperativity achievable by any design for this target structure.