Our previous work with fragment-assembly methods has demonstrated specific deficiencies in conformational sampling behaviour that, when addressed through improved sampling algorithms, can lead to more reliable prediction of tertiary protein structure when good fragments are available, and when score values can be relied upon to guide the search to the native basin. In this paper, we present preliminary investigations into two important questions arising from more difficult prediction problems. First, we investigated the extent to which native-like conformational states are generated during multiple runs of our search protocols. We determined that, in cases of difficult prediction, native-like decoys are rarely or never generated. Second, we developed a scheme for decoy retention that balances the objectives of retaining low-scoring structures and retaining conformationally diverse structures sampled during the course of the search. Our method succeeds at retaining more diverse sets of structures, and, for a few targets, more native-like solutions are retained as compared to our original, energy-based retention scheme. However, in general, we found that the rate at which native-like structural states are generated has a much stronger effect on eventual distributions of predictive accuracy in the decoy sets, as compared to the specific decoy retention strategy used. We found that our protocols show differences in their ability to access native-like states for some targets, and this may explain some of the differences in predictive performance seen between these methods. There appears to be an interaction between fragment sets and move operators, which influences the accessibility of native-like structures for given targets. Our results point to clear directions for further improvements in fragment-based methods, which are likely to enable higher accuracy predictions.