A modified molecular-replacement method is described that makes use of six-dimensional searches and the phased translation function, providing a systematic examination of all possible search-model orientations in an experimental electron-density map. As an example, the structure solution of the cofilin-homology domain of the Saccharomyces cerevisiae actin-binding protein 1 (ABP1) is presented in detail. Additional examples are presented in which these tools have significantly aided structure solutions in a variety of contexts. These results suggest that this approach might be of widespread utility for challenging structures involving weak phase information, complex asymmetric units and search models with weak structural homology. Furthermore, this approach supports an exhaustive molecular-replacement strategy in cases where an appropriate search model cannot readily be identified on the basis of sequence homology. The fully automated web-based implementation of this phased translation function is described.