Phases determined by the molecular-replacement method often suffer from model bias. In extreme cases, the re®nement of the atomic model can stall at high free R values when the resulting electron-density maps provide little indication of how to correct the model, sometimes rendering even a correct solution unusable. Here, it is shown that several recent advances in re®nement methodology allow productive re®ne-ment, even in cases where the molecular-replacement-phased electron-density maps do not allow manual rebuilding. In test calculations performed with a series of homologous models of penicillopepsin using either backbone atoms, or backbone atoms plus conserved core residues, model bias is reduced and re®nement can proceed ef®ciently, even if the initial model is far from the correct one. These new methods combine crossvalidation, torsion-angle dynamics simulated annealing and maximum-likelihood target functions. It is also shown that the free R value is an excellent indicator of model quality after re®nement, potentially discriminating between correct and incorrect molecular-replacement solutions. The use of phase information, even in the form of bimodal single-isomorphousreplacement phase distributions, greatly improves the radius of convergence of re®nement and hence the quality of the electron-density maps, further extending the limits of molecular replacement.