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The energy-based refinement of low-resolution protein structure models to atomic-level accuracy is a major challenge for computational structural biology. Here we describe a new approach to refining protein structure models that focuses sampling in regions most likely to contain errors while allowing the whole structure to relax in a physically realistic all-atom force field. In applications to models produced using nuclear magnetic resonance data and to comparative models based on distant structural homologues, the method can significantly improve the accuracy of the structures in terms of both the backbone conformations and the placement of core side chains. Furthermore, the resulting models satisfy a particularly stringent test: they provide significantly better solutions to the X-ray crystallographic phase problem in molecular replacement trials. Finally, we show that all-atom refinement can produce de novo protein structure predictions that reach the high accuracy required for molecular replacement without any experimental phase information and in the absence of templates suitable for molecular replacement from the Protein Data Bank. These results suggest that the combination of high-resolution structure prediction with state-of-the-art phasing tools may be unexpectedly powerful in phasing crystallographic data for which molecular replacement is hindered by the absence of sufficiently accurate previous models.