Molecular replacement procedures, which search for placements of a starting model within the crystallographic unit cell that best account for the measured diffraction amplitudes, followed by automatic chain tracing methods, have allowed the rapid solution of large numbers of protein crystal structures. Despite extensive work, molecular replacement or the subsequent rebuilding usually fail with more divergent starting models based on remote homologues with less than 30% sequence identity. Here we show that this limitation can be substantially reduced by combining algorithms for protein structure modelling with those developed for crystallographic structure determination. An approach integrating Rosetta structure modelling with Autobuild chain tracing yielded high-resolution structures for 8 of 13 X-ray diffraction data sets that could not be solved in the laboratories of expert crystallographers and that remained unsolved after application of an extensive array of alternative approaches. We estimate that the new method should allow rapid structure determination without experimental phase information for over half the cases where current methods fail, given diffraction data sets of better than 3.2 Å resolution, four or fewer copies in the asymmetric unit, and the availability of structures of homologous proteins with >20% sequence identity.