We have found that refinement of protein NMR structures using Rosetta with experimental NMR restraints yields more accurate protein NMR structures than those that have been deposited in the PDB using standard refinement protocols. Using 40 pairs of NMR and X-ray crystal structures determined by the Northeast Structural Genomics Consortium, for proteins ranging in size from 5 - 22 kDa, restrained-Rosetta refined structures fit better to the raw experimental data, are in better agreement with their X-ray counterparts, and have better phasing power compared to conventionally determined NMR structures. For 38 proteins for which NMR ensembles were available and which had similar structures in solution and in the crystal, all of the restrained-Rosetta refined NMR structures were sufficiently accurate to be used for solving the corresponding X-ray crystal structures by molecular replacement. The protocol for restrained refinement of protein NMR structures was also compared with restrained CS-Rosetta calculations. For proteins smaller than 10 kDa, restrained CS-Rosetta, starting from extended conformations, provides slightly more accurate structures, while for proteins in the size range of 10 - 25 kDa the less cpu intensive restrained-Rosetta refinement protocols provided more accurate structures. The restrained-Rosetta protocols described here can improve the accuracy of protein NMR structures, and should find broad and general for studies of protein structure and function.