Recent work has shown that NMR structures can be determined by integrating sparse NMR data with structure prediction methods such as Rosetta. The experimental data serve to guide the search for the lowest energy state towards the deep minimum at the native state which is frequently missed in Rosetta de novo structure calculations. However, as the protein size increases, sampling again becomes limiting; for example, the standard Rosetta protocol involving Monte Carlo fragment insertion starting from an extended chain fails to converge for proteins over 150 amino acids even with guidance from chemical shifts (CS-Rosetta) and other NMR data. The primary limitation of this protocol--that every folding trajectory is completely independent of every other--was recently overcome with the development of a new approach involving resolution-adapted structural recombination (RASREC). Here we describe the RASREC approach in detail and compare it to standard CS-Rosetta. We show that the improved sampling of RASREC is essential in obtaining accurate structures over a benchmark set of 11 proteins in the 15-25 kDa size range using chemical shifts, backbone RDCs and HN-HN NOE data; in a number of cases the improved sampling methodology makes a larger contribution than incorporation of additional experimental data. Experimental data are invaluable for guiding sampling to the vicinity of the global energy minimum, but for larger proteins, the standard Rosetta fold-from-extended-chain protocol does not converge on the native minimum even with experimental data and the more powerful RASREC approach is necessary to converge to accurate solutions.