The accuracy of the determination of longitudinal cross-relaxation rates in NMR can be improved by combining symmetrical reconversion with suitable operator swapping methods that lead to the averaging of differences in autorelaxation rates and eliminate the effects of cross relaxation with the environment. The principles are first discussed for an isolated two-spin system comprising a pair of 15N and 1HN nuclei subjected to chemical shift anisotropy and dipole-dipole relaxation, and then extended to include further protons. The gains in accuracy are demonstrated experimentally for the protein ubiquitin.