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The simultaneous interpretation of a suite of dipole-dipole and dipole-CSA cross-correlation rates involving the backbone nuclei 13Calpha, 1Halpha, 13CO, 15N and 1HN can be used to resolve the ambiguities associated with each individual cross-correlation rate. The method is based on the transformation of experimental cross-correlation rates via calculated values based on standard peptide plane geometry and solid-state 13CO CSA parameters into a dihedral angle probability surface. Triple resonance NMR experiments with improved sensitivity have been devised for the quantification of relaxation interference between 1Halpha(i)-13Calpha(i)/15N(i)-1HN(i) and 1Halpha(i-1)-13Calpha(i-1)/15N(i)-1HN(i) dipole-dipole mechanisms in 15N, 13C-labeled proteins. The approach is illustrated with an application to 13C, 15N-labeled ubiquitin.