We have investigated the underlying assumptions in estimating cross-correlation rates between chemical shift anisotropy (CSA) and dipolar coupling mechanisms in a scalar-coupled two-spin IS system, from laboratory frame relaxation experiments. It has been shown that for an arbitrary relaxation delay, the difference in relaxation rates of the individual components of an in-phase (or antiphase) doublet is not related to the CSA-dipolar coupling cross-correlation rate in a simple way. This is especially true in the case where the difference in the decay rates of the in-phase and antiphase terms of the density matrix becomes comparable to the magnitude of the scalar coupling between the two spins. Improved means of extracting cross-correlation rates in these cases are presented. Copyright 1998 Academic Press.