A routinely used assumption when interpreting two-dimensional NMR spectra obtained with a commonly used double-quantum (DQ) magic-angle-spining (MAS) pulse sequence referred to as the refocused incredible natural abundance double-quantum transfer experiment (INADEQUATE) [A. Lesage, M. Bardet, and L. Emsley, J. Am. Chem. Soc. 121, 10987 (1999)] has been that correlation peaks are only observed for pairs of nuclei with a through-bond connectivity. The validity of this assumption is addressed here by theory, experiment, and computer simulations. If the isotropic chemical shifts of the two nuclei are different and the MAS frequency is far from rotational resonance, the theoretical description demonstrates that DQ correlation peaks are indeed indicative of a J coupling. However, if the isotropic chemical shifts are the same, it is shown that DQ peaks can appear for pairs of nuclei even in the absence of a through-bond J coupling. These peaks appear in the specific case of a pair of nuclei with a nonzero through-space dipole-dipole coupling and chemical shift anisotropy tensors having different principal magnitudes or orientations, provided that the MAS frequency is comparable to or smaller than, the chemical shift anisotropies. Experimental P-31 Spectra recorded on a sample of TiP2O7 and computer simulations show that the magnitude of these anomalous peaks increases with increasing B-0 magnetic field and that they decrease with increasing MAS frequency. This behavior is explained theoretically. (c) 2005 American Institute of Physics.