In the procedure applied to extract the magnetic dipole moments of bare nuclei from NMR spectra of molecules the shielding of nuclei by electrons has been often described in a very crude manner. We determine the moments for C-13, N-14, N-15, O-17, F-19, P-31 and S-33 using more accurate shielding constants. Our gas phase NMR data are next used to improve the accuracy of the moments of C-13, O-17, F-19 and S-33 nuclei. We present a new, systematic analysis of the results, based on the relations between the nuclear magnetic dipole moments, the resonance frequencies and the shielding constants. (c) 2005 Elsevier B.V. All rights reserved.