The use of the proton relaxation enhancement (PRE) technique in solutions of macromolecules and paramagnetic ions to obtain information on molecular motion and ion-hydration numbers can be hazardous with the possibility of large errors in the derived parameters. Here we describe a method based on solvent proton-deuteron comparative relaxation measurements at a limited number of different magnetic fields for obtaining, reasonably accurately, rapidly, and unambiguously, certain of the parameters normally obtained from a PRE study. In the non-immune rabbit immunoglobulin G(IgG)-Gd(iii) system, we are able to obtain values for the ion hydration number (q), the residence lifetime of water molecules in the hydration sphere of the ion (tauM) and a correlation time of 5 ns, which can be associated to a large part with a rotational correlation time (tauR) for the Fc portion (C-terminal half of heavy-chain dimer) of the IgG molecule. This shows that there is a rapid internal motion in the Fc region. The limitations and possible applications of the method are discussed.