A compilation of the applied experimental conditions when studying metal ion adsorption onto kraft fibres, and the resulting conclusion, revealed that the ionic strength conditions used during the experiments were an important dividing factor. At low ionic strengths, the conclusion has regularly been that the Donnan ion-exchange model could correctly predict the adsorption while, at higher ionic strengths, it has often been concluded that the formation of specific metal-ion fibre complexes must be assumed. To study this apparent influence from the presence of monovalent sodium ions, Cu K-edge EXAFS spectra of Cu2+ ions adsorbed to kraft fibres were collected in media of "0" to 100 mM NaCl. Combined with previous data, these measurements confirmed that at very low ionic strength, the importance of specific interactions between the chemically modified cellulose fibres and the Cu(II) ions significantly decreased. For a detailed description of the adsorption phenomenon, both types of interactions must be considered simultaneously. For most technical and engineering applications, however, the Donnan model can be used at low ionic strength conditions, i.e. I ≤ 10 mM. At higher ionic strengths, though, the inclusion of specific complexes in the model is necessary for correctly describing the adsorption of di- and trivalent cations with strong complex forming properties.