Parallel factor analysis (PARAFAC) has successfully been used in many applications for the analysis of excitation-emission fluorescence data. However, some measurement "artefacts", such as Rayleigh or Raman scattering, can pose a problem for the extraction of the PARAFAC components and their interpretation. Replacing the spectral zones corresponding to these signals by missing values in the data is not necessarily a method of choice in the cases where informative signals lie in the same wavelength regions. In this article, independent component analysis (ICA) is used on the unfolded cubic array, and the independent components related to the Rayleigh and Raman scattering are identified and removed prior to the reconstruction of the excitation-emission fluorescence data cube. PARAFAC is then applied on these data reconstructed after selective artefact removal, and satisfactory models can be obtained. This procedure, although particularly useful for 3D fluorescence data, may be applied to other types of data as well.