A multiple-least-squares fitting procedure for quantitating electron energy loss spectra is demonstrated on some strongly overlapping core edges. The method, first applied by Shuman and Somlyo [Ultramicroscopy 21 (1987) 23], takes into account plural inelastic scattering and can be applied under conditions of non-uniform sample thickness where Fourier deconvolution techniques are invalid. By using appropriate reference spectra generated from pure compounds, quantitation of potassium and calcium (L23 edges) is possible in the presence of carbon (K edge), and sulfur in the presence of phosphorus (L23 edges). Some of the advantages and limitations of the multiple-least-squares approach are discussed.