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Elemental analysis of inhomogeneous materials can now routinely be performed at the nanometer level, using characteristic EELS signals. Major progress in spatial resolution and accuracy in quantification has recently been fostered by the practical implementation of the spectrum-image mode in a FEG-STEM environment. The required hardware and software have been elaborated to record, store and process these large amounts of data. In the present contribution we describe the routines which have been implemented for extracting quantitative elemental maps from spectrum-images: (i) the standard background subtraction method for which the availability of several hundreds of energy loss channels across the edge to be quantified reduces the errors and bias in background modelling and extrapolation; (ii) a non-negative multiple-least-squares routine for fitting the experimental spectrum acquired for each pixel with a linear combination of reference edges, if possible recorded during the same scan. The impact of these new tools is demonstrated in a series of situations encountered in materials science (composite materials, metallic multilayers) which all require nanometer resolution and accurate data processing of complex spectra with overlapping edges.