We describe a method for correcting plural inelastic scattering effects in elemental maps that are acquired in the energy filtering transmission electron microscope (EFTEM) using just two energy windows, one above and one below a core edge in the electron energy loss spectrum (EELS). The technique is demonstrated for mapping low concentrations of phosphorus in biological samples. First, the single-scattering EELS distributions are obtained from specimens of pure carbon and plastic embedding material. Then, spectra are calculated for different specimen thicknesses t, expressed in units of the inelastic mean free path lambda. In this way, standard curves are generated for the ratio k0 of post-edge to pre-edge intensities at the phosphorus L2,3 excitation energy, as a function of relative specimen thickness t/lambda. Thickness effects in a two-window phosphorus map are corrected by successive acquisition of zero-loss and unfiltered images, from which it is possible to determine a t/lambda image and hence a background k0-ratio image. Knowledge of the thickness-dependent k0-ratio at each pixel thus enables a more accurate determination of the phosphorus distribution in the specimen. Systematic and statistical errors are calculated as a function of specimen thickness, and elemental maps are quantified in terms of the number of phosphorus atoms per pixel. Further analysis of the k0-curve shows that the EFTEM can be used to obtain reliable two-window phosphorus maps from specimens that are considerably thicker than previously possible.