A methodology that extends the usability of low and medium resolution γ-ray detectors to a wide range of energies that appear in environmental radioactivity measurements is described. Results of the implementation of the methodology in the analysis of 20 granite samples measured with a (3″ x 3″) NaI(Tl) are presented. A comparison with the activity results obtained by a high-resolution detector (HPGe) for two samples was found in good agreement, within the uncertainties, validating the results of the proposed method