The basic excitation mechanism for the emission lines of Seyfert galaxies is generally believed to be photoionization by radiation emerging from the central power source. In order to deduce the essential physical parameters appropriate to the narrow line region (NLR) on this basis and to overcome some systematic deficiencies of existing photoionization models, we drop the frequent assumption of a constant ionization parameter throughout the NLR and, in particular, allow for a range of densities at fixed radius. We predict all observed emission-lines (ranging from CIV λ1549 in the UV- to [SIII]λ9069 in the NIR spectral region) for the sample of Sy 2 galaxies using the code CLOUDY (Ferland 1993).