Spectral computed tomography (CT) with photon-counting detectors (PCDs) has the potential to substantially advance diagnostic CT imaging by reducing image noise and dose to the patient, by improving contrast and tissue specificity, and by enabling molecular and functional imaging. However, the current PCD technology is limited by two main factors: imperfect energy measurement (spectral response effects, SR) and count rate non-linearity (pulse pileup effects, PP, due to detector deadtimes) resulting in image artifacts and quantitative inaccuracies for material specification. These limitations can be lifted with image reconstruction algorithms that compensate for both SR and PP. A prerequisite for this approach is an accurate model of the count losses and spectral distortions in the PCD. In earlier work we developed a cascaded SR-PP model and evaluated it using a physical PCD. In this paper we show the robustness of our approach by modifying the cascaded SR-PP model for a faster PCD with smaller pixels and a different pulse shape. We compare paralyzable and non-paralyzable detector models. First, the SR-PP model is evaluated at low and high count rates using two sets of attenuators. Then, the accuracy of the compensation is evaluated by estimating the thicknesses of three basis functions.