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. The current PCD technology, however, is limited by two main factors: imperfect energy measurement (spectral response effects, SRE) and limited count rate (pulse-pileup effects, PPE, due to detector dead-times). The overall goal of our research is to develop compensation algorithms for these sources of data distortions, to demonstrate that PCDs are suitable for clinical CT, and to identify key clinical applications for spectral CT with PCDs. We have already developed an iterative compensation scheme that includes a forward projection model of the imaging chain and that can compensate for either SRE or PPE distortions separately by maximizing a penalized log-likelihood function. In this paper we describe the evaluation of a combined, cascaded SRE and PPE model for PCDs and compare the models to data acquired with an experimental table-top PCD-CT system. The separation into count-rate independent effects (SRE) and count-rate dependent effects (PPE) allows cascading the forward model. First, the SRE model is evaluated using low count rates. Then the PPE model is cascaded and the combined SRE+PPE model is evaluated. Several different attenuators were used, including K-edge materials and the models and data were compared for various count-rate conditions.