Speech intelligibility models consist of a preprocessing part that transforms the stimuli into some internal (auditory) representation, and a decision metric that quantifies effects of transmission channel, speech interferers, and auditory processing on the speech intelligibility. Here, two recent speech intelligibility models, the spectro-temporal modulation index (STMI; Elhilali et al., 2003) and the speech-based envelope power spectrum model (sEPSM; Jørgensen and Dau, 2011) were evaluated in conditions of noisy speech subjected to reverberation, and to nonlinear distortions through either a phase jitter process or noise reduction via spectral subtraction. The contributions of the individual preprocessing stages in the models and the role of the decision metrics were analyzed in the different experimental conditions. It is demonstrated that an explicit across-frequency envelope processing stage, as assumed in the STMI, together with the metric based on the envelope power signal-to-noise ratio, as assumed in the sEPSM, are required to account for all three conditions. However, a simple across audio-frequency mechanism combined with a purely temporal modulation filterbank is assumed to be sufficient to describe the data, i.e., a joint two-dimensional modulation filterbank might not be required.