Consonant recognition was assessed in normal-hearing (NH) and hearing-impaired (HI) listeners in quiet as a function of speech level using a nonsense logatome test. Average recognition scores were analyzed and compared to recognition scores of a speech recognition model. In contrast to commonly used spectral speech recognition models operating on long-term spectra, a "microscopic" model operating in the time domain was used. Variations of the model (accounting for hearing impairment) and different model parameters (reflecting cochlear compression) were tested. Using these model variations this study examined whether speech recognition performance in quiet is affected by changes in cochlear compression, namely, a linearization, which is often observed in HI listeners. Consonant recognition scores for HI listeners were poorer than for NH listeners. The model accurately predicted the speech reception thresholds of the NH and most HI listeners. A partial linearization of the cochlear compression in the auditory model, while keeping audibility constant, produced higher recognition scores and improved the prediction accuracy. However, including listener-specific information about the exact form of the cochlear compression did not improve the prediction further.