Frequency selectivity, temporal fine-structure (TFS) processing, and speech reception were assessed for six normal-hearing (NH) listeners, ten sensorineurally hearing-impaired (HI) listeners with similar high-frequency losses, and two listeners with an obscure dysfunction (OD). TFS processing was investigated at low frequencies in regions of normal hearing, through measurements of binaural masked detection, tone lateralization, and monaural frequency modulation (FM) detection. Lateralization and FM detection thresholds were measured in quiet and in background noise. Speech reception thresholds were obtained for full-spectrum and lowpass-filtered sentences with different interferers. Both the HI listeners and the OD listeners showed poorer performance than the NH listeners in terms of frequency selectivity, TFS processing, and speech reception. While a correlation was observed between the monaural and binaural TFS-processing deficits in the HI listeners, no relation was found between TFS processing and frequency selectivity. The effect of noise on TFS processing was not larger for the HI listeners than for the NH listeners. Finally, TFS-processing performance was correlated with speech reception in a two-talker background and lateralized noise, but not in amplitude-modulated noise. The results provide constraints for future models of impaired auditory signal processing.