The ability to understand speech in quiet and in a steady noise was measured for 26 listeners with audiometric thresholds below 30 dB HL for frequencies up to 3 kHz and covering a wide range (0-80 dB HL) between 3 and 8 kHz. The stimulus components were restricted to the low (≤1.5 kHz) and middle (1-3 kHz) frequency regions, where audiometric thresholds were classified clinically as normal or near-normal. Sensitivity to inter-aural phase was measured at 0.5 and 0.75 kHz and otoacoustic emission and brainstem responses were measured. For each frequency region, about half of the listeners with high-frequency hearing loss showed extremely poor intelligibility for speech in quiet and in noise. These deficits could not be accounted for by reduced audibility. Scores for speech in quiet were correlated with age, audiometric thresholds at low and at high frequencies, the amplitude of transient otoacoustic emissions in the mid-frequency region, but not with inter-aural phase discrimination. The results suggest that large speech deficits may be observed in regions of normal or near-normal hearing for hearing-impaired listeners. They also suggest that speech deficits may result from suprathreshold auditory deficits caused by outer hair-cell damage and by factors associated with aging.