Listeners may report difficulty understanding speech, particularly in background noise, despite having normal audiograms that do not suggest a sensorineural hearing loss. One potential cause of this hearing difficulty is auditory neuropathy (AN), a disruption in the function of the auditory nerve. AN may specifically affect auditory nerve fibers that code intensity differences at higher sound levels, resulting in particular difficulty with speech recognition but preserved audiometric thresholds. This study aims to detect AN by measuring intensity discrimination thresholds at different frequencies and sound levels, comparing performance to self-reported measures of hearing difficulty. Listeners performed an intensity discrimination task where they heard pairs of tones and judged whether the first or second tone was louder. Psychophysical functions were computed to measure listeners' discrimination thresholds and point of subjective equality (PSE, i.e., point at which the two tones are judged to have equal intensity). Results showed that listeners who report greater speech-in-noise difficulty had shifted PSEs specifically at higher sound levels (60–70 dB SPL, the range used in conversational speech), such that they were more likely to perceive the second tone as louder than it was. The results suggest that an intensity discrimination task may be a useful test for AN.