Nonsimultaneous maskers can strongly impair performance in an auditory intensity discrimination task. Using methods of molecular psychophysics, we quantified the extent to which (1) a masker-induced impairment of the representation of target intensity (i.e., increase in internal noise) and (2) a systematic influence of the masker intensities on the decision variable contribute to these effects. In a two-interval intensity discrimination procedure, targets were presented in quiet, and combined with forward maskers. The lateralization of the maskers relative to the targets was varied via the interaural time difference. Intensity difference limens (DLs) were strongly elevated under forward masking but less with contralateral than with ipsilateral maskers. For most listeners and conditions, perceptual weights measuring the relation between the target and masker levels and the response in the intensity discrimination task were positive and significant. Higher perceptual weights assigned to the maskers corresponded to stronger elevations of the intensity DL. The maskers caused only a weak increase in internal noise, unrelated to target level and masker lateralization. The results indicate that the effects of forward masking on intensity discrimination are determined by an inclusion of the masker intensities in the decision variable, compatible with the hypothesis that the impairment in performance is to a large part caused by difficulties in directing selective attention to the targets. The effects of masker lateralization are evidence for top-down influences, and the observed positive signs of the masker weights suggest that the relevant mechanisms are located at higher processing stages rather than in the auditory periphery.