In a profile-analysis task, the effect of randomly perturbing the amplitudes of the components of multi-tone stimuli was studied in two experiments. In the first experiment, thresholds for a signal added in-phase to the central component of a standard were measured for different numbers of components in two conditions. In one condition thresholds were measured in blocks for six different “jagged” standards, and in another, thresholds were measured when one of the six standards was chosen randomly on a presentation-by-presentation basis. Regardless of condition, thresholds did not depend on the numbers of components and increased magnitude of perturbation increased thresholds. Moreover, the slope relating thresholds to number of components did not increase with increasing magnitude of perturbation. In the second experiment, the signal consisted of an increase in amplitude of the central components and a decrease in amplitude of the outer components of the standard (a stimulus type which has been shown to maximize the change in threshold with increasing number of components). The amplitudes of component tones were selected randomly on a presentation-by-presentation basis. Thresholds fell with increases in the number of components, but the slope relating thresholds to numbers of components did not change as the magnitude of perturbation increased. The latter result contrasts with that reported by Kidd et al. [J. Acoust. Soc. Am.90, 1340–1354 (1991)].