Masking period patterns (MPPs) were obtained for maskers consisting of harmonics 2–20 of a 100-Hz fundamental. The signal was always a 5-ms 1100-Hz sinusoid presented 152, 154, 156, 158, or 160 ms after the start of a 400-ms masker. Experiment 1 replicated the finding that, for a masker level of 69 dB component, the shape of the MPP depended strongly on the phases of the components: Summing them in positive Schroeder phase led to a threshold variation of about 18 dB across the MPP, but summing them in negative Schroeder phase produced a flat MPP [A. Kohlrausch and A. Sander, J. Acoust. Soc. Am.97, 1817–1829 (1995)]. Reducing the level of the positive-phase masker resulted in a systematic flattening of the MPP, whereas the negative-phase MPPs were flat both at high and at low levels. Experiment 2 showed that removing all components of a positive-phase masker except those close to the signal raised thresholds at the minimum of the MPP. In contrast, a similar manipulation applied to the negative-phase masker produced a uniform elevation of the MPP. Experiment 3 showed that an analogous effect could be obtained by manipulating the phases of masker components remote from the signal. It is shown that several features of the data can be simulated using a nonlinear model of the auditory periphery [C. Giguère and P. C. Woodland, J. Acoust. Soc. Am.95, 331–342 (1994)].