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When a digital data signal is received over a linear channel that distorts the signal, the resulting intersymbol-interference can be removed, or at least greatly reduced, by means of a decision-feedback equalizer. A conventional equalizer is adjusted adaptively to minimize the mean-square error in the equalized signal, where the error is caused partly by intersymbol interference and partly by noise. Alternatively, the equalizer may be adjusted adaptively to minimize the noise in the equalized signal, subject to the accurate equalization of the channel. The latter equalizer is usually easier to adjust close to its ideal setting, for both timeinvariant and time-varying channels. The paper compares the tolerances to additive white Gaussian noise of the two equalizers, for the particular application of digital data transmission at 9600 bit/s over telephone circuits. Theoretical analysis is used to compare the equalizers, first for the case where there is a very high signal/noise ratio, and then for the case where the channel introduces pure phase distortion. Computer-simulation tests over models of six different telephone circuits are used to compare the equalizers for more general situations where the signal/noise ratio is not very high and where there is amplitude distortion in the received signal.