The paper presents four schemes for the adaptive adjustment of a linear feedforward filter placed ahead of a conventional digital data detector. The filter is broadly adjusted according to two criteria, those of maximisation of the signal-tonoise ratio at the input of the detector where perfect equalisation of the detector input signal results in zero intersymbol interference, or minimising the mean-square error present in the equalised signal at the detector input. The paper presents the results of extensive computer simultions performed upon models of the four schemes when operating over four different voice-frequency bandpass channels. The results are arranged to show the relative accuracies and complexities (in terms of the number of arithmetic operations required to implement the algorithms) of the tested systems. Furthermore, the results have been arranged to show the behaviour of the four systems in the presence of additive white Gaussian noise and various amounts of distortion introduced by the channels, for different lengths of the linear pre-filter.