Some very recent work on equalisers has led to a simple development of a conventional nonlinear (decision-feedback) equaliser, that involves only changes to the equalisation process itself and can, under certain conditions, give a useful improvement in tolerance to additive white Gaussian noise. The technique is particularly effective when binary data symbols are transmitted, at a high signal/noise ratio, and there is severe amplitude distortion in the received data signal. The paper is concerned with a further development of the technique, suitable for applications where a binary data signal is transmitted at a high rate over a linear baseband channel and where the channel introduces severe amplitude distortion. The channel may be either minimum phase or linear phase, or else it may approximate to some compromise between these two. It is shown that, under the given conditions, the linear feedforward transversal filter that forms the first part of a conventional nonlinear equaliser can often be replaced by a simple two-tap feedforward transversal filter, with either an improvement in performance or, at least, no serious degradation in performance. The paper describes both the new equaliser and a further development of this for the case where the received data signal is sampled at twice the data symbol rate. Finally, results of computer-simulation tests are presented, comparing the tolerances to additive white Gaussian noise of the two new equalisers with those of more conventional detectors, for models of various channels. Three quite different applications have been considered, one of which involves the transmission of digital data at 140 Mbit/s over a length of coaxial cable.