The tolerances to additive white Gaussian noise of some recently developed near-maximum-likelihood detectors are compared by computer simulation, using models of two telephone circuits and an HF radio link for the transmission path. Each detector is here preceded by an adaptive allpass linear filter that is adjusted to make the sampled impulse response of the channel and filter minimum phase. For every channel, the near-maximum-likelihood detectors achieve a substantial advantage in tolerance to additive white Gaussian noise over a conventional nonlinear equaliser. An approximate estimate of the relative complexities of the different near-maximum-likelihood detectors suggests that the most recently developed of these detectors achieves a much better compromise between performance and complexity than the others, for both types of transmission path. It is also shown that the performances of all detectors tested can be seriously degraded, in operation with an HF radio link, if the adaptive linear prefilter is modified, but still maintained as an allpass network, such that the sampled impulse response of the channel and filter is no longer minimum-phase. Nevertheless, the near-maximum-likelihood detectors maintain their advantage over the nonlinear equaliser, when the same modification is applied to the latter.