The complexity of a turbo equalizer based on the Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm is manageable only for mildly dispersive channels having a small amount of memory. To enable turbo equalization of highly dispersive channels, we propose the soft-feedback equalizer (SFE). The SFE combines linear equalization and soft intersymbol-interference cancellation. Its coefficients are chosen to minimize the mean-squared error (MSE) between the equalizer output and the transmitted sequence, under a Gaussian approximation to the a priori information and the SFE output. The resulting complexity grows only linearly with the number of coefficients, as opposed to the quadratic complexity of previously reported minimum-MSE structures. We will see that an SFE-based turbo equalizer consistently outperforms another structure of similar complexity, and can outperform a BCJR-based scheme when complexity is taken into account.