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In this paper, fast techniques for computing the coefficients of a Kalman-based prefilter originally developed by Mulgrew are proposed. This prefilter approximates a minimum-phase overall impulse response. In conjunction with a reduced-complexity equalizer, near optimum performance compared to maximum-likelihood sequence estimation is demonstrated for wireless channels. We suggest an exact recursive solution as well as a new iterative solution. In both solutions, the computational complexity of calculating the prefilter coefficients is O(LWMF) with respect to LWMF, where LWMF is the number of prefilter coefficients. For comparison, the complexity of the original algorithm is O(LWMF3).