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In a multiple-target environment a radar signal processor often uses weighting filters that are not matched to the transmitted waveform. In this paper the mean-square range-estimation error, the detection Signal-to-noise ratio (SNR), and the effects of sidelobes are expressed in terms of the impulse response of an arbitrary mismatched filter. It is desired to find that impulse response that results in the minimum range-estimate variance subject to preassigned constraints on the side-lobes and the detection SNR. It is shown that for detecting the radar target and estimating its range, the form of the optimum filter is a modified transversal equalizer. If only detection is required, the optimum filter reduces to the transversal equalizer. Certain parameters upon which the solution depends can be found by solving a nonlinear programming problem. Numerical results are given for an interesting class of transmitted waveforms.