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This paper proposes a new strategy for establishing the LMS step-size parameter in the context of adaptive MLSE-PSP reception over time-varying frequency-selective fading channels. This strategy is based on the optimization of the step-size in the sense of minimizing the LMS steady-state mean square error (MSE) in the estimation of the channel impulse (IR) response. Analytical expressions of the optimum step-size are derived assuming Doppler spectrum models usually adopted for mobile communication channels. These expressions are used to choose the step-size of LMS based MLSE-PSP receivers under different conditions of Doppler spread. Several computer simulation results are provided which show the performance benefits so obtained.