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We study the statistical performance of two moment-based estimators for the K parameter of Rice fading distribution, as less complex alternatives to the maximum-likelihood estimator. Our asymptotic analysis reveals that both estimators are nearly asymptotically efficient, and that there is a compromise between the computational simplicity and the statistical efficiency of these two estimators. We also show, by Monte Carlo simulation, that the fading correlation among the envelope samples deteriorates the performance of both estimators. However, the simpler estimator, which employs the second and the fourth moments of the signal envelope, appears to be more suitable for real-world applications.