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The ability of a modified covariance method "maximum entropy" spectral estimator to estimate the frequencies of several sinusoids in additive white Gaussian noise is studied. Analytical expressions for the variance of the spectral estimate peak positions at high signal-to-noise ratios ate derived. The calculated variance is compared to the Cramer-Rao lower bound and to the results of similar variance calculations for the more familiar covariance method. It is shown that performance approaching the Cramer-Rao bound can be obtained. Simulations demonstrate substantial agreement with the analytical results over a wide range of signal-to-noise ratios.