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Sinusoidal frequency estimation based on discrete Fourier transform provides accurate results for well-separated spectral tones. However, if a single sinusoid is disturbed by other tones, estimation accuracy may suffer significantly. In particular, the bias can increase considerably when the frequencies of the disturbances are close to that of the desired sinusoid. In addition to frequency estimation by maximization of the Schuster periodogram, examining a frequency located on the opposite side of the disturbance at the edge of the cost function may reduce its influence on the bias of the estimator. In this paper, we present an empirical appraisal of this bias reduction. Since our edge estimation procedure increases the variance of the estimated frequency, we also present an analytical method for assessing this increase. Possible applications are measurement or tracking tasks where frequency estimates with low bias are essential to the working of an overall measurement system. Further, we describe a method that combines the advantages of peak and edge estimation. All results were validated using simulations and data obtained from a frequency-modulated continuous-wave radar system.