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The interpolated fast Fourier transform (IFFT) was one of the first methods for the highly accurate estimation of sine wave parameters, and its first successful descendant was analytical leakage compensation [which is commonly called analytical solution (AS)]. The AS estimate of frequency is a whole class of solutions whose variance depends on a free parameter K. Thus, to extract the minimum variance solution from a theoretically infinite set, we have to find the optimal value K opt. This paper clarifies the mathematical background of AS and proposes two new solutions for K opt, which reduce the variance of AS estimates of low and high frequencies close to an integer. All inferences are justified by simulations, which confirm the validity of theoretical considerations.