This paper investigates the accuracy of the sine-wave parameter estimators provided by the Weighted Three-Parameter Sine-Fit (W3PSF) algorithm when a generic cosine window is adopted. Simple expressions for the estimators are derived, which allows a very simple implementation of that algorithm. Moreover, it is shown that the W3PSF algorithm can be well approximated by the classical weighted Discrete Time Fourier Transform (DTFT) when the number of analyzed waveform cycles is high enough. Under that constraint the asymptotic mean square errors (MSEs) of the estimated parameters and the expected sum-squared fitting error can also be evaluated with good accuracy using very simple expressions. Then, the statistical performances of the W3PSF algorithm and the classical 3PSF algorithm are compared through computer simulations in the case of noisy or noisy and harmonically distorted sine-waves. The performed analysis allows us to identify when the W3PSF algorithm outperforms the classical 3PSF algorithm.