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The probability density function (pdf) of the multi-look interferometric phase between two complex synthetic aperture radar (SAR) images is parameterized by the number of looks and the complex correlation coefficient. In practice, adjacent pixels in a real SAR interferogram, are statistically dependent due to filtering, and hence, the number of looks is usually smaller than the number of samples averaged. It has been shown that compensation with an effective number of looks, rather than an intractable rederivation of the pdf, can account for the statistical dependence. This paper addresses the challenge of how to determine a suitable value for the effective number of looks. It is shown that an optimum value can be found via a maximum-likelihood estimator (MLE) based on the interferometric phase pdf. However, since such an MLE is computationally intensive and numerically unstable, an estimator based on the method of moments (MoM) possessing similar fidelity is proposed. MoM is fast and robust and can be used in operational applications, such as determining constant false alarm rate (CFAR) detection thresholds for moving-target detection in SAR along-track interferometry.