The sample intensity ratio estimator and the sample coherence estimator are test statistics which are generally used for detecting areas of change between two synthetic aperture radar (SAR) images of the same scene, taken at different times. Cha et al. have proposed a two-stage change detection method, where the first stage consists of the sample intensity ratio detector, and the second stage uses the Berger's statistic instead of the classical coherence estimator as an estimate of the true coherence between the corresponding pixels in the two images. It was shown with the help of experimental results that the two-stage change detector performs better than the sample intensity ratio as well as the sample coherence detector. However, they have used a heuristic approach to determine the thresholds for the two-stage change detection method. In this paper, using the joint distribution of the sample intensity ratio and the Berger's coherence estimate, an approach for determining the thresholds for this two dimensional detection problem is proposed. Theoretical receiver operating characteristics (ROC) curve analysis suggests that for a given probability of false alarm, using the proposed threshold selection method for the two-stage detector yields a higher overall performance as compared to the classical coherence estimator statistic. Also, it is shown that when some practical considerations are taken into account, a modified detector must be used in order to realize this improved change detection.