In synthetic aperture radar (SAR) imaging system speckle is modeled as a multiplicative noise which limits the performance of SAR image processing systems. In the literature, several SAR image despeckling algorithms have been presented, among them two simple, yet effective, approaches are using thresholding and Bayesian estimation in transform domains. In this article, we try to provide proper answer to this question: which one of these two despeckling methods works better? To this aim, we first introduce a new thresholding function with two thresholds, and show that when thresholds are determined through optimization procedures, an improved denoising performance in terms of joint speckle removal and edge saving efficiencies can be achieved. However, still a Bayesian LMMSE/MAP estimator can provide greater speckle removal efficiency in test images with high speckle power, and some thresholding methods produce better edge saving efficiency. Hence, aiming at joint exploitation of the superior edge saving ability of thresholding estimator and greater speckle removal efficiency of Bayesian estimator, we next propose the idea of using a combined despecking algorithm. The new denoising methods are applied for despeckling of true SAR images in the nonsubsampled contourlet transform domain and the situations they achieve superior performance have been highlighted.