Synthetic aperture radar (SAR) images are inherently affected by multiplicative speckle noise. Two approaches based on modeling the nonsubsampled Shearlet transform (NSST) coefficients are presented. Two-sided generalized Gamma distribution and normal inverse Gaussian probability density function have been used to model the statistics of NSST coefficients. Bayesian maximum a posteriori estimator is applied to the corrupted NSST coefficients in order to estimate the noise-free NSST coefficients. Finally, experimental results, according to objective and subjective criteria, carried out on both artificially speckled images and the true SAR images, demonstrate that the proposed methods outperform other state of art references via two points of view, speckle noise reduction and image quality preservation.