There has been a growing interest in synthetic aperture radar (SAR) imaging on account of its importance in a variety of applications. One attribute leading to its gain in popularity is its ability to image terrain at extraordinary rates. Acquiring data at such rates, however, has drawbacks in the form of exorbitant costs in data storage and transmission over relatively slow channels; thus, addressing these problems is clearly important. To abate these and related costs, we propose a segmentation-driven compression technique using hierarchical stochastic modeling within a multiscale framework. Our approach to SAR image compression is unique in that we exploit the multiscale stochastic structure inherent in SAR imagery. This structure is well captured by a set of scale auto-regressive (AR) models that accurately characterize the evolution in scale of homogeneous regions of different classes of terrain. We thus use them to generate a multiresolution segmentation of the image. The segmentation is subsequently used in tandem with the corresponding models in a pyramid encoder to provide a robust, hierarchical compression technique that, in addition to coding the segmentation, achieves high compression ratios with impressive image quality.