We present a new approach to SAR image segmentation based on a Poisson approximation to the SAR amplitude image. It has been established that SAR amplitude images are well approximated using Rayleigh distributions. We show that, with suitable modifications, we can model piecewise homogeneous regions (such as tanks, roads, scrub, etc.) within the SAR amplitude image using a Poisson model that bears a known relation to the underlying Rayleigh distribution. We use the Poisson model to generate an efficient tree-based segmentation algorithm guided by the minimum description length (MDL) criteria. We present a simple fixed tree approach, and a more flexible adaptive recursive partitioning scheme. The segmentation is unsupervised, requiring no prior training, and very simple, efficient, and effective for identifying possible regions of interest (targets). We present simulation results on MSTAR clutter data to demonstrate the performance obtained with this parsing technique.