A new promising method of speckle filtering is described and applied to both, synthetically generated and real SAR-images. The new method, which the authors call EPOS (Edge Preserving Optimized Speckle-filter), is based upon the statistical properties of speckle noise. The knowledge of speckle variance allows the distinction of homogeneous areas from those, containing edges or single scattering targets. This discrimination method is used within a variable sized filter matrix to choose a region, which is suitable for calculating an intensity average, that is typical for the center pixel. Also a method for estimating speckle noise parameters is presented.>