The presence of speckle in radar images reduces the radiometric resolution and renders less efficient the procedures for texture class discrimination. We present an algorithm devoted to speckle reduction in synthetic-aperture radar images based on a homomorphic filter coupled with a Wiener filter. To construct the Wiener filter we analytically evaluate the autocorrelation function of the noise, starting from the first two orders of statistics of the noise, before performing the homomorphic transformation (a logarithmic one, in the case of multiplicative noise), and the autocorrelation of the noise-free image is evaluated by an iterative procedure. The algorithm, tested on both simulated and actual synthetic-aperture radar images, provides very promising results and shows the usefulness of the proposed method.