We present a hierarchical implementation of an edge-preserving smoothing algorithm on the 2 × 2 pyramid structure. The smoothed pixel values are chosen from the first three levels of the pyramid and the original image. The reduced resolution representations are analyzed in a top-down fashion by comparing the local variances with the corresponding global noise variance estimates. The global estimates are also computed in the pyramid. Close to edges the pixel values are obtained by adaptive least squares. The artifacts of region-based smoothing are eliminated by pixelwise averaging over a set of outputs obtained with the input image shifted within the 8 × 8 block of the level three parent.