When an image is smoothed using small blocks or neighborhoods, the results may be somewhat unreliable due to the effects of noise on small samples. When larger blocks are used, the samples become more reliable, but they are more likely to be mixed, since a large block will often not be contained in a single region of the image. A compromise approach is to use several block sizes, representing versions of the image at several resolutions, and to carry out the smoothing by means of a cooperative process based on links between blocks of adjacent sizes. These links define 'block trees' which segment the image into regions, not necessarily connected, over which smoothing takes place. In this paper, a number of variations on the basic block linking approach are investigated, and some tentative conclusions are drawn regarding preferred methods of initializing the process and of defining the links, yielding improvements over the originally proposed method.