This paper discusses two examples of the design and use of order statistic filters in image compression. The first example is a pre-filter. The pre-filter is designed to gently smooth the image to promote better compression. However, this filter must not blur edges significantly. Various order statistic estimators, such as a simple median, are ideal at this. In the examples given, we are able to achieve between 10 and 20% fewer bits while actually improving image quality. The second example is as a postfilter. The post-filter, used at low bitrates when image degradation is present, is designed to "average out" contouring effects while not averaging across edges.