Compressing images in PDF files

How can I most effectively compress scanned page images in PDF files without unduly degrading the visual quality? I've been trying it with ImageMagick and a file that I want to compress, but so far without achieving much compression. The ImageMagick identify command, applied to one of the original pages shows: PDF 595x842 595x842+0+0 16-bit Bilevel DirectClass 63.2KB 0.000u 0:00.009 I've been experimenting a little with the -compress, -density and -quality commands of the convert command, but without as much progress as I would prefer. In most cases the output is larger than the input.