I remember reading an article where file data (a ZIP file I believe) was converted into a bitmap image, and then it was compressed with PNG for another few % of compression.
[1]: I remember when I was taking an information theory lesson at the university and told the (video/jpeg compression guru) professor that I compressed an AVI file with my dump arithmetic coding implementation, he was shocked, turns out the file had some large crappy header from the editor
ZIP consists of sections of both compressed and uncompressed data, so some compressibility is to be expected.