When I tried out Image Analyzer The other day, I was surpised to see that it had a lossy saving option for PNGs. Some research brought me to THIS page, which has another lossy PNG project. There is also Pack4PNG HERE, and LZD HERE. Image Analyzer appears to be the only program so far that has implemented this form of PNG compression. I have run some tests on 3 different images. One is a photograph with some text on it (usually best as JPG), one is a comic strip (usually best as 256 color PNG), and one is a video game screenshot (works pretty well as JPG or 256 PNG).
The comic strip is small and there are only three images, so I am putting them on this page. The others are larger and have many test images, so they are on their own pages.

Video game screenshots \ Photo with text

Image Analyzer defines lossy PNG levels as -1 through -30 quality, with -30 being as low quality as it goes.
As you can see in the following pictures, using lossy PNG compression on 256 color images actuallt INcreases the filesize while DEcreasing the quality. It does however, work quite well on true color images. Lossy PNG works best on images with lots of small details. It tends to produce a blocky effect on images with large sections of solid colors, and a smearing effect on gradients (especially noticeable in pictures of sky).

104k BMP

34.1k Lossless, 256 color PNG

40.4k Lossy (-30 quality) 256 color PNG