1.) I save them as pngs initially, then I save them separately as low-quality jpegs.
2.) I layer the jpeg copy on top of the original png so that I can make a clean selection around the image without the compression artifacts getting in the way.
3.) I use the clean selection on the png copy to cut out the white space on the compressed jpeg copy.
4.) Then I save it as a png so I can have the compression artifacts as well as the transparency.
So basically it's a png converted to a low-quality jpeg, cropped, and converted back into a png.