Suppose you have a .jpg photo such as this apple:

(.jpg 24KB)

You use GIMP to add an alpha channel and remove the white background. As .jpg does not support transparency (see this question), you have to export as a .png file (90KB).

The photo is meant to be used on a webpage or in a (LaTeX) document, and you do not which to have the increased file size. You open the .png file in GIMP and export it as .png, while selecting a compression level of 9 (the maximum). However, this yields a .png file of 96KB.

-> Why? Is there a way to obtain a .png file arount the original file size of 24KB?