Gunter,
After you crop/edit the .jpg click [File>save as], this should bring you to a file save box with the option of compressing the image (may have to click a "properties" button to get this option). Most I've seen are by pecentage, 10% is usually plenty to shrink the file size without real quality loss.
If you don't have a program which does this,
www.irfanview.com offers a frreware that is a breeze to work with.