JPG and PNG images are already compressed, so you can't reduce file size appreciably further unless you are prepared to lose image quality.
The Image.Save method calls GDI+ function
GdipSaveImageToFile [
^]with the encoderParams parameter set to null, which equates to 75%. You could use the function directly, supplying a "proper" parameter and change that to get a smaller file size, but the quality will suffer.