When the user uploads an image with a large file size, I would like to allow him/her doing this (not restricting the file size generally, because many users don't know how to resize an image by themselves), BUT after this, I would like to decrease the file size of this image (the original file!) somehow to save disk space (lossy compression/resizing/etc.).
My site is on a shared hosting, so unfortunately ImageMagick is not available.
This question is very closely related, but does not contain any detailed information about the specific solution: How can I reduce the file sizes of the original versions of uploaded image files?
I also found the ImageAPI Optimize module, which can solve the optimization of the image via the online Yahoo! Smush.It service, but optimization is not a restriction for the file size.
There are some related topics about limiting the file size of an image on Stack Overflow and Super User too:
Is there a Drupal-based solution for this task?
If it's unaccomplishable or too complex, maybe I should use an integrated solution with http://www.jpegmini.com/, but I don't know any modules which solves this.