By default the friendly URL generated is generated like so:
/<sitecodename>/media/<librarycodename>/<folders-or-files>
OR
/johnsmith/media/images/logo.png
If you do not use the permanent URL you will get something like above, otherwise the permanent URL is how it is unless you re-wrote a bunch of code.
You do have the ability to change the path that is setup in the settings which would modify the non-permanent URL although I'm not sure it will get much shorter than what I've shown above.