It's hard to say without knowing more about the file. One thing for certain...do not embed your images. Use Distiller to create a press ready PDF. And, as the previous post suggests, Save As > de-select PDF compatability. You can also use "Zip It" to Zip your files into a compressed file. This is important because if you are not sending a PDF, the print vendor will need all of your source files ( i.e., PS Files, Fonts, and Ai Files ).
Do you want to send a smaller Illustrator file (fully editable)? Do you want to send a smaller PDF file (not easily editable)? Do you want to take an existing file and compress it using other software like zip?
Since you are sending a file to a printer, I will assume the latter. You should never concern yourself with the size of a file you are getting printed. Size of file is at the very bottom of the list of your priorities, below the order of operations when putting on your shoes. Compressing a file or files with zip is a good way of keeping things organized and preventing a file from getting messed up in transit. The fact tat the file is usually smaller is incidental.
If you re on a Mac, just select the files you need in the Finder and right-click and select Compress X Items. You will get a zip file called Archive.zip if more than one file was selected. if only one file was selected you’ll get the full filename, with extension, plus .zip. So Letterhead.ai will become Letterhead.ai.zip. I like to edit the filename to strip out the middle extension. This only affects the name of the .zip file, not the Illustrator file embedded within. Now send that file. If it is too large for email, then use another method like Dropbox.com, FTP, or Yousendit.com.