A small trick if you are bordering on the cutoff point from one rate to another. Just add a little bit more size and weight in your admin page per item to get you over the border. It will help.

Just another point we have our site set up to send the suppliers an invoice for the customer, a packing slip for the supplier records and an address label.
Our drop ship suppliers know they are not to add in any of their own documentation or promotional fliers. It is OK if the supplier plays the game but some don't. I am sure you will know about this.
Good Luck