I used to work at a place that prints and sends out magazine renewal bills. I unfortunately know how they work. Look to see if the address is Boone, Harlan or Red Oak Iowa. If it is...this is the company that I worked for. They are really good at ignoring your requests to stop. Once you are in their system it is a royal pain to get out of it. This company is part of the Hearst Corporation that is called CDSGlobal. Once you order a mag, they send a renewal about a month after you first bought the subscription...just to get you to extend it. About 6 months later they do it again and usually every six months there after. There is another company that the return mail goes to Florida and they do the same with their renewals. Good luck with this and I hope that you don't fall into their traps.
I personally don't get mags thru them and if I do I throw away all renewal notices, even if it is about to expire.