Also if you've been late or missed a payment in the last six months it may be tough to get the credit card company to work with you.
Try the script below; if you have success let me know about it.- "Hi, my name is (your name here). I'm a good customer, but I've received several offers in the mail from other companies with lower annual percentage rates. I really want a lower rate on my card. Can you help me?"
If the answer is no, ask to speak to a supervisor. If the answer is still no, ask for another supervisor.
Also don't be shy about letting the company know you would consider closing the account unless they can lower your rate.