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Are you a valued customer? If you use your credit card and pay you minimum balance or more consistently, you should be considered a valued customer. The credit card company's ideal customer is someone who both spends money on their credit card AND pays the money back consistently. If you meet those criteria you can call them up and request a lower rate. Often they will comply especially if you mention that you are considering a change to a different credit card company.
Consider changing to a different credit card company. If you will have available funds within a relatively short amount of time, you may consider a balance transfer to another credit card which offers 0% interest or other benefits for transferring your debt. Be leery of these offers as they usually will jump to astronomical rates after the term has lapsed. You have to be prepared to pay the card off and cancel it by the end of the term or you will have gotten yourself into another high
Locked-rate cards are an interesting concept. It is exactly what it sounds like. The rate for a specific charge is locked in and can never change. If you negotiate a good rate, that can be helpful. Just remember that credit card companies pay off the lowest rate debt first so this is only beneficial if you larger purchases are made at a lower rate. The cards are not as beneficial as they seem at first, but they can be a viable option. Just don't pay extra for these types of agreements as it will cost you more in the long run.
If you credit card debt is causing you to struggle financially to the point of hardship, you may want to claim a hardship with the credit card company. Explain the situation to them thoroughly and they may be able to help. Remember that if you file for bankruptcy, no one wins so you should definitely ask. They may be able to offer a lower rate or a reduced monthly payment for a short term.