Q. My father has exceptional credit and has agreed to let me rebuild my own credit by becoming a cosigner on his card. He has been an American Express cardholder for many years, but American Express told me they would only allow my father to add me as a secondary cardholder. That won't help me rebuild my credit. Which cards will allow me to become a cosigner on his card?

A. As you've discovered, not every credit card company plays by the same rules. In some cases, the rules change depending on whether you're applying for a basic credit card or the company's Gold, Platinum or Kryptonite card.

The good news is that most banks are willing to add cosigners (sometimes called joint users) to a credit card account. For example, Chase simply requires the existing cardholder and the new cardholder to sign forms to add the cosigner.

Some banks define a cosigner as a backup person who's legally responsible for paying the account balance if the cardholder doesn't. Whether you're called a cosigner, joint user or a different name altogether, what's important is that you are legally responsible for the account balance. That way, the account activity shows up on your credit report to build up your credit history and score.

If your father doesn't have another credit card (Visa, MasterCard or Discover, for example), the two of you can apply for a new card as cosigners. A new account doesn't give your credit score the immediate boost that being a cosigner on his existing card would. His exceptional credit history, though, makes it easier to find a bank that will approve your application.

You didn't mention whether you have bad credit or a meager credit history. Either way, you also can apply for a credit card without your father's help. For example, credit unions and community banks often pride themselves on starting people out on the right foot financially.

Open a checking or savings account at a credit union or local bank. Then apply for a credit card.

A secured credit card is another option for jump-starting your credit history. With this type of card, you deposit money into a savings account at the financial institution. Your card limit is secured by the amount in the savings account. If you don't pay your balance -- you guessed it -- the bank takes the money from your savings account.

Credit unions are a great place to go for secured credit cards, too. Check out our advice on how to get the best secured credit card.