In the beginning, they go by FICO.
After about six months, your payment history with them begins to figure into their reckoning of you as a customer. Keep good history for a year or so, and at least some overall credit sins and marginal FICO can be forgiven. If your credit history is really checkered, you might need 15 to 18 months of good history.
I had FICOs in the mid to high 500s, with charge-offs, and got a secured BofA card. After getting my FICOs into the 600s, and maintaining a year of solid payment history and getting utilization down, they graduated the card last week.
The keys to getting CLIs are:
* don't get baddies anywhere else
* pay on time
* keep utilization 20% or less
* but DON'T sockdrawer the card. The CC cos want to see some usage.
Do this, and you will get CLIs. But like I said, if your CR is badly checkered, it might take some time.