Discover card has gone back and forth on this. They had a tool on their site to give you a throwaway CC #. I used it for almost all online purchases. It went away for a short time, then came back. Now it looks like it is gone for good. I quit using their card since that was the only reason I had to use it over others.

Now if they'd only stop sending me "checks" in the mail that are tied to my account... I'm just waiting for those to be spent by someone else.