Then I got back on with the computer company, and actually got through to the guy I needed to talk to - also named Bryan. He told me that the address had been verified, so I should stick with the same credit card, but that they said they needed to speak with me to verify the charge. Now, you may recall that I spoke with them on Sunday and on Monday. Both times I told them the amount and type of purchase and asked them to note it so it would go through. I was now Even Less Pleased.
So, I called the first credit card company, again. And, while I felt badly about it, I expressed my Extreme Displeasure to the customer service rep. She checked the account. She verified that my account already indicated that I would be making that charge - and that it had been held up anyway. She apologized profusely, took the hold off, and told me it would go through correctly.
I called back Computer Bryan, who had me wait on hold while he put the charge through again. This time it worked, finally.
Really, I'm glad that the computer company verifies shipping addresses. I'm glad that the credit card company flags large purchases, especially from computer companies. Both of those things are for my protection against identity theft, and I'm pleased that I am protected. I am, however, very annoyed that when I take the appropriate actions to let my own purchases go through, the idiot credit card customer service people can't get it right!