My credit union turns down charges all the time. At one point they told me that the credit card processor they contract with treated all e-commerce transactions with California companies as being fraudulent until verified otherwise! Needless to say, I don’t use that card except locally.
Amex has been great; hands down the easiest. Big purchases (and I’m pretty sure I got to specify the threshold) result in a text message telling me to notify them if it is not authorized. The other huge – huge – advantage with Amex is that there are separate card numbers for each user on the account. If I lose or have my Amex card compromised, it only requires replacement of that one card, not three. We went through about three rounds of card replacements with our Visa cards during the Target/Home Depot/Ross credit card data exposure – I’d shopped Target, H had shopped Home Depot, and D went to Ross. With each of them, all three cards had to be canceled and then replaced, and new card numbers provided for all the autopays. I’ve put most of my autopays on Amex for that reason alone.
