如何确定要添加到cookie白名单的网站？

There is a banking site that I cannot login to unless I allow all cookies to be accepted. I am using Firefox 3.0 and I have set it to not accept cookies except from the defined list (Tools - Options - Privacy - Cookies - Exceptions). I've added all the sites captured by Live HTTP Headers to the whitelist, but the login is still disabled. I've tried to enable all cookies and login, then look at the cookies I got - didn't see any new site to be added to the Exceptions list. Obviously the site is somehow checking if I'm accepting an arbitrary cookie. How can I find out what site needs to be whitelisted? Or do I not understand something about cookies, and accepting all cookies is somehow not the same as having all the right sites whitelisted?There is a banking site that I cannot login to