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Many thanks for that, Chris. (It seems that's what you would like to be called.) Needless to say, once again Firefox is so much better than bloody IE in practically every respect that it's beyond comparison. I hope I remember your instructions when I need a password remembered or unremembered.
But IE is so-o bloody ridiculous. Not only nothing like that, but nothing at all. There under Security Custom level I did find I hadn't checked 'Automatic login with current username and pw'. But neither that nor deleting all passwords under General, which I didn't want to do, checking and unchecking various Autocompletes under Content AutoComplete settings, re-opening IE every time, will make it remember or ask to remember the password once told not to. I have combed the help files till my BP is about to go asymptotic.
Any other ideas?