Thanks for the good advice. It does look like I can make it work with a POP account but would be wiser to use an IMAP and am thinking about changing to Google GMAIL and not have any other things interfere.
After I read what you wrote, aristobrat, I took a more detailed look at the mail section and came across the following point that you helped me look for. I just found that you can send messages with aliases, so they have gone pretty far on that score:
"Send email using an alias, a POP, or an external account
You can set up MobileMe Mail to send messages from an email alias you create or from a POP or an external account.
For example, you can use your main MobileMe Mail address with friends and family only and use an email alias for online registrations, purchasing products, joining mailing lists, and so on. This makes it easier to monitor the sources of unwanted messages."
So it looks like I should give that a try. If it works, great, if not, well get an IMAP account and switch my things over.
OK, Miles, I had to laugh. When you said "...your outdated POP account." Please please please don't think I am clinging to that thing because I love it or I am scared to get a new and better e-mail system. It's my ISP which does some amazingly outmoded things. Cincinnati Bell. I used them because I really had no reason to change the set up until now.