I agree with the original poster. This was one of the first things I asked
about some time ago and was told then also that there's nothing that can be
done about it. Since every time this happens it's nothing more than that one
of my many email accounts failed to get new mail from one server or another,
NEVER a big deal at all since it just gets it at the next schedule. It is
quite near infuriating to have to either watch that unnecessary bouncing icon
or stop what I'm doing to bow to the new master of my attention.

<grin>
I still say that there must be some way to block the "tell" to OS-X that there
is some catastrophe in the works. Even if it was something bigger than just
missed mail, I still can see the little exclaimation icon at the bottom and
know that something is there to look at. More than that is a major nuisance.