Russ,

I think you may have figured it out.  I just tried your suggestion -- and
after a reboot, it appears that the Outlook Outbox is no longer puzzling me.

FYI [and, esp. for others who may encounter the same puzzling behavior] -- a
bit more background now that your solution seems to have done the trick:

I am currently using Norton Internet Security 2005 [AV + Antispam +
Firewall] -- which came with the new machine.   The old machine used Norton
AV 2005, Zone Alarm Firewall and *no* dedicated anti-spam program.   The old
machine had Norton AV set to scan incoming email, and there were no problems
with Outlook's Outbox.

So, with your suggestion in mind,  I retained NAV's setting to always "scan
*incoming* email".   I turned off Norton AV's *outgoing* email scanning [it
defaults to scanning outgoing mail].  I also turned off, entirely, the
Norton Antispam feature, including its default integration with Outlook.  As
I more carefully investigated its configuration settings, I noticed that
Norton Antispam defaults to scanning incoming email [IMHO, a good idea] and
*outgoing* email [at my level of expertise, I am not at all clear as to why
I would want that as a feature].

I may go back later on, and try the Antispam with some tweaking, to see what
that does.  But frankly, after a month with the new machine, I have not yet
seen much value to the Norton Antispam setup -- as my ISP used Brightmail
and, spamwise, does a pretty good job lately.  Over the past month, using
its default settings, the Norton Antispam caught nothing.

Thanks again for your help.

albert