For no apparent reason, my G4 Macintosh PowerBook, running OS 10.4.7,
has started waking up only moments after I manually put it to sleep
(which I do several times each day.)

I've determined that the problem is my Logitech wireless mouse
(Mouseman Optical) and/or keyboard, the "receiver" for which plugs
into a USB outlet.

I unplugged the receiver and, Voila!, when I put the computer to
sleep, it stayed asleep. When I re-plugged in the receiver, the
computer awoke. When I put it to sleep again, it immediately
re-awakened.

Thinking that the problem might be traceable to the recently released
Security Update, which I installed (but NOT without first unplugging
all USB devices, something I realized only belatedly that I should
have done), I re-installed an earlier version of the OS (10.4.3) but
the "not sleeping" problem persisted. I've now upgraded to 10.4.7,
where I was originally, and, of course, the problem remains.

I visited the Logitech Web site looking for an updated version of their
Device Manager (version 1.0 is currently installed) but failed to find
ANY versions and was, instead, directed to something called an
"LCCDaemon" (Logitech Control Center) which I downloaded and
installed, but nothing changed. I have not uninstalled the Device
Manager.