My bad...
I added the line
ifconfig eth0 10.0.0.12 netmask 255.255.255.0 10.0.0.255
to /etc/init.d/dhcp3-server. I commented it out, and the problem went away.
Even stranger... Removing the line didn't break the DHCP server.
<shrug> It all seems to work now. ("Seems to work" is the key part
here...)
Now, IP forwarding... ;-)
William