I just downloaded and compiled tg3.ko kernel module. Where should I put it on a Debian system? There is one in /lib/modules/2.6.32-5-xen-amd64/kernel/drivers/net/tg3.ko already.Ideally, I would like to leave the original one where it is, and bump the priority for mine. So if mine doesn't get loaded or disappears, the original is still there as a fallback.The only way I know to do it is dpkg-divert, but I feel a slight shiver in my stomach when I use it. It is especially scary to do it on a server, with the network module. :)
proper way to overwrite debian kernel modules
debian;package management;kernel modules
Place your module in /lib/modules/2.6.32-5-xen-amd64/updates/ (make the directory if it doesn't exist) and re-run dpkg-reconfigure linux-image-2.6.32-5-xen-amd64 (or just run depmod if you know how).  Check that the new driver is found with modprobe -l tg3.Read man 5 depmod.conf for more details.