Shared printer and mapped drive waking up computer from sleep

I have a usb printer hooked up to the desktop in my office. I shared it so
that other computers in the house can use it. I also enabled the wake on lan
feature on the desktop in the office.

If I configure another computer to use that shared printer, the desktop that
it is hooked up to will keep on waking up from sleep. I checked the System
logs, and I see that the computer in the office is entering a sleep state,
but for only a couple of seconds. It will resume because it detects network
activity. It took me forever to figure out that it was the shared printer
that was waking it up... although there is nothing in the queue. If I remove
the shared printer from the other desktop, the desktop in the office goes to
sleep as scheduled and does not wake up unexpectedly.

I also noticed this if I map a network drive to the office computer.

Is there a way around this?