I thought I'd better show a more complete Console log...
4/20/12 11:56:17 PM kernel Wake reason = OHC1
4/20/12 11:56:17 PM kernel System Wake
4/20/12 11:56:17 PM kernel Previous Sleep Cause: 5
4/20/12 11:56:17 PM kernel The USB device Back-UPS CS 350 FW:805.q8.D USB FW:q8 (Port 3 of Hub at 0x4000000) may have caused a wake by issuing a remote wakeup (2)
4/20/12 11:56:18 PM kernel Trying to change a collection in the registry
4/20/12 11:56:18 PM kernel Backtrace 0x509f98 0x509c53 0x9cf403 0x9d1807 0x9d0572 0x9cc1dd 0x9c6f29
4/20/12 11:56:18 PM kernel Kernel Extensions in backtrace (with dependencies):
4/20/12 11:56:18 PM kernel com.Logitech.Control Center.HID Driver(3.4.0)@0x9ba000->0x9e5fff
4/20/12 11:56:18 PM kernel dependency: com.apple.iokit.IOUSBFamily(4.2.4)@0x941000
4/20/12 11:56:18 PM kernel dependency: com.apple.iokit.IOHIDFamily(1.6.6)@0x977000
4/20/12 11:56:18 PM kernel dependency: com.apple.iokit.IOUSBHIDDriver(4.2.0)@0x9b3000
4/20/12 11:56:18 PM kernel 00000000 00000020 NVEthernet::setLinkStatus - not Active
4/20/12 11:56:18 PM configd[13] network configuration changed.
4/20/12 11:56:19 PM kernel Ethernet [nvenet]: Link up on en0, 100-Megabit, Full-duplex, No flow-control, Debug [796d,0000,0de1,0005,41e1,0000]
4/20/12 11:56:19 PM kernel 05f5e100 00100026 NVEthernet::setLinkStatus - Active
4/20/12 11:56:19 PM kernel Ethernet [nvenet]: Link up on en0, 100-Megabit, Full-duplex, No flow-control, Debug [796d,0000,0de1,0005,41e1,0000]
4/20/12 11:56:19 PM kernel 05f5e100 00100026 NVEthernet::setLinkStatus - Active
4/20/12 11:56:20 PM configd[13] network configuration changed.
4/21/12 12:09:19 AM ScreenSaverEngine[771] __CFServiceControllerBeginPBSLoadForLocalizations timed out while talking to pbs....."
I know that OHC1 is "Open Host Controller" and that it usually refers to an external FW or USB device, which is what the UPS is....I reckon. It also mentions "Logitech Control Center" because I'm using a Logitech wireless mouse; but I don't think that's the problem; I believe that process happens on every 'awakening'.