FW800 drive spins up when laptop asleep

I've searched for similar issues, but haven't run across this one.

My rMBP is usually run in clamshell mode with a Thunderbolt Display attached, with one of two Lacie Firewire 800 drives attached to the monitor (an old 2006 Lacie 500GB dual-drive that's still chugging along, and a brand-new My Book Studio). The drives work fine when the computer is awake and active - but when I put the laptop to sleep, the drive spins down (like I expect) - but then maybe 10 seconds later, it spins back up. Then a few seconds later back down. Then back up - over and over. Even when I dismount the drive (but leave it plugged in) before sleeping.

Any suggestions on how to stop this, short of pulling the drive's power plug every time?

Jason