Debian :: Run Fsck During A Shutdown Sequence?

I want to be able to run fsck at, or near, shutdown at the end of the day, and not have to wait for it when booting (important now that I have 1TB drives!). As far as I can tell, the only way to arrange to run fsck on the root partition is if it is unmounted and I believe that only occurs at reboot time.

So, I thought of using the /forcefsck file that, when exists, will force file system check upon the next boot. So I envision having a script that touches that file, or issues the right shutdown command, then lets the system reboot and thus forcing a fsck of the root partition. However, I then want the system to turn right around and then shutdown, so that when I cold boot the system in the morning, I won't see the fsck run at that time, ever.

So I think this boils down to being able to run a one-time init script or something like that. Is there an established way or idiom for running an init script only one time? I know I can create a non-standard init-script that looks for a special file like is done for /forcefsck, and only shutdown if that file is seen, but surely someone else has already come up with a canned solution/init-script to what I want to do.