How to recover disk space after "filesystem full"

[Luke Dean]

Yes, it sounds like a stupid question, but let me tell the story.

The log for my dhcp server filled up /var last night, which meant that
dhcpd was also unable to hand out new leases, which meant that I had
effectively been DOSed.  I'll have to look into changing my logging
policies.

So, to correct the problem, I log into the router, removed the big
log and several other files in /var to free up some space, and assumed
this would correct the problem.

It did not.
Several minutes after freeing up a lot of space on /var, I continued
to get "filesystem full" messages and "df" continued to show the
capacity at >100%.  I checked "df -i" for the inodes too.  That was
fine.  I ran a quick fsck to see if that might shock the system into
seeing all the space that I'd freed up, but no good.

I ended up rebooting the box.

Was there any other possible solution I could've tried?

Why wouldn't the free space immediately appear as free?