df & du showing different usages for /var

[alex at schnarff.com]

After nearly running out of space on my /var partition recently, I went 
in to clean things up and ensure that it didn't happen again. Using the 
"du" command to look for offending directories and files, I wiped out a 
bunch of old Apache and Qmail logs...and then found that I was still 
using 90% of the partition. So I cd'd over to /var, and got this rather 
surprising set of results:

[alex at tms /var]$ sudo du -sh
395M    .
[alex at tms /var]$ df -h
Filesystem     Size    Used   Avail Capacity  Mounted on
/dev/ad4s1a    484M    126M    320M    28%    /
devfs          1.0K    1.0K      0B   100%    /dev
/dev/ad4s1f    269G     40G    207G    16%    /data
/dev/ad4s1d    9.7G    7.2G    1.7G    81%    /usr
/dev/ad4s1e    1.9G    1.6G    173M    90%    /var

These wildly different results have me confused. How in the world can 
there be a ~1.2GB difference between the disk space in use as reported 
by these two tools? Which is right? More importantly, how do I fix this?

Thanks,
Alex Kirk