Alpha 2.2.9: Too many open files problem

[John Connett <jrc art-render com>]

Can anyone suggest how to diagnose a "Too many open files in system"
problem?

The system is a Alpha 21164, UX2/Ruffian motherboard running Red Hat 6.0
for Alpha.  The kernel is 2.2.9 with the Linux Virtual Server
(ipvs-0.4-2.2.9.tar.gz) patch applied.

Symptoms are as follows:

Running the same workload repeatedly and monitoring /proc/sys/fs/file-nr
the file-nr count gradually increases until it reaches (4096 10 4096). 
If file-max is then raised by "echo 5000 > /proc/sys/fs/file-max" and
lsof(8) is run then ~500 files are reported as open.  What can be
happening with the other ~3500 files that the kernel thinks are open?

Are any other utilities more suitable than lsof(8) for investigating
this?

Thanks in anticipation
--
John Connett (jrc@art-render.com)