Lighttpd init script doesn't work on Debian Wheezy

Question

[EDIT] I have found why it did not work, I just had to add the directive

server.pid-file             = "/var/run/lighttpd.pid"

to the lighttpd.conf file.

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I can't figure out why the lighttpd init script doesn't work to stop the server. I'm running Debian 7 Wheezy and Lighttpd 1.4.31. My system is also up-to-date.

When issuing:

# /etc/init.d/lighttpd stop
[ ok ] Stopping web server: lighttpd.

But then lighttpd is still running:

# ps aux | grep lighttpd
root      2024  0.0  0.2  70696  1184 ?        S    15:16   0:00 /usr/sbin/lighttpd -f /etc/lighttpd/lighttpd.conf
root      2428  0.0  0.1   7832   880 pts/0    S+   15:27   0:00 grep lighttpd

When removing "quiet" from the stop part of the script to get more details which gives:

if start-stop-daemon --stop --retry 30 --oknodo \
            --pidfile $PIDFILE --exec $DAEMON

I get this output:

# /etc/init.d/lighttpd stop
[....] Stopping web server: lighttpdNo /usr/sbin/lighttpd found running; none killed.
. ok 

whereas /usr/sbin/lighttpd is actually running as shown by the ps command.

Thank you for your help.