How do you correctly close an Open Relay? Failed abuse.net mail relay test

[Vatoloco]

Originally I thought I was okay because I ran the test at dnsreport.com and it told me this:

PASS Open relay test OK: All of your mailservers appear to be closed to relaying. This is not a thorough check, you can get a thorough one here.

So I ran the thorough one here just to be sure:

http://www.abuse.net/relay.html

Abuse.net gave me the results with the following message:

Relay test result
Hmmn, at first glance, host appeared to accept a message for relay.
THIS MAY OR MAY NOT MEAN THAT IT'S AN OPEN RELAY.

Some systems appear to accept relay mail, but then reject messages internally rather than delivering them, but you cannot tell at this point whether the message will be relayed or not.

If it is really an open relay, the test message will be delivered to you. If you do not receive the test message in your e-mail in the next few hours, it IS NOT an open relay.

I DID receive this e-mail from abuse.net:

This is a test of third-party mail relay, generated via the
Network Abuse Clearinghouse at http://www.abuse.net.

Target host = cpanel.mywebsite.com [MY.IP.ADD.RES]
Test performed by <support@mywebsite.com> from MY.IP.ADD.RES

A well-configured mail server should NOT relay third-party email.
Otherwise, the server is subject to abuse by vandals and spammers,
and probable blacklisting by recipients of the unwanted third-party
e-mail.

So does anyone know what to do to close the open relay?

I found this post which suggested to run the following command:

/scripts/fixrelayd
/etc/rc.d/init.d/antirelayd restart
service exim restart

After doing that and re-checking at abuse.net, I still received the e-mail.

[GOT]

This deserves a close look. I got the same results. Havn't put an actual email address in there yet though.