I want to use a Postfix box to do two things:

• Relay mail from any host on the internet addressed to one of my domains to my Zimbra server
• Relay mail from my Zimbra server to any address on the internet.

To try and accomplish this I have configured Postfix thusly:

mynetworks = 127.0.0.0/8, zimbra_ip/32
myorigin = zimbra_server
mydestination = localhost, zimbra_server
relay_domains = example.com example.org
transport_maps = hash:/etc/postfix/transport_map
local_transport = error:no mailboxes on this host

transport_map looks like this:

example.com smtp:[zimbra_server]
example.org smtp:[zimbra_server]

Now, this works and passes the Open Relay tests. However, I am seeing in the maillog that the server is relaying spam that has a From: address of <> to domains that are not mine. How do I stop this behavior?