[exim] From and Return-Path rewrite problem

Hi list,

I am new to Exim (running it on Debian 6) and I have the following
problem. I hope my fellow Exim-users can help me!

I am sending mail from a PHP script. I have checked that it's really
sent by Exim. The From-Header I add in the script is, I guess,
overwritten by Exim. The scripts looks like this (excerpt).

$headers  =  "From: Display Name <do-not-reply@???>\r\n";
$headers = "Content-Type: text/plain; charset=\"utf-8\"" . "\r\n";
$subject = "=?UTF-8?B?".base64_encode("The subject")."?=";
if(mail("testaccount@???",$subject,"TEST",$headers)){
    echo "true";
} else {
    echo "false";
}

It works BUT the From-Header is overwritten to something like this:
From: www-data <www-data@???>. The domain3.com is also legit on
this server but not the domain I want to be used.

Above all, I need to know from where Exim possibly retrieves domain
names. I've already checked /etc/mailname and /etc/hostname. They are
IMHO okay!

Thanks for any help!
Bata