[Exim] Skip Sender: for other domans than qualify_domain?

Is there a way I can set up Exim to skip the Sender: header not only for
From: <user>@qualify_domain, but also for From: <user>@<other domain>,
where <other domain> is a different one of the official names of the
local domain? (Listed in local_domains on the MX, but not on other
(forwarding) hosts where local delivery is disabled.)

Still on Exim 3.3x...

- Toralf