[Exim] Sender header and intranet domain

My exim, configured as it is now, appends Sender header with false
domain to every mail I send out. I know exim isn't exactly supposed to
be run by dialups, but I need to use procmail and receive messages from
cron jobs. So, the question is how to disable completely appending
Sender header and possibly any other modifications to important headers.
I have weird feeling that some dumb spam filters and some misconfigured
mail servers might discard my mail.