[exim] generating a correct message-id

Hi,

how can I get exim to generate a correct message-id
in the form of <MSG-ID>@swanni-und-michi.de or
<MSG-ID>@mail.swanni-und-michi.de ?

Till now my exim 4.42 generates the message id - sorry,
my MUA isn't able to do this (Thunderbird) - taking
the internal network domain "stargate.swami.net"
whereby this is absolutely nonsense in my case, just
because of the fact that the domain "swami.net" exists
in real life but has absolutely no association with me.

So how can I tell exim to produce correct messages id's??

Any hints appreciated!

Thanks,

Michael