Exim4, ISPs and headers

[cothrige <cothrige@bellsouth.net>]

I recently took a look at the headers of some of my mail I sent to my
yahoo account from my ISP mail account, and saw some odd stuff which
made me wonder if perhaps my setup is goofed up.  I am curious if
perhaps something like this may cause my mail to be seen as spam or the
like, and thought I would ask here just to be sure.

I have set up exim4 with "mail send by smarthost; received via SMTP or
fetchmail" and told it to hide my local address and use bellsouth.net,
my ISP, instead.  However, in looking at the mail I have sent to my
yahoo mailbox I noticed that there are a couple of "Received:" headers,
and in a couple of these rather than bellsouth.net is my local machine
address and domain.  Because my from address is the ISP and these are
different I fear they will make the mail look like spam or suspicious
somehow.

Should I be concerned about these headers?  If so, how can I address
changing this behaviour.  Should exim4 be hiding the local address even
in these rather than just the from?

Thanks for any help.

Patrick