Re: [Exim] Cannot deliver mail to hotmail.com

After doing some more research, I'm guessing the problem has to do
with hotmail.com doing reverse dns lookups on my host and not liking
what it sees. I'm not sure what's wrong with my setup, so here's a
short summary:

My machine is assigned via dhcp the (usually* permanent ip
66.31.190.121, and the ugly hostname h00a0cc56d269.ne.mediaone.net. I
own the domain bignachos.com, whose dns entry points to the ip, and
the primary mx points to the ugly hostname.

I have the secondary mx point to the ip, but I believe this is a bad
idea. True?

In my exim.conf file, the relevant settings are:

qualify_domain = bignachos.com

# These ones probably aren't relevant...
local_domains = localhost:bignachos.com:h00a0cc56d269.ne.mediaone.net
local_domains_include_host = true
local_domains_include_host_literals = true
relay_domains_include_local_mx = true

Anything I missed? Does the problem have to do with my machine
thinking its hostname is h00a... but reports its name as bignachos.com
when delivering mail? How could I fix this?

Thanks for your time.

--
Brian Nelson <nelson@???>