hosting a subdomain only...

We're looking to setup hosting for a subdomain only. The main domain is hosted and managed elsewhere (we don't have control over it) and we're looking for the quickest/best way to transfer one of the subdomains to our dreamhost account. We don't have control over the DNS records, but can make requests for the subdomain be redirected.
Example:
www.mydomain.com (main site hosted elsewhere, will stay there)
mysub.mydomain.com (currently hosted elsewhere, but content to be transfered to DH)

Questions:
-What is the best way of going about this setup in DH?
-should we setup a fully hosted domain called mydomain.com on DH, then add a subdomain called mysub.mydomain.com, the transfer the content?
-What about the DNS setup? What request should we make for the subdomain?
-Is it better just to setup a fully hosted domain called something else (ex. mydomain1.com) with a dedicated IP and then just have the mysub.mydomain.com subdomain DNS point to our DH mydomain1.com?

Thank you in advance!

Best way: Yes, create mydomain.com first, then set up the subdomain. Being lazy, I'd just go with this, and add the IP address to your DNS and be diligent about keeping the DNS entry up to date.

Another option (but I've not tried) is to use a CNAME entry with your DNS provider. Create MYSUB.dreamhosters.com, then add a CNAME that points sub.domain.com to MYSUB.dreamhosters.com. This is similar to the last idea on your list, but without the hassle of a dedicated IP address.

-Scott