Subdomains and multisite

I’m using WordPress 3.0 in multisite mode. I’ve created sites under my primary domain: https://www.primarydomain.com/site1 and https://www.primarydomain.com/site2.

I want to create blogs from the same installation in a subdomain of that site, which is actually subdomain.primarydomain.com, but appears publicly as the separately registered subdomain.com. That is, I want to create the sites https://www.subdomain.com/site1, https://www.subdomain.com/site2, etc.

Don’t know how to get there from here.