Has anybody had any luck getting the mapped domains to KEEP the www?

For example:

http://www.myprimarydomain.com has WPMU installed and running with Donncha’s domain mapping plugin. I can create

subdomain1.myprimarydomain.com

with no problems. When I point http://www.subdomain1.com to my primary domain and set up the plugin, it works fine except that the website removes the wwws (shows up as subdomain1.com instead of http://www.subdomain1.com)

How can I keep the wwws as part of the mapped domain name?