URLs without www. subdomain not working

I have one WordPress 2.6.1 installation with a base URL that does not contain a www. subdomain prefix, and another installation with a base URL that does contain a www. subdomain prefix. I have the installation files in a wordpress directory for both.

Page preview is not working in the installation without the www. prefix. The link goes to:

http://mydomain1.tld/?page_id=6&preview=true

where the template shows up but the content is blank.

However, I can access the preview page by going to:

http://mydomain1.tld/wordpress/?page_id=6&preview=true

In the installation with a www. prefix, page preview works fine from the URL:

http://www.mydomain2.tld/?page_id=6&preview=true

Any ideas? Is WordPress supposed to work when not including the www. subdomain?