When I go to Settings > Web sites > Mappings (not sure if the names are exactly correct as I'm using localized version - sorry about that) I can map my own 3rd level domain like
www.mydomain.com to my Google Site such as
However, 3rd level domain must always be specified so mapping like
http://sites.google.com/a/mydomain.com/my-site is not allowed.
The workaround would be to set up some custom hosting and create a simple redirect for non-www version to the www one but isn't there a way to do that directly in Google Apps somehow? I don't want to set up some separate hosting just to support the shorter URL name.