Server Aliasing

I am decommissioning an NT server (OldServer) and have moved the data shares to a different NT server (NewServer). How do I make the users' shortcuts and drive mappings work?
I set up a cname entry in DNS so that OldServer.company.com is an alias for NewServer.company.com, and I've created a static WINS entry giving OldServer the same IP address as NewServer. 'PING OldServer' works fine, and I can search to \\OldServer.company.com, but if I try to search to \\OldServer (without the domain name attached) I get a 'Server not available' error message.
Unfortunately several hundred users have the \\OldServer NetBios name imbedded in shortcuts and other files, so changing the reference from 'OldServer' to 'NewServer' on their workstations is not an option.
Anybody got any ideas?

 

Yes

 

Thanks, unixfan. You're a genius.
You threw me off with the 'yes' answer. Took me a while to realize it was a link, not a put down

 

unixfan - great link.

Craig - just be aware that may be issues if you later want to alias to a 2K server.