You must disable "Strict Name Checking" on Windows 2003 server to allow the server to respond to a DNS alias. This is done via registry editing:
HKLM\System\CurrentControlSet\Services\LanmanServer\Parameters
Value name: DisableStrictNameChecking
Data type: REG_DWORD
Radix: Decimal
Value: 1
This allows the Server "Server1" or "Server1.MyDomain.Pri" to respond to a DNS entry like "CoolService" or "CoolService.MyDomain.Pri"... This is disabled by default, as it loosens security. It is not recommended to do this in a DMZ or Internet Zone.
FYI, a reboot is required to make the change work.