SQL Server 2000 - "must declare variable '@ID'" after USE statement

I have a variable scoping problem.  The following (simplified) script generates 2 "Must declare the variable" errors.

What do I need to do to overcome the scope issue and use the variable against both DB's?

Thanks!

Msg 137, Level 15, State 2, Line 1
Must declare the variable '@ID'.
Msg 137, Level 15, State 2, Line 3
Must declare the variable '@ID'.

begin tran
 
Declare @ID int
Set @ID = 5
 
use Database1
go
Select @ID
go
 
use Database2
go
Select @ID
 
rollback tran

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