Reaching another database using dynamic SQL

[InvisibleDuncan]

I want to get some data from another database. The name of the other database can change depending on the context, so I figured I'd build the SQL dynamically and execute it. However, it's not doing what I expected. My code is this:

Select  @SQL    =   '
Select      @PolicyName     =   PolicyName
From        ' + @DatabaseName + '..uvwSchemeAdministratorDetails
Where       PolicyNumber    =   ''' + @PolicyNumber + ''''

Select @SQL;

Execute @SQL;

The Select statement shows me that the @SQL variable says this:

Select      @PolicyName     =   PolicyName
From        OtherDatabase..uvwSchemeAdministratorDetails
Where       PolicyNumber    =   'MyPolicy'

However, the Execute bit gives me this error:

Msg 911, Level 16, State 4, Line 55
Database '
                        Select      @PolicyName     =   PolicyName
                        From        OtherDatabase' does not exist. Make sure that the name is entered correctly.

Now, I was expecting to have issues populating my variable using this, but I did think it would at least connect to the database correctly. I'm sure I've made a massively obvious mistake in my syntax - any ideas what it might be?

Thanks...