The data provider required to connect to the local data file cannot be found

I've been trying to get SQL Compact 3.5 working in Visual Studio 2008.  Since SQL Compact 3.5 ships with Visual Studio 2008, I thought that this wouldn't be a problem.  All I needed to do was to create a new Windows Forms project and add a Local Database item.  Sadly, this didn't work.  After added the local database, I received an error:

The data provider required to connect to the local data file cannot be found

I couldn't find any reference to this exact message anywhere, but I did find KB 945371.  Although the article refers to a different problem, it provided a solution to this one as well. 

It seems that when you install VS 2005 and VS 2008 side-by-side, some file paths are incorrectly specified.  The solution is to reinstall the SQL Compact Design tools from the installation DVD.  (I also reinstalled the Desktop and Device runtimes as well, as I had uninstalled these while trying to solve the problem.)

After reinstalling these bits, SQL Compact works just fine.