Rename project and folder within TFS 2010

There are many possible ways to rename project and folder within TFS 2010.

In order not to loose many hours changing around names within the solution, TFS, the csproj, ...
here is 2 possible ways that works for me :

SOLUTION ONE :
0. Rename DIRECTLY the folder within TFS Source Control Explorer; it's going to be marked as : ,
1. Open the Solution, that contains a broken project, since it has been renamed,
2. Add an existing project, and find the renamed folder,
3. Check in everything,

SOLUTION TWO :
0. Rename the project A into A' within the solution,
1. Remove (using "Delete" option) the project A' from the solution (that is checked in within TFS 2010)
2. Go to the location of this project A' (that is still called A), and rename the folder into A'
3. Go back to physical location of the solution, and add "existing " project A' (that is located in the folder A')
     ::: Nearly all things are synchronised !
4. From the Source Control Explorer, rename the folder A into A'
    ::: TFS marks A' in the Source Control Explorer view as a renamed folder with the icon :  

    ::: TFS marks A' in the Solution as checked in (again) :

That's as simple .... when done in this order !!