In the above photo I have removed the veneer, first from the front of the arm, and then, the thicker piece, from the inside. Although I think this is the better way, I would just like to say, that it really hurt me to remove this small block of wood. Below;
I thought that as the groove, or dado (groove is actually correct) was tapered in my favor, that removing the shelf would be relatively easy, once I got it going. I was wrong. The shelf was very badly warped in the groove, and I had to work hard, the whole way out. So the piano had a little bit of revenge.
The result was this.