As promised, I'll show you how to do the Disappearing 9-Patch. It starts out as just a regular 9-patch.
Cut the block in half vertically and horizontally.
Then, take the upper right-hand square and turn it so that the inside corner is the outside edge of the block. Turn the lower left-hand square so that it does the same thing. Leave the other squares as they are.
Sew the 4 squares together again and it looks like you pieced the block using lots of little pieces. I love the way this turns out. So simple, but looks like it's harder.