Hi, Karl:
I am really sorry to hear that you had trouble. Things that are that delicate however, need more support and thickness to give you the best control and to be successful. I highly recommend that you cut two or more layers of these types of designs at once - both for strength and better control.
If you don't want to 'waste wood' as some people had said to me before, you can use a piece of cardboard or chip board and layer it and stack cut it with your piece of wood. I even use old cereal boxes and cardboard of that type if I truly only want to cut one piece. That way there is no waste at all.
You can see the article on stack cutting right here on my site at
http://www.sheilalandrydesigns.com/articles/stack-cutting I hope it helps those of you who aren't familiar with this process and help you make more successful projects. I was cutting the second set of these birds today, which is a similar level of difficulty, and even though they are a bit fragile, with using a 2/0 blade and following the instructions, they will come out nice.
Good luck and have fun!
Sheila