That's a good solution. I've used the cookie recipe from joyofbaking.com which does have baking powder in it but my cutters are just shapes without detail. I don't remember them rising much but I roll them out really thin.

This is the recipe that I always use and it only calls for 1/2 tsp of baking powder. You mix it like a pie crust and they are very nice.
Sugar Cookies
3c flour
1/2 tsp baking powder
1/2 tsp baking soda
1 c butter or margarine
pinch of salt
Mix all together like piecrust dough cutting the butter into the dry ingredients.
Then add:
1 c sugar
2 beaten eggs
1 tsp vanilla.
Chill dough. Preheat oven to 375°, roll and cut cookies. Bake on ungreased cookie sheet for 6-8 minutes.
I always double this recipe and then frost and decorate.
RL`

Are you sure it's not more about too much sugar instead of baking powder? ...just a thought.

Marilyn

No, Marilyn, I'm not sure; just assumed baking powder was the leavening agent. (And we all know the results of assuming. . .)