Cream together butter, peanut butter and sugars. Beat in eggs.
In a separate bowl, sift together flour, baking powder, baking soda, and salt. Stir into batter. Put batter in refrigerator for 1 hour.
Roll into 1 inch balls and put on baking sheets. Flatten each ball with a fork, making a criss-cross pattern. Bake in a preheated 375 degrees F oven for about 10 minutes or until cookies begin to brown. Do not over-bake.