Cream together butter, peanut butter, and sugars. Beat in eggs and vanilla.
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, roll in sugar just enough to coat, and put on baking sheets. Flatten each ball with a fork, making a criss-cross pattern. Baked in a preheated 375° oven for about 9-10 minutes or until the cookies begin to brown. Do not overbake.
When cookies are done, remove from oven and let them set on the pan for at least 10 minutes until they have cooled and set enough to remove from the pan and transfer to a rack to cool thoroughly.
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