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Cream together butter, peanut butter and sugars.
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Beat in eggs just until well blended.
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Sift together flour, baking powder, baking soda, and salt in a medium bowl.
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Lower the mixer speed and stir in flour mixture just until well combined.
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Chill batter for 1 hour.
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Preheat oven to 375°F
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Remove batter from refrigerator. Roll into 1 inch balls and place on baking sheets. Flatten with a fork, creating a criss-cross pattern.
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Bake about 10 minutes or until the edges start to lightly brown. Do not overbake.