In a large bowl, cream butter and confectioners' sugar until light and fluffy. Beat in egg whites and vanilla. Combine the flour, baking powder and baking soda; gradually add to the creamed mixture and mix well.
Roll into 1-1/2-in. balls, then roll in sugar. Place 2 in. apart on greased baking sheets. Flatten with a fork. Bake at 350° for 12-14 minutes or until edges are lightly browned. Remove to wire racks to cool.
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