Preheat oven to 350 degrees. In a large bowl, cream butter and powdered sugar until light and fluffy. Beat in egg whites and vanilla. Combine flour, baking powder and baking soda. Gradually add to the creamed mixture and stir well.
Roll into 1 inch balls and then roll the balls in sugar. Place 2 inches apart on greased cookie sheets. Flatten with a fork horizontally and then again vertically to make a cross pattern. Bake for 12 to 14 minutes or until edges are lightly golden brown. Remove to wire racks to cool.