Cream butter in a large mixing bowl; gradually add sugar, beating until light and fluffy. Add eggs, one at a time, beating well after each addition. Stir in flour and baking powder, mixing well.
Divide dough in half; shape each half into a roll, 2 inches in diameter. Wrap in waxed paper, and chill overnight or until firm.
Cut into 1/4-inch slices; place 2 inches apart on ungreased cookie sheets. Bake at 375° for 8 minutes or until lightly browned. Remove from cookie sheets, and cool on wire racks.