In a large bowl, cream butter and confectioners' sugar until light and fluffy. Gradually add flour and cornstarch, beating until well blended.
With hands lightly dusted with additional cornstarch, roll dough into 1-in. balls. Place 1 in. apart on ungreased baking sheets. Press lightly with a floured fork. Top with nonpareils or cherry halves.
Bake at 300° for 20-22 minutes or until bottoms are lightly browned. Cool for 5 minutes before removing from pans to wire racks.