In a large bowl, add pecans, flour and 1c. sugar; set aside. In a small bowl, beat egg whites until foamy. Gradually add remaining sugar, beating until stiff peaks form. fold in butter rum and half the flour mixture. Fold in remaining flour mixture.
Drop by rounded teaspoonfuls 2" apart onto an ungreased foil lined baking sheets. Top each cookie with a cherry piece.
Bake at 375^ for 20 minutes or until edges are lightly browned. Cool completely before removing from pans.
* makes about 5 dozen