Cream together butter, shortening and sugar. Beat in eggs one at a time, beating well after each addition. Add lemon juice, orange juice and vanilla and beat well.
Sift flour and baking powder together. Beat into wet ingredients until well mixed. Form into a log, wrap tightly with plastic wrap and refrigerate over night.
Cut into 1/4" slices. Place onto ungreased baking sheet, 2" apart. Bake in preheated 350°F oven 12-15 minutes, until edges are just barely brown.