In mixing bowl, cream together butter, shortening and sugar until smooth. Add eggs and vanilla; stir in.
In separate bowl, combine dry ingredients (flour, baking powder and salt). Add to wet ingredients; mix until dough forms.
Roll 2 tablespoon-sized bits of dough into balls, and place on ungreased cookie sheet about 2 inches apart. Flatten balls gently with the bottom of a glass.
Bake 10 to 12 minutes, or until cookie bottom has lightly browned. Remove from oven; cool cookies on wire rack.
To glaze: mix together powdered sugar and juice with a whisk. Spoon over cooled cookies and let dry.
Notes
Add a drop of food coloring to glaze as desired. I added yellow to the Tropical, but the other two glazes are colored by the juice alone.