Cream shortening in a large mixing bowl; gradually add sugar, beating well. Add eggs, beating well.
Combine flour, baking powder, soda, and salt in a medium mixing bowl; add to creamed mixture, stirring well. Stir in remaining ingredients; mix well.
Shape into 1-inch balls; place 2 inches apart on greased cookie sheets. Bake at 350° for 10 to 12 minutes. Remove from cookie sheets, and cool on wire racks.