In a large mixer bowl beat shortening and butter for 30 seconds or till softened. Add sugar, spice, baking powder, baking soda, and salt. Beat till fluffy. Add eggs and vanilla; beat thoroughly. Beat in flour. Stir in oats, cherries or raisins, and orange peel. Generously fill a 1/3 cup dry measure with dough and drop onto a greased cookie sheet. Press into a 4 inch circle. Repeat with remaining dough, placing cookies 3 inches apart on greased cookie sheets.
Bake in a 375 oven for 8 to 10 minutes or till edges are golden. Let stand for 1 minute. Transfer cookies to wire rack to cool.
These cookies taste best when golden around the edges and moist and chewy in the center. To avoid overbaking, remove cookies from the oven when the edges are golden and the centers still look slightly underdone.