Combine butter and oil in a large mixing bowl; gradually add 1 cup sugar, beating well. Add eggs, beating well. Stir in vanilla.
Combine flour, baking powder, soda, and cream of tartar in a large mixing bowl; add to creamed mixture, stirring well.
Drop dough by teaspoonfuls 2 inches apart onto lightly greased cookie sheets. Bake at 325° for 12 to 15 minutes. Remove from cookie sheets, and cool on wire racks. Roll in powdered sugar.