In a large bowl, cream the shortening, oil and sugars until light and fluffy. Add eggs, one at a time, beating well after each addition. Beat in vanilla. Combine the flour, baking soda, cream of tartar and salt; gradually add to the creamed mixture. Cover and refrigerate for 1 hour or until easy to handle.
Roll into 1-in. balls; dip tops in sugar or colored sugar. Place sugar side up 2 in. apart on ungreased baking sheets. Bake at 350° for 12-14 minutes or until edges begin to brown. Remove to wire racks to cool.
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