In a small bowl, cream shortening and sugars until light and fluffy. Beat in egg and vanilla. Combine the flour, cream of tartar, baking soda and salt; gradually add to creamed mixture and mix well. Stir in pecans.
Roll into 1-in. balls. Place 2 in. apart on ungreased baking sheets. Coat the bottom of a glass with cooking spray; flatten cookies with glass.
Bake at 350° for 18-20 minutes or until edges are lightly browned. Cool for 1-2 minutes before removing to wire racks.