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Preheat oven to 350 degrees.
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Measure flour, cream of tarter, and baking soda together and set aside.
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Cream vegetable shortening and sugars together until fluffy.
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Add vanilla, salt, and egg to sugar mixture and beat until smooth.
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Add flour mixture to sugar mixture 1/3 at a time, beating after each addition until completely mixed.
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Dough will seem a little thick.
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Stir pecans into dough with a strong spoon.
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Chill dough for 30- 45 minutes.
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Roll dough into 1- 1 1/4 inch balls and place on ungreased cookie sheet.
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Flatten balls to 1/4 inch thickness.
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Bake for 12- 15 minutes, until slightly golden.
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Remove to cooling rack.
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When completely cool, store in air-tight container.