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Drain pineapple, reserving 3 tablespoons juice. Set pineapple aside.
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Set juice aside for frosting.
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In a mixing bowl, cream shortening and sugar.
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Add egg; mix well.
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Add pineapple and vanilla; mix well.
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Combine flour, baking powder, baking soda and salt; stir into the creamed mixture.
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Drop by tablespoonfuls, 2 inches apart onto greased baking sheets.
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Bake at 325°F for 17-20 minutes or until golden.
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Immediately remove to wire racks to cool.
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Frosting:.
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In a small bowl, combine confectioners' sugar with enough of reserved juice to achieve a smooth spreading consistency.
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Frost cooled cookies.