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1
Preheat oven to 375u00b0F Grease 4 large baking sheets.
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2
In a medium bowl, combine flour, baking soda and salt; set aside.
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3
Turn pineapple into a strainer set over a small bowl. Use your fingers or the back of a tablespoon to firmly press pineapple into strainer, extracting as much juice as possible. Set aside pineapple and juice.
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4
In a large mixing bowl, beat butter, sugars and vanilla until light and fluffy. Beat in egg. Stir in rum alternately with flour mixture, 1/3 at a time, blending well after each addition. Stir in coconut and pineapple, reserving juice for the glaze. Drop dough by rounded tablespoons, 1 1/2-inches apart, on prepared baking sheets.
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5
Bake 8 to 11 minutes, or until top springs back when lightly pressed with a fingertip.
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6
While cookies are baking, prepare glaze: In a medium bowl, combine powdered sugar, rum and vanilla. Add enough of the pineapple juice to make a smooth and creamy glaze of medium consistency. Brush glaze over hot cookies while still on baking sheets. Transfer cookies to racks to cool. Store in an airtight container at room temperature for up to 1 week or freeze for longer storage.
