Heat oven to 350 degrees F. Combine flour, pecans, butter, sugar, rum and vanilla in bowl.
With floured hands, roll rounded teaspoons of dough into 3/4-inch balls. Place on ungreased baking sheets. Refrigerate 1 hour.
Bake in 350 degree F oven 12 to 15 minutes, until golden brown. Remove to rack to cool. Store at room temperature or freeze. Dust with sugar before serving. Makes 3 dozen.