Cream butter or margarine in a bowl, gradually add confectioners' sugar and salt. Beat until light and fluffy. Add almonds and vanilla. Blend in flour gradually and mix well.
Shape into balls (or crescents) using about 1 teaspoon for each cookie. Place on ungreased cookie sheets, and bake for 15-20 min. Do not brown. Cool slightly, then roll in the extra confectioners' sugar.