Cream the butter with 1/2 cup of the confectioners' sugar and the vanilla. Mix in the flour, pecans, and salt. Roll about 1 tablespoon or so of dough into balls and place on an ungreased cookie sheet.
Bake in preheated oven until bottoms are golden, about 15 minutes. Do not allow these cookies to get too brown: it's better to undercook them than to overcook them. While cookies are still hot, roll them in confectioners' sugar. Once they have cooled, roll them in confectioners' sugar once more.