Cream butter with mixer untill light and fuffy.
Add sugar and salt and beat until no longer grainy.
Gradually add flour a little at a time, beating at low speed untill dough forms.
Mix in vanilla.
Form dough into balls, one heaping tablespoon = 1 ball.
Place balls on ungreased cookie sheet spaced widely- about 9 per sheet.
Put 1/4 cup of sugar on saucer. Press first 3 fingers into sugar, then press down on ball to flatten to a 3 inch circle wide and 1/4 to 1/2 inch thick.
Bake in preheated 350 degree oven 12-15 minutes, until faintly browned around the egdes.
Gently remove cookies from sheet with a spatula, cool completely on wire racks.