Mix shortening, sugar, eggs and vanilla thoroughly.  Measure flour by dipping method or by sifting. Stir flour, baking powder and salt together; blend in to shortening mixture.  Chill at least 1 hour.
Heat oven to 350 degrees.  Roll dough 1/8" thick on lightly floured board.  Cut with 3" cookie cutter.  Place on ungreased baking sheet.  Bake 6 to 8 minutes or until cookies are a delicate golden color.