Beat egg whites until stiff. Slowly beat in 1/3 cup powdered sugar. Fold in vanilla and egg yolks.
Sift together the flour, salt and the 1/3 cup powdered sugar which has first been sifted 4 times. Carefully fold in the beaten egg mixture, small quantities at a time, mixing will after each addition. Press through a cookie press onto an ungreased baking sheet, making finger-length strips or other shapes desired. Dust with sifter powdered sugar. Bake in a moderate oven, preheated to 350 degrees, about 10 minutes. Split or leave whole, depending on how you intend to use them.