The invention relates to perforated films comprising at least one layer, and to packages prepared from the same. Such packages contain a combination of perforation sizes and perforation densities that allows for effective air removal, during a filling, conveying, and palletizing process, and especially during the pressurized filling of fine powder substances. In particular, the invention provides a perforated film, comprising at least one layer, and wherein the at least one layer comprises perforations that are individually of a size less than, or equal to, 100 microns (.mu.m), and wherein the ratio of the total perforation area to the total film surface area is from 400,000 to 2,000,000 square micron per square inch of film (.mu.m.sup.2)/(in).sup.2.