A source computer 2 having a copy of a computer file that it is desired to download to a plurality of target computers issues broadcast messages via a computer network linked to those target computers. The broadcast messages indicate the availability of the computer file for download and include a download qualifying parameter. The download qualifying parameter is used by receiving target computers to determine whether or not they qualify to attempt a download from the source computer in response to the received broadcast message. Only those target computers that do qualify attempt a download. The source computer monitors how many target computers make a download attempt in response to a particular broadcast message and adjusts the download qualifying parameters in subsequent broadcast messages so that the target computers progressively download the new computer file without overloading the source computer.