A form of stochastic random distribution is used to print an invisible watermark using a typical, e.g., 600 dpi, printer. The watermark contains such information as “Do Not Copy,” or other such information. Although the watermark is not visible on a first generation version of a document that is printed, various techniques are used to print the watermark in such a way that it becomes readily apparent when the first generation document is photocopied. The preferred embodiment of the invention is concerned with a technique for improving such techniques, for example so that gray levels are improved to address variations from printer to printer. Another preferred embodiment of the invention is also concerned with a technique for performing error diffusion watermarking without the need for performing a calibration step.