The watermark grid signal and the watermark payload signal are separately applied to an image. The process is particularly useful in situations where variable data such as serial numbers (or other image specific data) is being embedded in a series of images. In such situations the grid signal can be uniform over an entire sequence of images and only the payload signal need be changed before being printed on each image. The time, computational and labor intensive processes can be applied to the task of embedding the grid signal in the image to insure that visual artifacts are not created. After the image has been changed to embed the grid signal, the payload data can be inserted into at least a selected part of the image. Since the payload signal is less likely to create visual artifacts than the uniform grid signal, less effort need be used to avoid creating visual artifacts due to the payload signal. The relatively random nature of the payload data can be relied upon to avoid creating significant visual artifacts. The same bifurcated process can be used to apply digital watermarks to other media such as sound recordings where potential artifacts are in the nature of sound anomalies rather that visual artifacts.