1. A process for printing printing substrates, the process comprising the following steps: assigning pixels of a multilevel map to image dots of a printer-ready copy and assigning values to the pixels depending on a tonal value of the image dot, permitting n+1 different values to be assigned to each pixel, where n is greater than 1; representing different amounts of ink of a printed pixel with the different values; assigning threshold values of any threshold value matrix to the pixels of the multilevel map with respect to their positions relative to the printing substrate; calculating tonal values of the image dot with color separation; fixing the values of the pixels depending on the threshold value and on the tonal value of the assigned image dot; and printing the multilevel map on a printing substrate in a multilevel printing process.