With the emergence of high-end digital printing technologies, it is of interest to analyze the nature and causes of image graininess in order to understand the factors that prevent high-end digital presses from achieving the same print quality as commercial offset presses. In this paper, we report on a study to understand the relationship between image graininess and halftone technology. With high-end digital printing technology, irregular screens can be considered since they can achieve a better approximation to the screen sets used for commercial offset presses. This is due to the fact that the elements of the periodicity matrix of an irregular screen are rational numbers, rather than integers, which would be the case for a regular screen. To understand how image graininess relates to the halftoning technology, we recently performed a Fourier-based analysis of regular and irregular periodic, clustered-dot halftone textures. From the analytical results, we showed that irregular halftone textures generate new frequency components near the spectrum origin; and that these frequency components are low enough to be visible to the human viewer, and to be perceived as a lack of smoothness. In this paper, given a set of target irrational screen periodicity matrices, we describe a process, based on this Fourier analysis, for finding the best realizable screen set. We demonstrate the efficacy of our method with a number of experimental results.