With digital printing systems, the achievable screen angles and frequencies are limited by the finite address- ability of the marking engine. In order for such screens to generate dot clusters in which each cluster is identical, the elements of the periodicity matrix must be integer-valued, when expressed in units of printer-addressable pixels. To achieve a better approximation to the screen sets used for commercial offset printing, irregular screens can be used. With an irregular screen, the elements of the periodicity matrix are rational numbers. In this paper, we describe a procedure for design of high-quality irregular screens. We start with the design of the midtone halftone pattern. We then propose an algorithm to determine how to add dots from midtone to shadow and how to remove dots from mid-tone to highlight. We present experimental results illustrating the quality of the halftones resulting from our design procedure by comparing images halftoned with irregular screens using our approach and a template-based approach. Publisher’s Note: The first printing of this volume was completed prior to the SPIE Digital Library publication and this paper has since been replaced with a corrected/revised version.