Optimal rehalftone screen frequencies are found by searching frequency space for points that are maximally spaced from significant frequency components of an input image halftone screen or screens. Selecting a rehalftone screen having a maximally spaced frequency produces moire of the highest frequency possible. High frequency moire are visually unobjectionable. Optimal rehalftone frequencies may be found near the maximally spaced points where system or other constraints limit the usefulness of the maximally spaced points. Rehalftone screen frequencies in the range of about 1.4 to about 1.8 times the fundamental frequency of the input image halftone screen are often optimal. A rehalftone screen frequency of 1.5 times the fundamental frequency of the input image halftone screen is often optimal when the input image is monochrome and uses a dot screen.