A method for halftoning a gray scale image to generate a halftoned image uses a stochastic screen is designed to provide visually pleasing, blue noise dot profiles when thresholded at any gray level and wherein substantially all the threshold values corresponding to gray levels between g.sub.s1 and g.sub.s2 coincide with black positions in a constraining checkerboard pattern and substantially all the threshold values corresponding to gray levels between g.sub.s2 and g.sub.s3 coincide with white positions in the constraining checkerboard pattern.