Methods and apparatuses for halftoning an image are provided using a parametrically controlled hexagonal halftone dot shape threshold function that reduces tone reproduction irregularities in the halftoned image which can occur at darker gray levels. The halftoning transforms image data representing contone image pixels into halftoned image data in the form of clustered-dot hexagonal halftone screens for representing halftone dots of a halftoned image. Weight parameters can be used to control the rate at which a respective vertex of a halftone dot approaches a vertex of a neighboring halftone dot in relation to gray level. The hexagonal halftone dot shape threshold function can also control the shape of the sides of the halftone dots.