A method and a printing system are described capable of rendering more than 2 density levels at the device pixel level using precalculated rectangular screening tiles of finite size that define a spatially repetitive screening operation according to geometric clustered dot screen definitions for first, second and third separation screens that has the following characteristics: (A) the set of at least three separation screens is free of second order moiré; (B) the set of at least three separation screens consists of screens that have no internal moiré and/or screens that have a reduced sensitivity to amplification by process instability of any remaining level of intrinsic internal moiré; and (C) the screens have an optimized and balanced rosette structure leading to a reduction of visible patterning in overlays of the separation screens.