Abstract: This invention involves approximating a gray scale tone with a more limited range image producer, a process known as screening. This invention reduces the time needed for such screening by discriminating when screening is not needed. In a first embodiment, the rendering process produces a minimally enclosing bounding box surrounding all rendered objects. In an alternative embodiment, scan lines including any part of a rendered object are noted. The screening makes better use of memory by dividing each row of a preference matrix into segments. The lookup tables associated with these segments are sequentially loaded into a memory cache. Input pixels mapping into the loaded segment lookup tables are screened. Then the lookup table associated with the next segment of the preference matrix are loaded into the memory cache and used to screen input pixels mapping into that segment.