A screening method in a printer for approximating a gray scale tone with a more limited range image producer using a tree search. An input pixel packed data word is compared with a second data word packed with threshold values. The result of the comparison enables selection of a next second data word with thresholds is a narrower range. This process repeats until a comparison with a second data word having adjacent threshold values. The comparing is preferably performed by subtracting the second data word from the first data word in a splittable arithmetic logic unit and storing respective carry outs from each section. The selection of the next second data word uses the stored carry outs from each section. The next second data word can be determined by extracting a left most one of the stored carry outs for use as an index into a table. Alternatively, the stored carry outs can be used directly as an index into a table. An output pixel value is determined for each pixel. This may be computed from the stored carry outs or extracted from a table.