Characterizing a scanner well enough to calibrate a printer continues to be challenging. Barriers include the inherent noisiness of scan bars, and the lack of colorimetric response, leading to substantial sensitivity to black addition strategy as well as changes in materials (media or colorant set). Most scanner characterization work has been designed to improve the utility of the scanner for capturing arbitrary print input, an inherently difficult problem given that neither the materials nor the black addition strategy are in general known. If these are both known, the problem becomes tractable, and noise is the largest remaining issue. This paper deals with reducing the errors in patch averages when the patches are scanned from prints made on printers that use halftoning.