In this paper we compare and contrast two well known approaches for designing screen functions: direct binary search (DBS) and void and cluster (V&C). They are both iterative, search based methods that minimize a metric of error between the perceived halftone and the perceived continuous-tone original image. Despite the many differences between these two approaches, these is a close correspondence between them. In this paper, we will explore these links in detail, and examine their implications for the performance of both algorithms.