In electrophotographic printing, a periodic clustered-dot halftone pattern is preferred for a smooth and stable result. In addition, the screen frequency should be high enough to minimize the visibility of the halftone textures and to ensure good detail rendition. However, at these frequencies, the halftone cell may contain too few pixels to provide a sufficient number of distinct gray levels. This will result in contouring and posterization. The traditional solution is to grow the clusters asynchronously within a repeating block of clusters known as a supercell. The growth of each individual cluster is governed by a microscreen. The order in which the clusters grow within the supercell is determined by a macroscreen. Typically, the macroscreen is a recursive pattern due to Bayer. In highlights and shadows, this ordering results in visible artifacts. Replacing the Bayer screen by a stochastic macroscreen eliminates these artifacts, but results in new artifacts. In this paper, we propose a new composite screen architecture that employs multiple microscreens and multiple macroscreens in the highlights and shadows. These screens are jointly designed by using the direct binary search (DBS) algorithm.