`Model-based' halftoning techniques use models of visual perception and printing to produce high quality images using standard laser printers. Blue-noise screening is a dispersed-dot ordered dither technique that attempts to approximate the performance of error diffusion with much faster execution time. We use printer and visual system models to improve the design of blue-noise screens using the `void-and-cluster' method. We show that, even with these improvements, the performance of blue-noise screens does not match that of the model-based techniques. We show that using blue-noise screened images as the starting point of the least- squares model-based (LSMB) algorithm results in halftones inferior to those obtained with modified error diffusion (MED) starting points. We also use simulated annealing to try to find the global optimum of the least-squares problem. Images found this way do not have significantly lower error than those resulting from the simple iterative LSMB technique starting with MED. This result indicates that the simple iterative LSMB algorithm with a MED starting point yields a solution close to the globally optimal solution of the least-squares problem.