We present a design method based on the Gerchberg-Saxton algorithm for the design of high-performance diffractive optical elements. Results from this algorithm are compared with results from simulated annealing and the iterative Fourier-transform algorithm. The element performance is comparable with those designed by simulated annealing, whereas the design time is similar to the iterative Fourier-transform method. Finally, we present results for a demanding beam-shaping task that was beyond the capabilities of either of the traditional algorithms. The element performances demonstrate greater than 85% efficiency and less than 2% uniformity error. © 2004 Optical Society of America.