Two iterative algorithms for synthesis of binary computer-generated holograms (CGHs) for image reconstruction are described: alternating projections onto constraint sets (POCS) and direct binary search (DBS). Comparisons with conventional methods for CGH synthesis show that POCS and DBS yield substantially lower mean-squared reconstruction error and higher diffraction efficiency. The best method is DBS, but it is also the most computationally intensive. To ameliorate this disadvantage, an acceleration technique is presented for DBS. With this technique, the design of binary holograms with moderate space-bandwidth product becomes feasible. For example, the computation required to design a hologram with 256K elements is reduced by a factor of 121.