Error diffusion (ED) and pseudorandom encoding (PRE) methods of designing Fourier transform holograms are compared in Brms of their properties and the optical performance of the resulting far-field diffraction patterns. Although both methods produce a diffuse noise pattern due to the error between the desired fully complex pattern and the encoded modulation, the PRE errors reconstruct uniformly over the nonredundant band-width of the discrete-pixel spatial Light modulator, while the ED errors reconstruct outside the window of the designed diffraction pattern. Combining the two encoding methods produces higher-fidelity diffraction patterns than either method produces individually. For some designs the fidelity of the ED-PRE algorithm is even higher over the entire nonredundant bandwidth than for the previously reported [J. Opt. Sec. Am. A 16, 2425 (1999)] minimum-distance-PRE algorithm. (C) 2000 Optical Society of America [S0740-3232(00)00609-8] OCIS codes: 230.6120, 090.1760, 070.2580, 030.6600.