Compared with slice-by-slice approaches for SPECT reconstruction, three-dimensional iterative methods provide a more accurate physical model and an improved SPECT image. Clinical application of these methods, however, is limited primarily to their computational demands. This paper investigates the methods for approximate 3D iterative reconstruction that greatly reduce this demand by excluding from the reconstruction the smaller magnitude elements of the system matrix. A new method is described which is designed to control the resulting bias in the SPECT image for a given reduction in computation. The approximate methods were compared to fully 3D iterative reconstruction in terms of SPECT image bias and visual quality. All methods were incorporated into the ML-EM algorithm and applied to data from 3D mathematical and experimental brain phantoms. The SPECT images reconstructed by the approximate methods exhibited a positive bias throughout the image that was in general smaller with the new method (in the rage of 2%-6%). The bias was smallest in locally hot regions and largest in locally cold regions. The high quality brain phantom images demonstrated the capability of the new method in realistic imaging contexts. The time per iteration for an entire 3D brain phantom on a modern workstation using the approximate 3D method was 7.0 s.