An iterative process for improving the completeness and quality of atomic models automatically built at moderate resolution (up to about 2.8 A) is described. The process consists of cycles of model building interspersed with cycles of refinement and combining phase information from the model with experimental phase information (if any) using statistical density modification. The process can lead to substantial improvements in both the accuracy and completeness of the model compared with a single cycle of model building. For eight test cases solved by MAD or SAD at resolutions ranging from 2.0 to 2.8 A, the fraction of models built and assigned to sequence was 46-91% (mean of 65%) after the first cycle of building and refinement, and 78-95% (mean of 87%) after 20 cycles. In an additional test case, an incorrect model of gene 5 protein (PDB code 2gn5; r.m.s.d. of main-chain atoms from the more recent refined structure 1vqb at 1.56 A) was rebuilt using only structure-factor amplitude information at varying resolutions from 2.0 to 3.0 A. Rebuilding was effective at resolutions up to about 2.5 A. The resulting models had 60-80% of the residues built and an r.m.s.d. of main-chain atoms from the refined structure of 0.20 to 0.62 A. The algorithm is useful for building preliminary models of macromolecules suitable for an experienced crystallographer to extend, correct and fully refine.