An algorithm has been developed for placing three-dimensional atomic structures into appropriately scaled cryoelectron microscopy maps. The first stage in this process is to conduct a three-dimensional angular search in which the center of gravity of an X-ray crystallographically determined structure is placed on a selected position in the cryoelectron microscopy map. The quality of the fit is measured by the sum of the density at each atomic position. The second stage is to refine the three angles and three translational parameters for the best (usually 25 to 100) fits. Useful criteria for this refinement include the sum of densities at atomic sites, the lack of atoms in negative or low density, the absence of atomic clashes between symmetry-related positions of the atomic structure, and the distances between identifiable features in the map and their positions on the fitted atomic structure. These refinements generally lead to a convergence of the originally chosen, top scoring fits to just a few (about 3 to 8) acceptable possibilities. Usually, the best remaining fit is clearly superior to any of the others. (C) 2002 Elsevier Science (USA).