Structures of highly ordered biological bundles have unique features which call for special experimental and computational methods in electron cryomicroscopy. They can be considered as three dimensional quasi-crystals and reconstructed using a crystallographic approach. However, they are neither "infinitely" large with respect to the borders of the bundle, nor are they a single unit cell in thickness along the viewing direction, Also, because of their shape, bundles do not generally have a preferred azimuthal orientation, which poses challenges for orientation estimation and refinement. We developed a strategy for recording and processing electron cryomicroscopic images that differs fi om classical two-dimensional crystalline reconstruction techniques. These developments allowed us to merge data hom tomographic tilt series of ice-embedded acrosomal bundles. The goal is to determine accurately amplitudes and phases at the diffraction maxima in terms of hkl indices, and compute a three-dimensional map from the diffraction data. (C) 1997 Academic Press.