Cryoelectron microscopy provides the means of studying macromolecules in their native state. However, the contrast transfer function (CTF) makes the images and the three-dimensional (3D) maps derived from them difficult to interpret. We developed methods to determine the CTF from experimental data and to obtain a CTF-corrected 3D reconstruction. The CTF correction and 3D reconstruction accomplished in one step make it easy to combine different defocus data sets and decrease the error accumulation in the computation. These methods were applied to energy-filtered images of the 70S Escherichia coli ribosome, resulting in a distortion-free 3D map of the ribosome at 1/24.5 Angstrom(-1) resolution, as determined by the differential phase residual resolution criterion. (C) 1997 Academic Press.