Three-dimensional electron cryomicroscopy of randomly oriented single particles is a method that is suitable for the determination of three-dimensional structures of macromolecular complexes at molecular resolution. However, the electron-microscopical projection images are modulated by a contrast transfer function (CTF) that prevents the calculation of three-dimensional reconstructions of biological complexes at high resolution from uncorrected images. We describe here an automated method for the accurate determination and correction of the CTF parameters defocus, twofold astigmatism and amplitude-contrast proportion from single-particle images. At the same time, the method allows the frequency-dependent signal decrease (B factor) and the nonconvoluted background signal to be estimated. The method involves the classification of the power spectra of single-particle images into groups with similar CTF parameters; this is done by multivariate statistical analysis (MSA) and hierarchically ascending classification (HAC). Averaging over several power spectra generates class averages with enhanced signal-to-noise ratios. The correct CTF parameters can be deduced from these class averages by applying an iterative correlation procedure with theoretical CTF functions; they are then used to correct the raw images. Furthermore, the method enables the tilt axis of the sample holder to be determined and allows the elimination of individual poor-quality images that show high drift or charging effects. (C) 2003 Elsevier Science (USA). All rights reserved.