We describe an implementation of maximum likelihood classification for single particle electron cryomicroscopy that is based on the FREALIGN software. Particle alignment parameters are determined by maximizing a joint likelihood that can include hierarchical priors, while classification is performed by expectation maximization of a marginal likelihood. We test the FREALIGN implementation using a simulated dataset containing computer-generated projection images of three different 70S ribosome structures, as well as a publicly available dataset of 70S ribosomes. The results show that the mixed strategy of the new FREALIGN algorithm yields performance on par with other maximum likelihood implementations, while remaining computationally efficient. (c) 2013 Elsevier Inc. All rights reserved.