Single particles embedded in ice pose new challenges for image processing because of the intrinsically low signal-to-noise ratio of such particles in electron micrographs. We have developed new techniques that address some of these problems and have applied these techniques to electron micrographs of the Escherichia coli ribosome. Data collection and reconstruction follow the protocol of the random-conical technique of Radermacher et al. [J. Microscopy 146 (1987) 113]. A reference-free alignment algorithm has been developed to overcome the propensity of reference-based algorithms to reinforce the reference motif in very noisy situations. In addition, an iterative 3D reconstruction method based on a chi-square minimization constraint has been developed and tested. This algorithm tends to reduce the effects of the missing angular range on the reconstruction, thereby facilitating the merging of random-conical data sets obtained from differently oriented particles.