A model-free method to determine the three-dimensional structure of icosahedral viruses is described. The novel strategy is based upon the approximate principle that correct virus structures have high variance as do all other well-detailed structures, even wrong ones. The original projections of individual particles are reduced to a radius of 25 pixels and are used to compute single particle reconstruction models by assigning them 1800 different Enter triads. The variance of the models obtained from all projections is stored in maps and a decimation process is carried out, In a first stage, thresholds are adopted for the variance values, and in a second stage, carried out by correspondence analysis and classification, 30 clusters of models are sorted out. The clusters are refined to yield models contained in boxes of 64(3) voxels. The refined models with highest variance and closest similarity represent the correct solution. Once enlarged, these models can be used to align all available projections in their original scale in a customary projection-matching process. The method has proved successful in determining the structures of poliovirus, of the empty and filled capsids of L-virus, and of a modified capsid of hepatitis B virus. (C) 2002 Elsevier Science (USA). All rights reserved.