Cryo-electron microscopy and three-dimensional image reconstruction are powerful tools for analyzing icosahedral virus capsids at resolutions that now extend below 1 nm, However, the validity of such density maps depends critically on correct identification of the viewing geometry of each particle in the data set. In some cases-for example, round capsids with low surface relief-it is difficult to identify orientations by conventional application of the two most widely used approaches-"common lines" and model-based iterative refinement. We describe here a strategy for determining the orientations of such refractory specimens. The key step is to determine reliable orientations for a base set of particles, For each particle, a list of candidate orientations is generated by common lines: correct orientations are then identified by computing a single-particle reconstruction for each candidate and then systematically matching their reprojections with the original images by visual criteria and crosscorrelation analysis. This base set yields a first-generation reconstruction that is fed into the model-based procedure. This strategy has led to the structural determination of two viruses that, ill our hands, resisted solution by other means.