We describe a novel approach to sorting class averages of a structure in multiple conformational states in order to generate 3D reconstructions that account for conformational variability present in the sample. The method assumes that the relative Euler angles between class averages are known, then uses a common lines approach to match any given class against a set of distinct conformations from a selected view of the structure. We show the effectiveness of the method both on model data and on an experimental dataset for which the conformational variability is limited to a defined region within the structure. During our studies of hepatitis C virus (HCV) internal ribosome entry site (IRES) interaction with the human translation initiation factor eIF3, we observed that the IRES RNA included a flexible region holding multiple conformations. While current classification methods were used to produce two-dimensional averages of the complex showing these different conformations, no method existed for relating these averages in three dimensions. Our approach overcame these limitations, giving us structural insight that was previously not possible.