Generating reliable initial models is a critical step in the reconstruction of asymmetric single-particles by 3D electron microscopy. This is particularly difficult to do if heterogeneity is present in the sample. The Random Conical Tilt (RCT) method, arguably the most robust presently to accomplish this task, requires significant user intervention to solve the "missing cone" problem. We present here a novel approach, termed the orthogonal tilt reconstruction method, that eliminates the missing cone altogether, making it possible for single-class volumes to be used directly as initial references in refinement without further processing. The method involves collecting data at +45 degrees and -45 degrees tilts and only requires that particles adopt a relatively large number of orientations on the grid. One tilted data set is used for alignment and classification and the other set-which provides views orthogonal to those in the first-is used for reconstruction, resulting in the absence of a missing cone. We have tested this method with synthetic data and compared its performance to that of the RCT method. We also propose a way of increasing the level of homogeneity in individual 2D classes (and volumes) in a heterogeneous data set and identifying the most homogeneous volumes. (C) 2005 Elsevier Inc. All rights reserved.