Recently the resolution attainable in density maps calculated from cryo-electron micrographs of freestanding virus capsids has advanced to resolutions below 1 nm. This represents a significant milestone in that resolutions of this order potentially allow direct visualization of individual elements of protein secondary structure (i.e., alpha-helices), in addition to the shapes and connectivity of subdomains. We describe here a computational strategy for structural analyses at this level of detail: its principal innovation is a procedure for correcting the contrast transfer function of the electron microscope. Also important is the practice of combining data from pairs of differently defocused micrographs to improve the signal-to-noise ratio of the images, thereby allowing more precise determinations of the particles' orientations and origins and contributing to higher resolution reconstructions. These procedures proved instrumental in our analysis of the capsid of hepatitis B virus at 9-Angstrom resolution (Conway ef al, 1997, Nature 386, 91-94). Finally, we discuss the prospects for achieving comparable resolutions for isolated macromolecular complexes with lower symmetry or no symmetry and for further extension of the resolution.