This paper shows that it is possible markedly to improve the resolution obtainable in electron micrographs by deliberately using low beam divergence (2 × 10-4 rad) and by minimizing thermal spread in the electron gun. Point-to-point resolutions in the sub-3 Å range will be illustrated for the hollandite structure. Image matching, including the effects of both beam divergence and chromatic aberration, showed that the experimental images could be fitted using 2 Å objective aperture, with no divergence and defocus ripple of only 50 Å. In fact, these stringent experimental requirements must be met if useful structural information is to be obtained in the 2-3 Å range.