Electron diffraction patterns and images of three-dimensional (3D) objects are limited by the range of specimen tilt angles. This range is commonly limited by the specimen holder, but for angles >60°, the slab-like nature of most specimens is itself a fundamental limitation. At 60° the beam path is twice the thickness of the untilted specimen, at 70° it is three times, and at 90° it is infinite. For angles > ± 60°, the information is severely degraded or unattainable This causes serious problems for electron crystallography, and for electron microscopic tomography. For the former, it can result in series termination errors in the computation of electrostatic potential maps from the structure factor amplitudes, and for the latter, it results in reconstructions with anisotropic resolution. To overcome these limitations, we are developing specimen stages and preparation procedures based on a “cylindrical” geometry i.e. all dimensions transverse to the tilt axis are a few micrometers or less.