The 'missing wedge' is a long-standing problem in electron tomography, caused by the use of slab-like flat specimens, which increase in thickness when tilted to high angles. Attempts have been made to reduce the undesirable effects caused by the missing wedge, but the problem remains, particularly for the radiation-sensitive frozenhydrated specimens used for high resolution imaging. Specimens with cylindrical symmetry offer a way to overcome this problem, since the thickness remains constant at all viewing angles. However, while this has been suggested before, it has never been demonstrated for frozen-hydrated specimens. In this work, I present a way to make cylindrical specimens for electron cryo-tomography, using thin-walled carbon tubes as specimen holders. The tubes are made in a multi-step process, involving carbon deposition on glass micropipette templates and subsequent removal of the glass. Tube diameters are typically a few hundred nanometres, with a wall thickness of 10-20 nm. To make frozen-hydrated specimens, the tubes are filled with an aqueous sample and then plunge-frozen in liquid ethane. Electron images acquired from the tubes have equal quality at all viewing angles, with a tilt range restricted only by the physical limits of the microscope. Tomograms from specimens such as gold particles and liposomes show that the effects of the missing wedge are substantially reduced, with much improved resolution along the electron beam axis. Structural features oriented in all directions are visible in the reconstructions, in marked contrast to tomograms acquired over a more restricted angular range. These results are promising, however some technical challenges remain before this method can be used routinely.