A laser method for accelerating electrons is described, based on the inverse Cherenkov effect in a gas. The laser fields are in the form of a cylindrical cone of plane waves on whose axis travel the electrons, with the cone angle and the gas refraction index such that each electron sees constant fields in time. Expressions are obtained relating the overall energy transfer to total laser power and wavelength, and to gas index and interaction length. With laser powers now available, energy increments of tens of GeV are possible. For comparative purposes, a related alternative scheme involving electrons in vacuum and evanescent laser fields is also analyzed. It is found that the method applies particularly well to adding energy to the electron bunches produced by large microwave accelerators, as collision effects are less troublesome at high injection energies.