A method is developed to calculate waveguide modes in a plane stratified duct of enhanced or reduced ionization density in an otherwise uniform magneto-ionic medium. It may in principle be applied to ducts with an arbitrary electron density profile, and with dimensions of the order of the wavelength in the medium. Computations are carried out for one simple model with enhanced ionization density and parameters typical of whistler propagation. The fields inside and outside the duct are discussed. It is shown that the energy flux in the inhomogeneous wave outside the physical boundaries of the duct may in certain circumstances be important. The types of waveguide mode which may occur are discussed. In particular there is one mode called the zero-order mode which always propagates even when the duct is very narrow or when the electron density in the duct differs only infinitesimally from that in the uniform medium outside. In the limit where the duct no longer exists this mode becomes a plane wave. When the axis of the duct is curved and there are transverse gradients of ionization density and of magnetic field in the medium outside the duct, all modes may tunnel through a barrier region, in which the wave is evanescent, to a region where the energy is refracted away from the duct. Consideration of this process leads to a criterion for deciding whether a duct is sufficiently strong to maintain guiding.