The authors calculated the propagation losses of a dielectric image guide using the effective dielectric constant (EDC) method to a higher order of approximation. It was found that there exist a minimum in the waveguide attenuation that has not been alluded to in the literature, and also a peak in the imaginary parts of the transverse propagation constant relate to dimensional resonances within the waveguide. These results imply that the propagation losses will be lowered and the fields will be more effectively confined within the waveguide at frequencies close to the cutoff. >