An inset dielectric guide (IDG) is a dielectric-filled rectangular groove which is recognized as an alternative to the image line. In this paper, the inset dielectric guide with a conductor cover is examined using the Fourier-transform and mode-matching technique. The boundary conditions are enforced in the spectral domain to obtain a dispersion equation in rapidly-converging series. An approximate dispersion equation of the fundamental mode is shown to be accurate for most practical applications.