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It has previously been shown that the propagation constants of step-index dielectric waveguides of arbitrary cross section and small index contrast can be computed accurately by using a related metallic waveguide of a certain “effective cross-section.” In this paper we extend the method to treat waveguides whose cladding is inhomogeneous and whose refractive index is not necessarily close to that of the core (guiding) region. The results are applied to dielectric waveguides embedded into or embossed upon a dense substrate region. The expressions obtained are, again, quite simple and require knowledge only of the TM-mode eigenvalues of a similarly shaped metallic waveguide.