a co-planar, superconductor-constriction-superconductor (ScS) junction. For short junctions having a Kulik-Omelyanchuk current-phase relationship, we find that the ScS transmon has an improved charge dispersion compared to the SIS transmon, with a tradeoff of 50% smaller anharmonicity. These calculations provide a framework for estimating the superconductor material properties and junction dimensions needed to provide proper ScS transmon operation at typical gigahertz frequencies.