The paper is devoted to the study of a high-pressure short-arc xenon discharge, which is widely used as a light source. Cathodes of such lamps are often doped with thorium for better cathode operation. As a result, thorium can evaporate into a discharge. The study is based on a model of a short-arc xenon discharge plasma, which includes presence of thorium atoms in the plasma. The data obtained show that thorium atoms strongly affect the characteristics of the plasma, reducing its temperature, changing the ionic composition near the cathode, energy balance and generation of optical radiation. Especially interesting is the case when the discharge electrodes have a different shape of the working surface: the anode has a convex or concave shape; the cathode has a different cone angle. The obtained data make it possible to propose a new way to increase the luminous efficiency of xenon lamps due to the appropriate choice of the electrodes working surface shape, which turned out to be an unexpectedly strong factor of affecting plasma characteristics. This, in turn, allows us to develop xenon lamps with the desired characteristics providing optical radiation in the required range of the spectrum and better use of energy.