In this report a method is presented to determine optimum shapes of bodies of revolution taking into account the shape dependent part of the base drag. The latter is achieved by using the Chapman assumption that the base pressure coefficient, when correlated with conditions at a suitable point near the base, depends only on the free-stream Mach number if the boundary layer is turbulent. The present method enables the determination of quantitative results, which show the known trend that the optimum bodies have their maximum cross section ahead the base area. The drag reductions obtained are the most significant for relatively slender bodies in the lower supersonic Mach number range.