The problem of maximizing the lift-to-drag ratio of a slender, flat-top hypersonic body is investigated under the assumptions that the pressure distribution is Newtonian and the skin-friction coefficient is constant. Direct methods are employed, and the analysis is confined to the class of bodies whose transversal contour is semicircular and whose longitudinal contour is a power law. First, unconstrained configurations are considered, and the combination of power law exponent and the thickness ratio maximizing the lift-to-drag ratio is determined. It is found that the maximum lift-to-drag ratio LID = 0.360 Cf1/3 and corresponds to a conical configuration of thickness ratio t/l = 1.18 Cf1/3, where Cf is the skin-friction coefficient. Next, constrained configurations are considered, that is, conditions are imposed on the length, the thickness, the volume, the wetted area, and the center of pressure. For each combination of constraints, an appropriate similarity parameter is introduced, and the optimum power law exponent, thickness ratio, and the lift-to-drag ratio are determined as functions of the similarity parameter.