Lee waves are considered in the framework of nonlinear motion of an inviscid perfect gas with constant specific heats and gravity taken into account. Perturbations are assumed to be confined to the troposphere with vanishing vertical velocity at the top. An asymptotic analysis is then worked out under the hypothesis that the Mach number is small and that the ratio of the horizontal scale to the height of the troposphere is of the order of the Mach number. Long’s (1953) equation and Miles’s (1968) model are recovered as an inner approximation. It is shown that the upper boundary condition belongs to an outer approximation. Such an outer asymptotic approximation is worked out and it is shown that the upper and lower boundaries of the troposphere alternately reflect internal short waves excited by the lee waves of the inner approximation. The important point is that to lowest order, there is no feedback from these waves to the inner approximate solution. It is suggested that the upper boundary condition is an artificial one and that it should be replaced by matching with a set of waves in the upper part of the atmosphere.