Much of our understanding of wave generation by flow over topography has been obtained through the use of linear theory and their solution by Fourier integrals. When nonlinear effects are significant and rotation is absent, Long's theory (1953,1955) represents a powerful reduction of the steady primitive equations to a single, linear Helmholtz problem. We have constructed a similarly concise, but nonlinear, analog of Long's theory to include the effect of rotation -- a case where considerably less is understood about the wave generation process. This new reduced equation is used to explain the enhanced wave generation apparent in the steady flows computed by Trub and Davies (1995). In addition, our exact reformulation of the primitive equations also suggests a resolution to the singular breakdown that occurs in the (small Rossby number) semi-geostrophic approximation of Pierrehumbert (1985).