It is shown that for Boussinesq flows in which rotation and stratification are equally strong, the forward cascade of potential enstrophy constrains the spectral distribution of horizontal kinetic energy and potential energy. Horizontal kinetic energy is suppressed in the small aspect- ratio wave modes, and potential energy in suppressed in the large aspect-ratio wave modes. Scaling estimates based on phenomenological arguments yield scaling of k_h^-3 and k_z^-3, respectively, of the two spectra. High-resolution numerical simulations of the Boussinesq equations in the relevant parameter regimes show spectral scaling exponent closer to -4, and hence even stronger suppression than is predicted by dimensional estimates.