||Canonical Van Vleck perturbation theory (CVPT) is used to calculate electric dipole intensities for one-, two-, and three-dimensional models of HCN and a six-dimensional model of H2CO. Lehmann and Smith [J. Chem. Phys. 93, 6140 (1990)] have shown that the intensities of overtone transitions are sensitive to the details of the inner wall of the potential. Dipole intensities calculated for several, similar one-dimensional CH stretch potentials demonstrate that perturbation theory correctly predicts this sensitivity. The perturbation intensities of a two-dimensional ab initio dipole surface indicate the importance of selected stretch-stretch resonance interactions in interpreting the CH stretch overtone spectra of HCN. The inclusion of the bend confirms that this degree of freedom plays a significant role in weakening the intensity of the CN overtones. The CH stretch overtone spectra of H2CO is calculated to illustrate the utility of the perturbative approach for predicting the transition intensities for a system in which there are multiple Fermi interactions.