  On the basis of features observed in the exact perturbation approach solution
for the eigenspectrum of the dilute A_3 model, we propose expressions for
excitations in the dilute A_4 and A_6 models. Principally, we require that
these expressions satisfy the appropriate inversion relations. We demonstrate
that they give the expected E_7 and E_6 mass spectra, and universal amplitudes,
and agree with numerical expressions for the eigenvalues.
