The Lawrance-Knight (L-K) deconvolution method is a spectral inversion scheme which allows one to relate an absorption or a fluorescence spectrum to the energies and couplings of the zero-order states via analytical expressions. In order to obtain accurate results, the L-K method can only be applied to spectra that arise from one precisely defined zero-order picture. Namely, a single bright state must be coupled directly to a background of noninteracting dark states, the "direct coupling model." In most situations, the zero-order picture that gives rise to a particular absorption or a fluorescence spectrum is not known a priori. Nonetheless, it is typically assumed that the zero-order circumstances governing the spectral intensities are as described above, and the L-K method has been applied indiscriminantly to the spectra of a variety of systems such as pyrazine, acetylene, and naphthalene to extract zero-order parameters. We show here that if the L-K algorithm is applied to spectra where the underlying zero-order picture departs from the direct coupling limit, the resulting output has characteristic qualitative and quantitative features that reflect this situation. By applying the L-K method to a series of simulated spectra, we recover from a pattern of patterns new information about the couplings among the dark states. We have specifically considered the alternative picture of a single bright state coupled to a background of non-interacting states by a doorway-mediated mechanism. We demonstrate here that the L-K algorithm can be employed to distinguish between the contrasting doorway-mediated and direct coupling schemes, and also to obtain coupling matrix elements.