We investigated a series of structurally and chemically different dye-DNA complexes via the specific behavior of spectral holes under pressure. In all samples chromophore and solvent were the same, only the DNA strands were different. The dominant interaction with the solvent is mainly electrostatic via the strongly polar BF2 group of the chromophore. The relative change of the dipole moment upon excitation can be estimated from the experimental data. There is a significant color effect in the pressure-induced broadening of the holes, which signals a breakdown of the Gaussian approximation. The origin of this breakdown is associated with ordered structures around the chromophore due to the DNA strands but also because of the formation of ordered solvent cage structures as a consequence of the hydrophobic nature of the chromophore. The various DNA strands show characteristic features in the spectra under pressure that reflect specific structural features.