Most alkali halides crystallize in the fcc sodium chloride structure. In contrast, with the exception of CsF, the Cs-halides form the simple cubic cesium chloride (CsCl) structure at ambient conditions and they have a substantially different electronic structure than other alkali halides; in particular, they have several nearly degenerate electronic levels near the Brillouin zone center. Highly resolved Three-Photon Spectroscopy (TPS) measurements allow direct observation of the near band edge structure and, in the case of CsI, probe more states than one-photon techniques. A number of interesting phenomena, among them level repulsion (Fermi resonance), occur as these levels are tuned through one another by application of hydrostatic pressure. To the best of our knowledge, this has been