The thermoluminescence (TL) dose response of a common Israeli table salt (NaCl) was measured following 137Cs gamma ray and 125 kVp X-ray irradiation. The dose response is linear, then turns supralinear and finally enters into saturation. The phenomenon of TL linear/supralinear response and the dependence of the supralinearity on ionization density/photon energy is of major interest theoretically and also impacts the practical use of the material as a reliable dosimeter. Prior to this investigation only the supralinearity of the glow peaks of TLD-100 had been investigated. The supralinearity of the major glow peaks (peaks 3 and 5) of the investigated NaCl is strongly dependent on photon energy which lends credence to the probability that the ionization density dependence of TL supralinearity is a common if not universal phenomenon. The Unified Interaction Model used herein is based on the joint action of geminate and conduction band mediated recombination and was used to simulate the dose response of peaks 3 and 5. The simulated dose response allows a reliable estimate of the dose threshold where the supralinearity begins to appear. This information is useful in the evaluation of the Israeli salts as pragmatic retrospective dosimeters in the event of a radiological event.