In luminescence dating, dose-response curve fitting is critical to obtain dose estimates that are equivalent to the natural dose. For high natural doses several fitting functions are in use, but dose underestimation remains a common result. To address this, we analyse two functions directly derived from the one trap one recombination centre (OTOR) model alongside the single-saturating exponential function (SSE), typically used for data generated by a single-aliquot regenerative dose protocol (SAR) and, we test fit parameters using a set of natural samples.</p> <p>Combining theory with empirical evidence we show, in agreement with earlier studies, that OTOR and SSE functions are the same in terms of their parameterisations, with OTOR allowing for one extra degree of freedom represented by the parameter <em>R</em>=<em>A<sub>n</sub></em>/<em>A<sub>m</sub></em>. By allowing <em>R</em> to vary, OTOR produces dose-response curves with high statistical significance. SSE produces dose-response curves that show “early” bending towards a dose plateau because, as theory reveals, it assumes that <em>A<sub>n</sub></em>/<em>A<sub>m </sub></em>is fixed at unity. Empirically however, <em>R</em> values are ~0.26 (quartz) and ~0.40 (K-rich feldspars) confirming the observed sublinear response to increasing doses, which is stronger with quartz than with feldspars. For both dosimeters extracted from our natural samples, the OTOR-derived characteristic saturation dose is 30–50 % higher than the <em>D<sub>0</sub></em> value obtained from the SSE function. We provide full explanation why the <em>D<sub>0 </sub></em>parameter is always underestimated for quartz and feldspars. Overall, the OTOR solutions are beneficial, not least due to the physical meaning of the fit parameters derived from the simplest possible model.