In optical dating, equivalent dose (De) values for a sample are commonly obtained from measurement of the luminescence signals of individual mineral grains or aliquots and projection of the natural signals onto the corresponding regenerative-dose response curves. A final De estimate is calculated by using a statistical model to combine the individual De values. This method can be problematic for samples that contain large numbers of ‘saturated’ grains, which may result in underestimation of the final De value due to truncation of the full De distribution at high doses. To circumvent this problem, Li et al. (2017) proposed a new method—the so-called LnTn method—in which the re-normalised sensitivity-corrected natural signals (Ln/Tn) are analysed for all measured grains from a particular sample, and the weighted mean re-normalised Ln/Tn value is projected onto a standardised growth curve to estimate the final sample De. As no grains or aliquots are rejected because they are ‘saturated’, a full (untruncated) distribution of re-normalised Ln/Tn ratios is obtained. In this study, we use numerical simulations of ‘samples’ with a variety of assigned burial dose (palaeodose) distributions to systematically investigate the shape of the resulting Ln/Tn distributions. We test application of the central age, minimum age and finite mixture models to Ln/Tn ratios (rather than to De values) for well-bleached, insufficiently bleached and post-depositionally mixed samples. Our results show that application of statistical models to Ln/Tn ratios from single grains or aliquots is reliable, and that the LnTn method can be used to date samples with De values up to 4 times the characteristic saturation dose (D0), which is well above the conservative upper limit of 2D0.