The establishment of standardised growth curve (SGC) for equivalent dose (De) determination can substantially reduce the amount of instrument time required for OSL measurements. In this study, we investigated the applicability of SGC for the optically stimulated luminescence (OSL) signal from single grains and small aliquots of sedimentary quartz from Haua Fteah cave, in Libya. The samples exhibit large inter-grain and inter-aliquot variation in the shape of their single grain and small aliquot dose response curves (DRCs) constructed from a range of sensitivity-corrected regenerative dose signals (Lx/Tx), which prevents the establishment of a single common SGC among different grains or small aliquots. Instead, the DRCs for the small aliquots can be divided into a minimum of three groups using the Finite Mixture Model, with the DRC saturating at a different dose level for each group. In order to establish a common DRC, or SGC, for each group, we propose a new normalisation method, the so-called least-squares normalisation procedure (‘LS-normalisation’), which largely reduces the variation between aliquots within the same group and allows the establishment of a common DRC, or SGC, for each group. In order to apply the SGC method for these samples, two regenerative dose points are needed for each aliquot to attribute it to one of the groups based on the ratio of the Lx/Tx signals for two sensitivity-corrected regenerative dose points. Equivalent dose (De) values for each aliquot can be estimated using the fitting parameters calculated for the SGC of the relevant group to which it belongs, together with measurements of the natural signal (Ln), one regenerative dose signal (Lx1) and their corresponding test dose signals (Tn, Tx1). For the samples investigated from Haua Fteah, we found that De estimates obtained from the SGCs are consistent with those obtained using a full SAR procedure. Our results suggest that small single-aliquot and single-grain De values obtained from application of the SGC may be underestimated if there is a significant proportion of early-saturating grains present in the sample; such grains or aliquots are mostly rejected due to saturation when analysed using the full SAR procedure. In this case, it is necessary to calculate the De values based only on those grains or aliquots that have relatively high saturation levels.