In equivalent dose (De) determination of quartz using the single aliquot regenerative dose (SAR) technique, it is commonly observed that the De values are strongly dependent on the stimulation time for some well bleached samples. Such dependence is not controlled by the degree of recuperation of the optically stimulated luminescence (OSL) signals. Instead, this behavior is interpreted as being due to the medium component being thermally unstable for these samples and giving a lower De value than the fast component. An alternative method is described for the De determination of samples that exhibit such a phenomenon.