A single saturating exponential (SSE) function is classically used in ESR dating to fit the experimental ESR data points derived from the aluminum (Al) center in quartz. However, this function has some obvious limits as it does not accurately fit the data points of the dose response curve. This results in unreliable equivalent dose (DE) values which are highly dependent on the maximum irradiation dose. Dose response curves of Al center in quartz show that the dose response data contain at least two components: a first one dominating at low dose (usually < 5 kGy) and saturating quite quickly and a second one dominating at higher doses with an almost linear behavior. These data are more appropriately fitted with a function combining an exponential with a linear term (EXP+LIN). Two variations of the EXP+LIN function were studied, each one corresponding to distinct physical assumptions. Since it is still unclear which one should be preferred, the mean DE value extracted from the fitting of the two equations may be reasonably considered as the most reliable estimate of the true DE value. In addition, to ensure accurate fitting of the linear part, it is important to have at least three data points at high doses (>10 kGy). It is also suggested to pool all the ESR intensities derived from repeated ESR measurements of each aliquot in the fitting process, in order to reduce the error in the DE value.