The parameters of traps in quartz determine the thermal stability of OSL components and define the time range of dating. Their precise values are crucial for the thermal history of rock modelled in OSL thermochronometry. The values of trap parameters appearing in the literature depend on the quartz sample tested and the method used, even in the case of the most widely researched fast OSL component. Recently, it was found that it is possible to effectively separate the fast OSL component in quartz when the thermally modulated OSL (TM-OSL) method is conducted using a wavelength of 620 nm. Here, the possibility of fast component separation by the TM-OSL method for measuring OSL thermal depletion curves (OTDC) (isothermal OSL decay) and so-called TL difference curves (the TL signal bleached during the optical stimulation) is used. Trap parameters obtained independently in the OTDC experiments and by the IR and VHR methods applied to TL difference curves are compared. The parameter values stay in agreement in all methods used for three quartz samples from sediments of various origins. The new approach to measuring the OTDCs with the TM-OSL method enables the best precision. The mean value of trap parameters obtained in all methods and for all samples (E = 1.66 ± 0.02 eV, s = (4.1 ± 2.4) × 1013 s−1) is consistent with the literature data. TL difference curves are fitted with satisfactory quality by a first-order kinetics peak using the obtained trap parameters.