Methods of improving the measurement of knee stress in an ion-exchanged chemically strengthened Li-containing glass sample that includes a knee are disclosed. One of the methods includes compensating for a shift in the location of the TIR-PR transition location associated with the critical angle location, wherein the shift is due to the presence of a leaky mode. Another method includes applying select criteria to the captured mode spectra image to ensure a high-quality image is used for the knee stress calculation. Another method combines direct and indirect measurements of the knee stress using the mode spectra from multiple samples to obtain greater accuracy and precision as compared to using either the direct measurement method or the indirect measurement method alone. Quality control methods of forming the glass samples using measured mode spectra and related techniques for ensuring an accurate measurement of the knee stress are also disclosed.