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The two-temperature method (TTM) is known to be sensitive to noise, and therefore, land-surface temperature (LST) and emissivity (LSE) retrievals based on TTM are in general not reliable when obtained by algebraic procedures. Accordingly, the added value of using TTM together with a nonlinear mathematical optimization approach is investigated, focusing on the effect that an increase in the temperature difference as well as in the number of observations might have on LST and LSE retrievals. TTM has provided values of LST and LSE with a bias (root mean square error) ranging from 0.1-0.4 K (2.1-2.8 K) and from 0.005-0.010 (0.040-0.055), respectively. Obtained results were almost the same for both well-determined and overdetermined cases, as well as for the considered temperature differences, suggesting that increasing the number of observations and the temperature difference does not lead to significant improvements on the results. On the other hand, it was found out that a greater temperature difference between the first and the last observation acts like a natural constraint by restricting the solutions to a narrower region. In this case, the estimated LST and LSE values do not strongly depend upon the initial guess, and therefore, the use of several initial guess vectors may be avoided, turning TTM computationally more efficient.