Global sea-surface temperatures (SST) from MODIS measured brightness temperatures generated using the regression methods, have been available to users for more than a decade, and are used extensively for a wide range of atmospheric and oceanic studies. However, as evidenced by a number of studies, there are indications that the retrieval quality and cloud detection are somewhat sub-optimal. To improve the performance of both of these aspects, we endorse a new physical deterministic algorithm, based on truncated total least squares (TTLS), using multiple channels and parameters, in conjunction with a hybrid cloud detection scheme using a radiative transfer model atop a functional spectral difference method. The TTLS method is a new addition that improves the information content of the retrieval compared to our previous work using modified total least squares (MTLS), which is feasible because more measurements are available, allowing a larger retrieval vector. A systematic study is conducted to ascertain the appropriate channel selection for SST retrieval from the 16 thermal infrared channels available from the MODIS instrument. Additionally, since atmospheric aerosol is a well-known source of degraded quality of SST retrieval, we include aerosol profiles from numerical weather prediction in the forward simulation and include the total column density of all aerosols in the retrieval vector of our deterministic inverse method. We used a slightly modified version of our earlier reported cloud detection algorithm, namely CEM (cloud and error mask), for this study. Time series analysis of more than a million match-ups shows that our new algorithm (TTLS+CEM) can reduce RMSE by~50% while increasing data coverage by~50% compared to the operationally available MODIS SST.